AI Chatbot Development

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  Non-native speech database

  A non-native speech database is a speech database of non-native pronunciations of English. Such databases are used in the development of: multilingual automatic speech recognition systems, text to speech systems, pronunciation trainers, and second language learning systems. == List == The actual table with information about the different databases is shown in Table 2. === Legend === In the table of non-native databases some abbreviations for language names are used. They are listed in Table 1. Table 2 gives the following information about each corpus: The name of the corpus, the institution where the corpus can be obtained, or at least further information should be available, the language which was actually spoken by the speakers, the number of speakers, the native language of the speakers, the total amount of non-native utterances the corpus contains, the duration in hours of the non-native part, the date of the first public reference to this corpus, some free text highlighting special aspects of this database and a reference to another publication. The reference in the last field is in most cases to the paper which is especially devoted to describe this corpus by the original collectors. In some cases it was not possible to identify such a paper. In these cases a paper is referenced which is using this corpus is. Some entries are left blank and others are marked with unknown. The difference here is that blank entries refer to attributes where the value is just not known. Unknown entries, however, indicate that no information about this attribute is available in the database itself. As an example, in the Jupiter weather database no information about the origin of the speakers is given. Therefore this data would be less useful for verifying accent detection or similar issues. Where possible, the name is a standard name of the corpus, for some of the smaller corpora, however, there was no established name and hence an identifier had to be created. In such cases, a combination of the institution and the collector of the database is used. In the case where the databases contain native and non-native speech, only attributes of the non-native part of the corpus are listed. Most of the corpora are collections of read speech. If the corpus instead consists either partly or completely of spontaneous utterances, this is mentioned in the Specials column.

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  Social computing

  Social computing is an area of computer science that is concerned with the intersection of social behavior and computational systems. It is based on creating or fostering existing social conventions and social contexts through the use of software and technology. Blogs, email, instant messaging, social network services, wikis, social bookmarking and other instances of what is often called social software illustrate ideas from social computing. The rise in social computing is attributed to the prevalence of personal devices and increased overall computing power. This enables a growing number of users to participate in sharing content and interact with another. == Definitions == Humans—and human behavior—are profoundly social. Humans tend to orient to one another and develop abilities to interact with each other and other species. This ranges from expression and gesture through spoken, written, and body language. Humans are influenced by the behavior of those around them and can rely on social context and cues to make decisions. An example of a behavior relying on social contexts is applauding at the end of the play. This is based on the context that the show ended, and other audience members are applauding. Social information provides a basis for inferences, planning, and coordinating activity. == Examples == Common tools include blogs, email, instant messaging, social networking sites, wikis, and social bookmarking platforms. These technologies enable users to generate content, share knowledge, and interact in real time. == Applications == The rise of social computing has highlighted opportunities for businesses. Businesses are interacting on social computing platforms and investing in facilities to support and research social computing.Business models can leverage the massive customer bases that accumulate through social computing channels. Some organizations have started their own blogs and networks (McAfee, 2006, Joe, 2005). Organizations from diverse industry sectors such as Google, Cisco, and Fox, have sought to acquire or invest in successful social computing enterprises. A business blog can serve as a source of information and promotion for the company. This allows the company to share content about the company and their initiatives. Businesses have also interacted with social computing to market themselves and interact with customers. A notable example is Wendy's with their X (formerly Twitter) account. The account was primarily used to promote business promotions and interact with users in a playful or meaningful way. E-commerce web sites have allowed users to leave reviews and feedback on purchases which has improved online shopping experience for sellers and consumers.As another example of social computing’s business applications, many e-commerce Web sites have adopted online product/vendor feedback/reputation systems. Such systems provide an asynchronous platform for the consumer community to share experiences collectively and influence their purchasing behavior. They also provide a vehicle for eliciting feedback information valuable to the vendors and e-commerce site operators.Consumers can use the feedback systems to make a more educated choice on a purchase by comparing reviews between products or vendors. Sellers can track consumer behaviors and trends regarding a product and adjust their supply according to the demand. == Challenges and criticism == Social computing raises several concerns related to privacy, data security, and algorithmic bias. The widespread collection and analysis of user-generated data can lead to ethical dilemmas, especially when users are unaware of how their information is used. Critics also highlight issues of digital labor, surveillance, and the spread of misinformation, which can influence public opinion and social dynamics. === Term appearance === The term appeared in the mid 1990s after technology advancements and development of the web. In 1994, the concept of social computing was first proposed by Schuler. He thought, "Social computing is a computing application, with software as the medium or focus of social relationships." === Premise === The premise of social computing is that it is possible to design digital systems that support useful functionality by making socially produced information available to their users. This information may be provided directly, as when systems show the number of users who have rated a review as helpful or not. Or the information may be provided after being filtered and aggregated, as is done when systems recommend a product based on what else people with similar purchase history have purchased. Alternatively, the information may be provided indirectly, as is the case with Google's page rank algorithms which orders search results based on the number of pages that (recursively) point to them. In all of these cases, information that is produced by a group of people is used to provide or enhance the functioning of a system. Social computing is concerned with systems of this sort and the mechanisms and principles that underlie them. Social computing can be defined as follows: "Social Computing" refers to systems that support the gathering, representation, processing, use, and dissemination of information that is distributed across social collectivities such as teams, communities, organizations, and markets. Moreover, the information is not "anonymous" but is significantly precise because it is linked to people, who are in turn linked to other people. More recent definitions, however, have foregone the restrictions regarding anonymity of information, acknowledging the continued spread and increasing pervasiveness of social computing. As an example, Hemmatazad, N. (2014) defined social computing as "the use of computational devices to facilitate or augment the social interactions of their users, or to evaluate those interactions in an effort to obtain new information." Social computing has to do with supporting "computations" that are carried out by groups of people, an idea that has been popularized in James Surowiecki's book, The Wisdom of Crowds. Examples of social computing in this sense include collaborative filtering, online auctions, reputation systems, computational social choice, tagging, and verification games. The social information processing page focuses on this sense of social computing. == History == === Technology infrastructure === Users were able to interact more with websites after the development of Web 2.0. This was an advancement from Web 1.0. Comode G. and Krishnamurthy B. (2008) note that "content creators were few in Web 1.0 with the vast majority of users simply acting as consumers of content." Web 2.0 provided functionalities that allowed for low-cost web-hosting services and introduced features with browser windows that used basic information structure and expanded it to as many devices as possible using HTTP, or Hypertext Transfer Protocol. Sometimes referred to as "Enterprise 2.0", a term derived from Web 2.0, social software for enterprise generally refers to the use of social computing in corporate intranets and in other medium- and large-scale business environments. It consisted of a class of tools that allowed for networking and social changes to businesses at the time. It was a layering of the business tools on Web 2.0 and brought forth several applications and collaborative software with specific uses. FinanceElectronic negotiation, which first came up in 1969 and was adapted over time to suit financial markets networking needs, represents an important and desirable coordination mechanism for electronic markets. Negotiation between agents (software agents as well as humans) allows cooperative and competitive sharing of information to determine a proper price. Recent research and practice has also shown that electronic negotiation is beneficial for the coordination of complex interactions among organizations. Electronic negotiation has recently emerged as a very dynamic, interdisciplinary research area covering aspects from disciplines such as Economics, Information Systems, Computer Science, Communication Theory, Sociology and Psychology.Social computing has become more widely known because of its relationship to a number of recent trends. These include the growing popularity of social software and Web 3.0, increased academic interest in social network analysis, the rise of open source as a viable method of production, and a growing conviction that all of this can have a profound impact on daily life. A February 13, 2006 paper by market research company Forrester Research suggested that: === Developments === PLATO was one of the earliest examples of social computing in a live production environment with initially hundreds and soon thousands of users. The PLATO computer system was developed by the University of Illinois at Urbana Champaign in 1960s. In the 70s, the system supported social software applications for multi-us

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  Computer network engineering

  Computer network engineering is a technology discipline within engineering that deals with the design, implementation, and management of computer networks. These systems contain both physical components, such as routers, switches, cables, and some logical elements, such as protocols and network services. Computer network engineers attempt to ensure that the data is transmitted efficiently, securely, and reliably over both local area networks (LANs) and wide area networks (WANs), as well as across the Internet. Computer networks often play a large role in modern industries ranging from telecommunications to cloud computing, enabling processes such as email and file sharing, as well as complex real-time services like video conferencing and online gaming. == Background == The evolution of network engineering is marked by significant milestones that have greatly impacted communication methods. These milestones particularly highlight the progress made in developing communication protocols that are vital to contemporary networking. This discipline originated in the 1960s with projects like ARPANET, which initiated important advancements in reliable data transmission. The advent of protocols such as TCP/IP revolutionized networking by enabling interoperability among various systems, which, in turn, fueled the rapid growth of the Internet. Key developments include the standardization of protocols and the shift towards increasingly complex layered architectures. These advancements have profoundly changed the way devices interact across global networks. == Network infrastructure design == The foundation of computer network engineering lies in the design of the network infrastructure. This involves planning both the physical layout of the network and its logical topology to ensure optimal data flow, reliability, and scalability. === Physical infrastructure === The physical infrastructure consists of the hardware used to transmit data, which is represented by the first layer of the OSI model. ==== Cabling ==== Copper cables such as ethernet over twisted pair are commonly used for short-distance connections, especially in local area networks (LANs), while fiber optic cables are favored for long-distance communication due to their high-speed transmission capabilities and lower susceptibility to interference. Fiber optics play a significant role in the backbone of large-scale networks, such as those used in data centers and internet service provider (ISP) infrastructures. ==== Wireless networks ==== In addition to wired connections, wireless networks have become a common component of physical infrastructure. These networks facilitate communication between devices without the need for physical cables, providing flexibility and mobility. Wireless technologies use a range of transmission methods, including radio frequency (RF) waves, infrared signals, and laser-based communication, allowing devices to connect to the network. Wi-Fi based on IEEE 802.11 standards is the most widely used wireless technology in local area networks and relies on RF waves to transmit data between devices and access points. Wireless networks operate across various frequency bands, including 2.4 GHz and 5 GHz, each offering unique ranges and data rates; the 2.4 GHz band provides broader coverage, while the 5 GHz band supports faster data rates with reduced interference, ideal for densely populated environments. Beyond Wi-Fi, other wireless transmission methods, such as infrared and laser-based communication, are used in specific contexts, like short-range, line-of-sight links or secure point-to-point communication. In mobile networks, cellular technologies like 3G, 4G, and 5G enable wide-area wireless connectivity. 3G introduced faster data rates for mobile browsing, while 4G significantly improved speed and capacity, supporting advanced applications like video streaming. The latest evolution, 5G, operates across a range of frequencies, including millimeter-wave bands, and provides high data rates, low latency, and support for more device connectivity, useful for applications like the Internet of Things (IoT) and autonomous systems. Together, these wireless technologies allow networks to meet a variety of connectivity needs across local and wide areas. ==== Network devices ==== Routers and switches help direct data traffic and assist in maintaining network security; network engineers configure these devices to optimize traffic flow and prevent network congestion. In wireless networks, wireless access points (WAP) allow devices to connect to the network. To expand coverage, multiple access points can be placed to create a wireless infrastructure. Beyond Wi-Fi, cellular network components like base stations and repeaters support connectivity in wide-area networks, while network controllers and firewalls manage traffic and enforce security policies. Together, these devices enable a secure, flexible, and scalable network architecture suitable for both local and wide-area coverage. === Logical topology === Beyond the physical infrastructure, a network must be organized logically, which defines how data is routed between devices. Various topologies, such as star, mesh, and hierarchical designs, are employed depending on the network’s requirements. In a star topology, for example, all devices are connected to a central hub that directs traffic. This configuration is relatively easy to manage and troubleshoot but can create a single point of failure. In contrast, a mesh topology, where each device is interconnected with several others, offers high redundancy and reliability but requires a more complex design and larger hardware investment. Large networks, especially those in enterprises, often employ a hierarchical model, dividing the network into core, distribution, and access layers to enhance scalability and performance. == Network protocols and communication standards == Communication protocols dictate how data in a network is transmitted, routed, and delivered. Depending on the goals of the specific network, protocols are selected to ensure that the network functions efficiently and securely. The Transmission Control Protocol/Internet Protocol (TCP/IP) suite is fundamental to modern computer networks, including the Internet. It defines how data is divided into packets, addressed, routed, and reassembled. The Internet Protocol (IP) is critical for routing packets between different networks. In addition to traditional protocols, advanced protocols such as Multiprotocol Label Switching (MPLS) and Segment Routing (SR) enhance traffic management and routing efficiency. For intra-domain routing, protocols like Open Shortest Path First (OSPF) and Enhanced Interior Gateway Routing Protocol (EIGRP) provide dynamic routing capabilities. On the local area network (LAN) level, protocols like Virtual Extensible LAN (VXLAN) and Network Virtualization using Generic Routing Encapsulation (NVGRE) facilitate the creation of virtual networks. Furthermore, Internet Protocol Security (IPsec) and Transport Layer Security (TLS) secure communication channels, ensuring data integrity and confidentiality. For real-time applications, protocols such as Real-time Transport Protocol (RTP) and WebRTC provide low-latency communication, making them suitable for video conferencing and streaming services. Additionally, protocols like QUIC enhance web performance and security by establishing secure connections with reduced latency. == Network security == As networks have become essential for business operations and personal communication, the demand for robust security measures has increased. Network security is a critical component of computer network engineering, concentrating on the protection of networks against unauthorized access, data breaches, and various cyber threats. Engineers are responsible for designing and implementing security measures that ensure the integrity and confidentiality of data transmitted across networks. Firewalls serve as barriers between trusted internal networks and external environments, such as the Internet. Network engineers configure firewalls, including next-generation firewalls (NGFW), which incorporate advanced features such as deep packet inspection and application awareness, thereby enabling more refined control over network traffic and protection against sophisticated attacks. In addition to firewalls, engineers use encryption protocols, including Internet Protocol Security (IPsec) and Transport Layer Security (TLS), to secure data in transit. These protocols provide a means of safeguarding sensitive information from interception and tampering. For secure remote access, Virtual Private Networks (VPNs) are deployed, using technologies to create encrypted tunnels for data transmission over public networks. These VPNs are often used for maintaining security when remote users access corporate networks but are also used ion other settings. To enhance threat detection and r

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  Cryptosystem

  In cryptography, a cryptosystem is a suite of cryptographic algorithms needed to implement a particular security service, such as confidentiality (encryption). Typically, a cryptosystem consists of three algorithms: one for key generation, one for encryption, and one for decryption. The term cipher (sometimes cypher) is often used to refer to a pair of algorithms, one for encryption and one for decryption. Therefore, the term cryptosystem is most often used when the key generation algorithm is important. For this reason, the term cryptosystem is commonly used to refer to public key techniques; however both "cipher" and "cryptosystem" are used for symmetric key techniques. == Formal definition == Mathematically, a cryptosystem or encryption scheme can be defined as a tuple ( P , C , K , E , D ) {\displaystyle ({\mathcal {P}},{\mathcal {C}},{\mathcal {K}},{\mathcal {E}},{\mathcal {D}})} with the following properties. P {\displaystyle {\mathcal {P}}} is a set called the "plaintext space". Its elements are called plaintexts. C {\displaystyle {\mathcal {C}}} is a set called the "ciphertext space". Its elements are called ciphertexts. K {\displaystyle {\mathcal {K}}} is a set called the "key space". Its elements are called keys. E = { E k : k ∈ K } {\displaystyle {\mathcal {E}}=\{E_{k}:k\in {\mathcal {K}}\}} is a set of functions E k : P → C {\displaystyle E_{k}:{\mathcal {P}}\rightarrow {\mathcal {C}}} . Its elements are called "encryption functions". D = { D k : k ∈ K } {\displaystyle {\mathcal {D}}=\{D_{k}:k\in {\mathcal {K}}\}} is a set of functions D k : C → P {\displaystyle D_{k}:{\mathcal {C}}\rightarrow {\mathcal {P}}} . Its elements are called "decryption functions". For each e ∈ K {\displaystyle e\in {\mathcal {K}}} , there is d ∈ K {\displaystyle d\in {\mathcal {K}}} such that D d ( E e ( p ) ) = p {\displaystyle D_{d}(E_{e}(p))=p} for all p ∈ P {\displaystyle p\in {\mathcal {P}}} . Note; typically this definition is modified in order to distinguish an encryption scheme as being either a symmetric-key or public-key type of cryptosystem. == Examples == A classical example of a cryptosystem is the Caesar cipher. A more contemporary example is the RSA cryptosystem. Another example of a cryptosystem is the Advanced Encryption Standard (AES). AES is a widely used symmetric encryption algorithm that has become the standard for securing data in various applications. Paillier cryptosystem is another example used to preserve and maintain privacy and sensitive information. It is featured in electronic voting, electronic lotteries and electronic auctions.

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  Crackme

  A crackme is a small computer program designed to test a programmer's reverse engineering skills. Crackmes are made as a legal way to crack software, since no intellectual property is being infringed. == Description == Crackmes often incorporate protection schemes and algorithms similar to those used in proprietary software. However, they can sometimes be more challenging because they may use advanced packing or protection techniques, making the underlying algorithm harder to analyze and modify. == Keygenme == A keygenme is specifically designed for the reverser to not only identify the protection algorithm used in the application but also create a small key generator (keygen) in the programming language of their choice. Most keygenmes, when properly manipulated, can be made self-keygenning. For example, during validation, they might generate the correct key internally and compare it to the user's input. This allows the key generation algorithm to be easily replicated. Anti-debugging and anti-disassembly routines are often used to confuse debuggers or render disassembly output useless. Code obfuscation is also used to further complicate reverse engineering.

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  G.9972

  G.9972 (also known as G.cx) is a Recommendation developed by ITU-T that specifies a coexistence mechanism for networking transceivers capable of operating over electrical power line wiring. It allows G.hn devices to coexist with other devices implementing G.9972 and operating on the same power line wiring. G.9972 received consent during the meeting of ITU-T Study Group 15, on October 9, 2009, and final approval on June 11, 2010. G.9972 specifies two mechanisms for coexistence between G.hn home networks and broadband over power lines (BPL) Internet access networks: Frequency-division multiplexing (FDM), in which the available spectrum is divided into two parts: frequencies below 10 or 14 MHz (specific value can be selected by the access network) are reserved for the access network, while frequencies above them are reserved for the in-home network. Time-division multiplexing (TDM), in which the available channel time is split equally between both networks. 50% of time slots are allocated for the access network, and 50% are allocated to the in-home network.

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  Clustered file system

  A clustered file system (CFS) is a file system which is shared by being simultaneously mounted on multiple servers. There are several approaches to clustering, most of which do not employ a clustered file system (only direct attached storage for each node). Clustered file systems can provide features like location-independent addressing and redundancy which improve reliability or reduce the complexity of the other parts of the cluster. Parallel file systems are a type of clustered file system that spread data across multiple storage nodes, usually for redundancy or performance. == Shared-disk file system == A shared-disk file system uses a storage area network (SAN) to allow multiple computers to gain direct disk access at the block level. Access control and translation from file-level operations that applications use to block-level operations used by the SAN must take place on the client node. The most common type of clustered file system, the shared-disk file system – by adding mechanisms for concurrency control – provides a consistent and serializable view of the file system, avoiding corruption and unintended data loss even when multiple clients try to access the same files at the same time. Shared-disk file-systems commonly employ some sort of fencing mechanism to prevent data corruption in case of node failures, because an unfenced device can cause data corruption if it loses communication with its sister nodes and tries to access the same information other nodes are accessing. The underlying storage area network may use any of a number of block-level protocols, including SCSI, iSCSI, HyperSCSI, ATA over Ethernet (AoE), Fibre Channel, network block device, and InfiniBand. There are different architectural approaches to a shared-disk filesystem. Some distribute file information across all the servers in a cluster (fully distributed). === Examples === == Distributed file systems == Distributed file systems do not share block level access to the same storage but use a network protocol. These are commonly known as network file systems, even though they are not the only file systems that use the network to send data. Distributed file systems can restrict access to the file system depending on access lists or capabilities on both the servers and the clients, depending on how the protocol is designed. The difference between a distributed file system and a distributed data store is that a distributed file system allows files to be accessed using the same interfaces and semantics as local files – for example, mounting/unmounting, listing directories, read/write at byte boundaries, system's native permission model. Distributed data stores, by contrast, require using a different API or library and have different semantics (most often those of a database). === Design goals === Distributed file systems may aim for "transparency" in a number of aspects. That is, they aim to be "invisible" to client programs, which "see" a system which is similar to a local file system. Behind the scenes, the distributed file system handles locating files, transporting data, and potentially providing other features listed below. Access transparency: clients are unaware that files are distributed and can access them in the same way as local files are accessed. Location transparency: a consistent namespace exists encompassing local as well as remote files. The name of a file does not give its location. Concurrency transparency: all clients have the same view of the state of the file system. This means that if one process is modifying a file, any other processes on the same system or remote systems that are accessing the files will see the modifications in a coherent manner. Failure transparency: the client and client programs should operate correctly after a server failure. Heterogeneity: file service should be provided across different hardware and operating system platforms. Scalability: the file system should work well in small environments (1 machine, a dozen machines) and also scale gracefully to bigger ones (hundreds through tens of thousands of systems). Replication transparency: Clients should not have to be aware of the file replication performed across multiple servers to support scalability. Migration transparency: files should be able to move between different servers without the client's knowledge. === History === The Incompatible Timesharing System used virtual devices for transparent inter-machine file system access in the 1960s. More file servers were developed in the 1970s. In 1976, Digital Equipment Corporation created the File Access Listener (FAL), an implementation of the Data Access Protocol as part of DECnet Phase II which became the first widely used network file system. In 1984, Sun Microsystems created the file system called "Network File System" (NFS) which became the first widely used Internet Protocol based network file system. Other notable network file systems are Andrew File System (AFS), Apple Filing Protocol (AFP), NetWare Core Protocol (NCP), and Server Message Block (SMB) which is also known as Common Internet File System (CIFS). In 1986, IBM announced client and server support for Distributed Data Management Architecture (DDM) for the System/36, System/38, and IBM mainframe computers running CICS. This was followed by the support for IBM Personal Computer, AS/400, IBM mainframe computers under the MVS and VSE operating systems, and FlexOS. DDM also became the foundation for Distributed Relational Database Architecture, also known as DRDA. There are many peer-to-peer network protocols for open-source distributed file systems for cloud or closed-source clustered file systems, e. g.: 9P, AFS, Coda, CIFS/SMB, DCE/DFS, WekaFS, Lustre, PanFS, Google File System, Mnet, Chord Project. === Examples === == Network-attached storage == Network-attached storage (NAS) provides both storage and a file system, like a shared disk file system on top of a storage area network (SAN). NAS typically uses file-based protocols (as opposed to block-based protocols a SAN would use) such as NFS (popular on UNIX systems), SMB/CIFS (Server Message Block/Common Internet File System) (used with MS Windows systems), AFP (used with Apple Macintosh computers), or NCP (used with OES and Novell NetWare). == Design considerations == === Avoiding single point of failure === The failure of disk hardware or a given storage node in a cluster can create a single point of failure that can result in data loss or unavailability. Fault tolerance and high availability can be provided through data replication of one sort or another, so that data remains intact and available despite the failure of any single piece of equipment. For examples, see the lists of distributed fault-tolerant file systems and distributed parallel fault-tolerant file systems. === Performance === A common performance measurement of a clustered file system is the amount of time needed to satisfy service requests. In conventional systems, this time consists of a disk-access time and a small amount of CPU-processing time. But in a clustered file system, a remote access has additional overhead due to the distributed structure. This includes the time to deliver the request to a server, the time to deliver the response to the client, and for each direction, a CPU overhead of running the communication protocol software. === Concurrency === Concurrency control becomes an issue when more than one person or client is accessing the same file or block and want to update it. Hence updates to the file from one client should not interfere with access and updates from other clients. This problem is more complex with file systems due to concurrent overlapping writes, where different writers write to overlapping regions of the file concurrently. This problem is usually handled by concurrency control or locking which may either be built into the file system or provided by an add-on protocol. == History == IBM mainframes in the 1970s could share physical disks and file systems if each machine had its own channel connection to the drives' control units. In the 1980s, Digital Equipment Corporation's TOPS-20 and OpenVMS clusters (VAX/ALPHA/IA64) included shared disk file systems.

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  Tropical cryptography

  In tropical analysis, tropical cryptography refers to the study of a class of cryptographic protocols built upon tropical algebras. In many cases, tropical cryptographic schemes have arisen from adapting classical (non-tropical) schemes to instead rely on tropical algebras. The case for the use of tropical algebras in cryptography rests on at least two key features of tropical mathematics: in the tropical world, there is no classical multiplication (a computationally expensive operation), and the problem of solving systems of tropical polynomial equations has been shown to be NP-hard. == Basic Definitions == The key mathematical object at the heart of tropical cryptography is the tropical semiring ( R ∪ { ∞ } , ⊕ , ⊗ ) {\displaystyle (\mathbb {R} \cup \{\infty \},\oplus ,\otimes )} (also known as the min-plus algebra), or a generalization thereof. The operations are defined as follows for x , y ∈ R ∪ { ∞ } {\displaystyle x,y\in \mathbb {R} \cup \{\infty \}} : x ⊕ y = min { x , y } {\displaystyle x\oplus y=\min\{x,y\}} x ⊗ y = x + y {\displaystyle x\otimes y=x+y} It is easily verified that with ∞ {\displaystyle \infty } as the additive identity, these binary operations on R ∪ { ∞ } {\displaystyle \mathbb {R} \cup \{\infty \}} form a semiring.

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  Computational heuristic intelligence

  Computational heuristic intelligence (CHI) refers to specialized programming techniques in computational intelligence (also called artificial intelligence, or AI). These techniques have the express goal of avoiding complexity issues, also called NP-hard problems, by using human-like techniques. They are best summarized as the use of exemplar-based methods (heuristics), rather than rule-based methods (algorithms). Hence the term is distinct from the more conventional computational algorithmic intelligence, or symbolic AI. An example of a CHI technique is the encoding specificity principle of Tulving and Thompson. In general, CHI principles are problem solving techniques used by people, rather than programmed into machines. It is by drawing attention to this key distinction that the use of this term is justified in a field already replete with confusing neologisms. Note that the legal systems of all modern human societies employ both heuristics (generalisations of cases) from individual trial records as well as legislated statutes (rules) as regulatory guides. Another recent approach to the avoidance of complexity issues is to employ feedback control rather than feedforward modeling as a problem-solving paradigm. This approach has been called computational cybernetics, because (a) the term 'computational' is associated with conventional computer programming techniques which represent a strategic, compiled, or feedforward model of the problem, and (b) the term 'cybernetic' is associated with conventional system operation techniques which represent a tactical, interpreted, or feedback model of the problem. Of course, real programs and real problems both contain both feedforward and feedback components. A real example which illustrates this point is that of human cognition, which clearly involves both perceptual (bottom-up, feedback, sensor-oriented) and conceptual (top-down, feedforward, motor-oriented) information flows and hierarchies. The AI engineer must choose between mathematical and cybernetic problem solution and machine design paradigms. This is not a coding (program language) issue, but relates to understanding the relationship between the declarative and procedural programming paradigms. The vast majority of STEM professionals never get the opportunity to design or implement pure cybernetic solutions. When pushed, most responders will dismiss the importance of any difference by saying that all code can be reduced to a mathematical model anyway. Unfortunately, not only is this belief false, it fails most spectacularly in many AI scenarios. Mathematical models are not time agnostic, but by their very nature are pre-computed, i.e. feedforward. Dyer [2012] and Feldman [2004] have independently investigated the simplest of all somatic governance paradigms, namely control of a simple jointed limb by a single flexor muscle. They found that it is impossible to determine forces from limb positions- therefore, the problem cannot have a pre-computed (feedforward) mathematical solution. Instead, a top-down command bias signal changes the threshold feedback level in the sensorimotor loop, e.g. the loop formed by the afferent and efferent nerves, thus changing the so-called ‘equilibrium point’ of the flexor muscle/ elbow joint system. An overview of the arrangement reveals that global postures and limb position are commanded in feedforward terms, using global displacements (common coding), with the forces needed being computed locally by feedback loops. This method of sensorimotor unit governance, which is based upon what Anatol Feldman calls the ‘equilibrium Point’ theory, is formally equivalent to a servomechanism such as a car's ‘cruise control’.

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  Coreu

  COREU (French: Correspondance Européenne – Telex network of European correspondents, also EUKOR-Netzwerk in Austria) is a communication network of the European Union for the communication of the Council of the European Union, the European correspondents of the foreign ministries of the EU member states, permanent representatives of member states in Brussels, the European Commission, and the General Secretariat of the Council of the European Union. The European Parliament is not among the participants. COREU is the European equivalent of the American Secret Internet Protocol Router Network (SIPRNet, also known as Intelink-S). COREU's official aim is fast communication in case of crisis. The network enables a closer cooperation in matters regarding foreign affairs. In actuality the system's function exceeds that of mere communication, it also enables decision-making. COREU's first goal is to enable the exchange of information before and after decisions. Relaying upfront negotiations in preparation of meetings is the second goal. In addition, the system also allows the editing of documents and the decision-making, especially if there is little time. While the first two goals are preparatory measures for a shared foreign policy, the third is a methodical variant marked by practise that is defining for the image of the Common Foreign and Security Policy. == Members == (The following information dates from 2013): There is one representative in each of the capital cities in the EU.(since 1973) In Germany for example, this is the European correspondent (EU-KOR) from the Foreign Office. In Austria it is the European correspondent from the Referat II.1.a in the Federal Ministry for Europe, Integration and Foreign Affairs They are the correspondents (since 1982) for the European Commission They comprise the secretariat for the European Council They also make up the European External Action Service (EEAS) (responsible for foreign policy issues, since 1987) == Data volume and technical details == COREU functions as a spoke-hub distribution paradigm system with the hub in Brussels. The network is operated by the European Union Intelligence and Situation Centre (formerly Joint Situation Center, JSC). The technical infrastructure is located in a building of the European Council. COREU may be described as an advanced telex system with encrypted messages via dedicated terminals. Once a message has reached the destination, it is then redistributed via the local media. In contrast, messages of governments are transmitted via local media to the correspondents and from there delivered point-to-point to Brussels via COREU. In 2010, approximately 8500 communications had been distributed over this network. == History == A telex-based communication system under the name COREU was established in 1973. Originally, only the ministries of Foreign Affairs in the European capitals were connected to it. This telex system was replaced in 1997 by the mail system CORTESY (COREU Terminal Equipment System). The name was retained despite the technical innovation. COREU was reportedly compromised by hackers working for the People's Liberation Army Strategic Support Force, allowing for the theft of thousands of low-classified documents and diplomatic cables.

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  WhoSay

  WhoSay was an American social media service and branding platform for celebrities and their fans. Founded in Los Angeles in 2010, with financing by Creative Artists Agency (CAA), Amazon.com and other investors, it is notable for allowing its users to retain ownership rights over the content that they post to their accounts, through copyright branding, and for enabling users to post content to other social media sites like Twitter, Facebook, Instagram and Tumblr simultaneously. WhoSay describes itself as a "social celebrity magazine" whose editorial team keeps its users informed about the latest celebrity and entertainment news. Clients such as Dylan McDermott and Chris Rock lauded the service for its ability to add content to multiple social network sites easily. Rock in particular has commented on its ease of use for those who are not part of a tech-savvy demographic, commenting, "It's perfect for someone that's not 25." WhoSay's competitors included theAudience, which is operated by the William Morris Endeavor. == History == WhoSay was founded in March 2010, by Steve Ellis and the Los Angeles-based talent agency Creative Artists Agency (CAA). It was financed through investments Amazon.com (who along with CAA, holds a minority stake in the company), Comcast, Greylock Partners, and High Peak Ventures. The company's main headquarters are in The New York Times Building in Manhattan, with additional headquarters in CAA's office building in the Silicon Beach area of Los Angeles, and in London. The company was founded to protect celebrities' intellectual property and enable the celebrities themselves to profit themselves from their own content through copyright branding. Its chief executive is co-founder Steve Ellis, who, after leaving Getty Images, was contacted by CAA, who were looking to resolve the issue of celebrities losing the rights to their own photos and videos when uploading them to social network sites. Ellis explained WhoSay's mission thus: "We work with people who are constantly being utilized by third parties for the wrong reasons. [The company was formed] to give celebrities and other influential people a set of tools to allow them to manage and control their presence in the digital world." In this way, WhoSay is likened by Ellis to "a People magazine by the people themselves who are in it." The company started slowly, until CAA client Tom Hanks signed onto WhoSay three months after the service's launch. The company continued to maintain a low profile for the first three years of operation, during which it accumulated a client list of 1,500 actors, musicians and artists. Clients are accepted by the service on an invitation-only basis, although they are not restricted to Creative Artists clients. Among them are Kelly Clarkson, Julia Louis-Dreyfus, Paula Patton, Kevin Spacey, Jim Carrey, John Cusack, Bill Maher, Johnny Knoxville, Chelsea Handler, Eva Longoria, Spike Lee, Enrique Iglesias and Katie Couric. Clients are not charged for the service, and are given a share of any revenue that is generated by advertisements. They are also given the ability share in the database of e-mail addresses that come with registration, in order to communicate directly with fans. Actor Dylan McDermott was introduced to WhoSay by his agent, as a way of easily posting content to Facebook, Twitter, Tumblr and even China's Tencent social network with relative ease. McDermott comments, "When you put something out there, you can hit everything at one time. It makes it easy for me." Comedian Chris Rock has commented that WhoSay is ideal for people like him have developed difficulty in keeping track of different websites as they get older, saying, "It's perfect for someone that's not 25." In September 2013 WhoSay introduced a mobile application for consumers. By October 2013, the company's website attracted 12 million monthly visitors. In July 2014 Rob Gregory left his role as president of Newsweek's The Daily Beast to become WhoSay's chief revenue officer. Among his responsibilities are developing ways to monetize WhoSay's web and mobile products, such as premium advertising strategies and brand partnerships. WhoSay does not allow consumers to create accounts, nor does it include search features, making it difficult to access a celebrity's account unless a user is directed there from one of their other social pages. According to Ellis, consumers have enough social media choices, saying, "Frankly they don't really need the services that we provide, and there are a lot of very specific features built into our service that really only benefit someone who is of a high profile." By February 2015, WhoSay had amassed 4.8 million unique users, and expanded its accounts to companies that employ celebrities for branded content. Such companies include Lexus, which partnered with the company to promote a campaign in which actress Rosario Dawson, during the lead up to the 87th Academy Awards, released five short videos on her social media accounts. The videos feature her driving through Los Angeles in preparation for the grand opening of her pop-up store, which sells Studio One Eighty Nine, a clothing line tied to her foundation promoting African culture and content. That April, WhoSay partnered with Chevrolet's #BestDayEver social media campaign for April Fool's Day, enlisting Olivia Wilde, Norman Reedus, Alec Baldwin, Ian Somerhalder, and Nikki Reed to surprise students in four U.S. classrooms as their substitute teachers. For example, Baldwin, dressed as Abraham Lincoln, surprised students in an Occidental College class on U.S. Culture and Society. Other companies that WhoSay has partnered with include KFC, JCPenney, Dunkin' Donuts and Crest. In January 2018, the website was acquired by Viacom (now Paramount Global).

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  Out-of-band control

  Out-of-band control is a method used by network protocols for sending control information (commands, logins, or session signals) separately from the main data, improving reliability and preventing interference. File Transfer Protocol (FTP) employs an out-of-band approach, using one connection for control commands, like logging in or requesting files, and a separate connection for transferring the files themselves.

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  Automated restaurant

  An automated restaurant or robotic restaurant is a restaurant that uses robots to do tasks such as delivering food and drink to the tables or cooking the food. Restaurant automation means the use of a restaurant management system to automate some or occasionally all of the major operations of a restaurant establishment. More recently, restaurants are opening that have completely or partially automated their services. These may include: taking orders, preparing food, serving, and billing. A few fully automated restaurants operate without any human intervention whatsoever. Robots are designed to help and sometimes replace human labour (such as waiters and chefs). The automation of restaurants may also allow for the option for greater customization of an order. == History == === Vending machines === In the late 19th and early 20th century a number of restaurants served food solely through vending machines. These restaurants were called automats or, in Japan, shokkenki. Customers ordered their food directly through the machines. === Sushi conveyors === Yoshiaki Shiraishi is a Japanese innovator who is known for the creation of conveyor belt sushi. He had the idea following difficulty staffing his small sushi restaurant and managing the restaurant on his own. He was inspired seeing beer bottles on a conveyor belt in an Asahi brewery. Yoshiaki's restaurants are an early example of restaurant automation; they used a conveyor belt to distribute dishes around the restaurant, eliminating the need for waiters. This example of automation dates back to the Japanese economic miracle; the first of Yoshiaki's conveyor belt sushi restaurants was opened under the name Mawaru Genroku Sushi in 1958, in Osaka. === Partial automation === As of 2011, across Europe, McDonald's had already begun implementing 7,000 touch screen kiosks that could handle cashiering duties. From 2015 to 2020, Zume had an automated pizza parlor. Later companies would try to produce smaller, less ambitious devices, with one robotics company producing a machine that could automate the slowest and most repetitive parts of assembling a pizza, such as spreading pizza sauce or placing slices of pepperoni, while leaving other customizations to employees. In 2020, a restaurant in the Netherlands began trialling the use of a robot to serve guests. In September 2021, Karakuri's 'Semblr' food service robot served personalised lunches for the 4,000 employees of grocery technology solutions provider ocado Group's head offices in Hatfield, UK. 2,700 different combinations of dishes were on offer. Customers could specify in grams what hot and cold items, proteins, sauces and fresh toppings they wanted. In 2021, Columbia University School of Engineering and Applied Science engineers developed a method of cooking 3D printed chicken with software-controlled robotic lasers. The “Digital Food” team exposed raw 3D printed chicken structures to both blue and infrared light. They then assessed the cooking depth, colour development, moisture retention and flavour differences of the laser-cooked 3D printed samples in comparison to stove-cooked meat. In June 2022 a California nonprofit chain of residential communities, Front Porch, experimented with robots in dining rooms at two locations to supplement wait staff by carrying plated food and drink to tables, and removing dishes. 65% of residents found the robots helpful, with 51% saying they let the staff spend more quality time with diners. 51% of staff were "excited" and 58% said they enabled more quality time with diners. The chain has 19 senior living communities (and 35 affordable housing communities), so it has potential to expand robots to more dining rooms. It is shifting to memory care, which may affect plans. == Rationales == === Advantages === Efficiency: Automated restaurants can significantly enhance operational efficiency by minimizing human error and reducing service time. With automated ordering, payment, and food preparation systems, customers can enjoy faster service and reduced waiting times. Cost savings: By reducing the need for human staff, automated restaurants can potentially lower labor costs. This can be particularly beneficial in areas with high labor expenses, as it allows for better resource allocation and cost management. Consistency: Automation ensures consistency in food quality and presentation. With precise portion control and standardized cooking methods, customers can expect the same quality and taste in their meals every time they visit. Enhanced customer experience: Self-service kiosks and automated systems provide customers with control and convenience. They can customize their orders, browse through menu options, and pay seamlessly, creating a more interactive and satisfying dining experience. === Disadvantages === Lack of personal touch: Automated restaurants may lack the personal interaction and warmth that traditional restaurants provide. Some customers prefer the human touch, personalized recommendations, and the social aspect of dining out. Technical issues: Reliance on technology means that technical glitches and malfunctions can occur, resulting in service disruptions or delays. Maintenance and technical support become critical in ensuring smooth operations. Limited menu complexity: The automation process may be better suited for standardized menu items rather than complex or customized dishes. The ability to cater to unique dietary preferences or accommodate special requests may be limited. Employment implications: Automated restaurants may result in job losses for traditional restaurant staff, potentially impacting the local workforce. It is important to consider the social and economic implications of adopting such technology. == Locations == Automated restaurants have been opening in many countries. Examples include: Nala Restaurant in Naperville, Illinois Fritz's Railroad Restaurant in Kansas City, Kansas Výtopna, a Railway Restaurant using model trains: franchise of various restaurants and coffeehouses in the Czech Republic Bagger's Restaurant in Nuremberg, Germany FuA-Men Restaurant, a ramen restaurant located in Nagoya, Japan Fōster Nutrition in Buenos Aires, Argentina Dalu Robot Restaurant in Jinan, China Haohai Robot Restaurant in Harbin, China Robot Kitchen Restaurant in Hong Kong Robo-Chef restaurant in Tehran, Iran, started in 2017, is the first robotic and "waiterless" restaurant of the Middle East. MIT graduates opened Spyce Kitchens in downtown Boston, Massachusetts, in 2018 Foodom, under Country Garden Holdings, opened January 12, 2020, in Guangzhou, China Robot Chacha, the first robot restaurant of India, is planning to open in the capital city of New Delhi. Kura Revolving Sushi Bar, with a number of locations in the United States, uses a tablets at tables for ordering, a conveyor belt to deliver food, and robots to deliver drinks and condiments. Chipotle Mexican Grill is beginning to deploy the Hyphen Makeline, which assembles up to 350 bowls and salads automatically per hour, and Chippy, an automatic tortilla chip fryer made by Miso Robotics. Serious Dumplings in Boca Raton, Florida

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  Back-Up Interceptor Control

  Backup Interceptor Control (BUIC, ) was the Electronic Systems Division 416M System to backup the SAGE 416L System in the United States and Canada. BUIC deployed Cold War command, control, and coordination systems to SAGE radar stations to create dispersed NORAD Control Centers. == Background == Prior to the SAGE Direction Centers becoming operational, the USAF deployed data link systems at NORAD Control Centers with ground computers for controlling crewed interceptors. After SAGE IBM AN/FSQ-7 Combat Direction Centrals became operational and the Super Combat Centers with improved (digital) computers were cancelled, a backup to SAGE was planned in the event the above-ground SAGE Air Defense Direction Center failed. == General Electric AN/GPA-37 Course Directing Group == BUIC began with deployment of General Electric AN/GPA-37 Course Directing Groups to several Long Range Radar stations. Units designated included the "U.S. Air Force 858th Air Defense Group (BUIC) [which became] a permanent operating facility" at Naval Air Station Fallon in Nevada. == BUIC II == BUIC II was used to command and control sites using the Burroughs AN/GSA-51 Radar Course Directing Group. North Truro AFS became the first ADC installation configured for BUIC II. == BUIC III == The AN/GYK-19 (initially AN/GSA-51A) was an upgraded version of the BUIC II system designated AN/GSA-51A and required a larger building than the AN/GSA-51. The first BUIC III site was Fort Fisher AFS, and Air Defense Command's was first installed at Fort Fisher Air Force Station, North Carolina. Although more advanced systems were contemplated, the final design of the BUIC III system was an upgraded version of the BUIC II with around twice the performance. == Closure and upgrade == In 1972, the USAF decided to shut down most of the BUIC sites; most of the sites mothballed by 1974, except for the BUIC III site at Tyndall Air Force Base. In Canada the BUIC site at Senneterre was shut down, but St Margarets remained open. The remaining sites were closed between 1983-1984 when SAGE was replaced by the Joint Surveillance System. The AN/FYQ-47 Common Digitizer for the Joint Surveillance System, and the Radar Video Data Processor (RVDP) was a combined system for the Air Force and Federal Aviation Administration (FAA), it replaced the SAGE Burroughs AN/FST-2 Coordinate Data Transmitting Sets.

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  Factorization of polynomials over finite fields

  In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them. All factorization algorithms, including the case of multivariate polynomials over the rational numbers, reduce the problem to this case; see polynomial factorization. It is also used for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory. As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article. == Background == === Finite field === The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches of mathematics. Due to the applicability of the concept in other topics of mathematics and sciences like computer science there has been a resurgence of interest in finite fields and this is partly due to important applications in coding theory and cryptography. Applications of finite fields introduce some of these developments in cryptography, computer algebra and coding theory. A finite field or Galois field is a field with a finite order (number of elements). The order of a finite field is always a prime or a power of prime. For each prime power q = pr, there exists exactly one finite field with q elements, up to isomorphism. This field is denoted GF(q) or Fq. If p is prime, GF(p) is the prime field of order p; it is the field of residue classes modulo p, and its p elements are denoted 0, 1, ..., p−1. Thus a = b in GF(p) means the same as a ≡ b (mod p). === Irreducible polynomials === Let F be a finite field. As for general fields, a non-constant polynomial f in F[x] is said to be irreducible over F if it is not the product of two polynomials of positive degree. A polynomial of positive degree that is not irreducible over F is called reducible over F. Irreducible polynomials allow us to construct the finite fields of non-prime order. In fact, for a prime power q, let Fq be the finite field with q elements, unique up to isomorphism. A polynomial f of degree n greater than one, which is irreducible over Fq, defines a field extension of degree n which is isomorphic to the field with qn elements: the elements of this extension are the polynomials of degree lower than n; addition, subtraction and multiplication by an element of Fq are those of the polynomials; the product of two elements is the remainder of the division by f of their product as polynomials; the inverse of an element may be computed by the extended GCD algorithm (see Arithmetic of algebraic extensions). It follows that, to compute in a finite field of non prime order, one needs to generate an irreducible polynomial. For this, the common method is to take a polynomial at random and test it for irreducibility. For sake of efficiency of the multiplication in the field, it is usual to search for polynomials of the shape xn + ax + b. Irreducible polynomials over finite fields are also useful for pseudorandom number generators using feedback shift registers and discrete logarithm over F2n. The number of irreducible monic polynomials of degree n over Fq is the number of aperiodic necklaces, given by Moreau's necklace-counting function Mq(n). The closely related necklace function Nq(n) counts monic polynomials of degree n which are primary (a power of an irreducible); or alternatively irreducible polynomials of all degrees d which divide n. === Example === The polynomial P = x4 + 1 is irreducible over Q but not over any finite field. On any field extension of F2, P = (x + 1)4. On every other finite field, at least one of −1, 2 and −2 is a square, because the product of two non-squares is a square and so we have If − 1 = a 2 , {\displaystyle -1=a^{2},} then P = ( x 2 + a ) ( x 2 − a ) . {\displaystyle P=(x^{2}+a)(x^{2}-a).} If 2 = b 2 , {\displaystyle 2=b^{2},} then P = ( x 2 + b x + 1 ) ( x 2 − b x + 1 ) . {\displaystyle P=(x^{2}+bx+1)(x^{2}-bx+1).} If − 2 = c 2 , {\displaystyle -2=c^{2},} then P = ( x 2 + c x − 1 ) ( x 2 − c x − 1 ) . {\displaystyle P=(x^{2}+cx-1)(x^{2}-cx-1).} === Complexity === Polynomial factoring algorithms use basic polynomial operations such as products, divisions, gcd, powers of one polynomial modulo another, etc. A multiplication of two polynomials of degree at most n can be done in O(n2) operations in Fq using "classical" arithmetic, or in O(nlog(n) log(log(n)) ) operations in Fq using "fast" arithmetic. A Euclidean division (division with remainder) can be performed within the same time bounds. The cost of a polynomial greatest common divisor between two polynomials of degree at most n can be taken as O(n2) operations in Fq using classical methods, or as O(nlog2(n) log(log(n)) ) operations in Fq using fast methods. For polynomials h, g of degree at most n, the exponentiation hq mod g can be done with O(log(q)) polynomial products, using exponentiation by squaring method, that is O(n2log(q)) operations in Fq using classical methods, or O(nlog(q)log(n) log(log(n))) operations in Fq using fast methods. In the algorithms that follow, the complexities are expressed in terms of number of arithmetic operations in Fq, using classical algorithms for the arithmetic of polynomials. == Factoring algorithms == Many algorithms for factoring polynomials over finite fields include the following three stages: Square-free factorization Distinct-degree factorization Equal-degree factorization An important exception is Berlekamp's algorithm, which combines stages 2 and 3. === Berlekamp's algorithm === Berlekamp's algorithm is historically important as being the first factorization algorithm which works well in practice. However, it contains a loop on the elements of the ground field, which implies that it is practicable only over small finite fields. For a fixed ground field, its time complexity is polynomial, but, for general ground fields, the complexity is exponential in the size of the ground field. === Square-free factorization === The algorithm determines a square-free factorization for polynomials whose coefficients come from the finite field Fq of order q = pm with p a prime. This algorithm firstly determines the derivative and then computes the gcd of the polynomial and its derivative. If it is not one then the gcd is again divided into the original polynomial, provided that the derivative is not zero (a case that exists for non-constant polynomials defined over finite fields). This algorithm uses the fact that, if the derivative of a polynomial is zero, then it is a polynomial in xp, which is, if the coefficients belong to Fp, the pth power of the polynomial obtained by substituting x by x1/p. If the coefficients do not belong to Fp, the pth root of a polynomial with zero derivative is obtained by the same substitution on x, completed by applying the inverse of the Frobenius automorphism to the coefficients. This algorithm works also over a field of characteristic zero, with the only difference that it never enters in the blocks of instructions where pth roots are computed. However, in this case, Yun's algorithm is much more efficient because it computes the greatest common divisors of polynomials of lower degrees. A consequence is that, when factoring a polynomial over the integers, the algorithm which follows is not used: one first computes the square-free factorization over the integers, and to factor the resulting polynomials, one chooses a p such that they remain square-free modulo p. Algorithm: SFF (Square-Free Factorization) Input: A monic polynomial f in Fq[x] where q = pm Output: Square-free factorization of f R ← 1 # Make w be the product (without multiplicity) of all factors of f that have # multiplicity not divisible by p c ← gcd(f, f′) w ← f/c # Step 1: Identify all factors in w i ← 1 while w ≠ 1 do y ← gcd(w, c) fac ← w / y R ← R · faci w ← y; c ← c / y; i ← i + 1 end while # c is now the product (with multiplicity) of the remaining factors of f # Step 2: Identify all remaining factors using recursion # Note that these are the factors of f that have multiplicity divisible by p if c ≠ 1 then c ← c1/p R ← R·SFF(c)p end if Output(R) The idea is to identify the product of all irreducible factors of f with the same multiplicity. This is done in two steps. The first step uses the formal d

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