In automata theory, a permutation automaton, or pure-group automaton, is a deterministic finite automaton such that each input symbol permutes the set of states. Formally, a deterministic finite automaton A may be defined by the tuple (Q, Σ, δ, q0, F), where Q is the set of states of the automaton, Σ is the set of input symbols, δ is the transition function that takes a state q and an input symbol x to a new state δ(q,x), q0 is the initial state of the automaton, and F is the set of accepting states (also: final states) of the automaton. A is a permutation automaton if and only if, for every two distinct states qi and qj in Q and every input symbol x in Σ, δ(qi,x) ≠ δ(qj,x). A formal language is p-regular (also: a pure-group language) if it is accepted by a permutation automaton. For example, the set of strings of even length forms a p-regular language: it may be accepted by a permutation automaton with two states in which every transition replaces one state by the other. == Applications == The pure-group languages were the first interesting family of regular languages for which the star height problem was proved to be computable. Another mathematical problem on regular languages is the separating words problem, which asks for the size of a smallest deterministic finite automaton that distinguishes between two given words of length at most n – by accepting one word and rejecting the other. The known upper bound in the general case is O ( n 2 / 5 ( log n ) 3 / 5 ) {\displaystyle O(n^{2/5}(\log n)^{3/5})} . The problem was later studied for the restriction to permutation automata. In this case, the known upper bound changes to O ( n 1 / 2 ) {\displaystyle O(n^{1/2})} .
Information extraction
Information extraction (IE) is the task of automatically extracting structured information from unstructured and/or semi-structured machine-readable documents and other electronically represented sources. Typically, this involves processing human language texts by means of natural language processing (NLP). Recent activities in multimedia document processing like automatic annotation and content extraction out of images/audio/video/documents could be seen as information extraction. Recent advances in NLP techniques have allowed for significantly improved performance compared to previous years. An example is the extraction from newswire reports of corporate mergers, such as denoted by the formal relation: MergerBetween ( c o m p a n y 1 , c o m p a n y 2 , d a t e ) {\displaystyle \operatorname {MergerBetween} (\mathrm {company} _{1},\mathrm {company} _{2},\mathrm {date} )} , from an online news sentence such as: "Yesterday, New York based Foo Inc. announced their acquisition of Bar Corp." A broad goal of IE is to allow computation to be done on the previously unstructured data. A more specific goal is to allow automated reasoning about the logical form of the input data. Structured data is semantically well-defined data from a chosen target domain, interpreted with respect to category and context. Information extraction is the part of a greater puzzle which deals with the problem of devising automatic methods for text management, beyond its transmission, storage and display. The discipline of information retrieval (IR) has developed automatic methods, typically of a statistical flavor, for indexing large document collections and classifying documents. Another complementary approach is that of natural language processing (NLP) which has solved the problem of modelling human language processing with considerable success when taking into account the magnitude of the task. In terms of both difficulty and emphasis, IE deals with tasks in between both IR and NLP. In terms of input, IE assumes the existence of a set of documents in which each document follows a template, i.e. describes one or more entities or events in a manner that is similar to those in other documents but differing in the details. An example, consider a group of newswire articles on Latin American terrorism with each article presumed to be based upon one or more terroristic acts. We also define for any given IE task a template, which is a(or a set of) case frame(s) to hold the information contained in a single document. For the terrorism example, a template would have slots corresponding to the perpetrator, victim, and weapon of the terroristic act, and the date on which the event happened. An IE system for this problem is required to "understand" an attack article only enough to find data corresponding to the slots in this template. == History == Information extraction dates back to the late 1970s in the early days of NLP. An early commercial system from the mid-1980s was JASPER built for Reuters by the Carnegie Group Inc with the aim of providing real-time financial news to financial traders. Beginning in 1987, IE was spurred by a series of Message Understanding Conferences. MUC is a competition-based conference that focused on the following domains: MUC-1 (1987), MUC-3 (1989): Naval operations messages. MUC-3 (1991), MUC-4 (1992): Terrorism in Latin American countries. MUC-5 (1993): Joint ventures and microelectronics domain. MUC-6 (1995): News articles on management changes. MUC-7 (1998): Satellite launch reports. Considerable support came from the U.S. Defense Advanced Research Projects Agency (DARPA), who wished to automate mundane tasks performed by government analysts, such as scanning newspapers for possible links to terrorism. == Present significance == The present significance of IE pertains to the growing amount of information available in unstructured form. Tim Berners-Lee, inventor of the World Wide Web, refers to the existing Internet as the web of documents and advocates that more of the content be made available as a web of data. Until this transpires, the web largely consists of unstructured documents lacking semantic metadata. Knowledge contained within these documents can be made more accessible for machine processing by means of transformation into relational form, or by marking-up with XML tags. An intelligent agent monitoring a news data feed requires IE to transform unstructured data into something that can be reasoned with. A typical application of IE is to scan a set of documents written in a natural language and populate a database with the information extracted. == Tasks and subtasks == Applying information extraction to text is linked to the problem of text simplification in order to create a structured view of the information present in free text. The overall goal being to create a more easily machine-readable text to process the sentences. Typical IE tasks and subtasks include: Template filling: Extracting a fixed set of fields from a document, e.g. extract perpetrators, victims, time, etc. from a newspaper article about a terrorist attack. Event extraction: Given an input document, output zero or more event templates. For instance, a newspaper article might describe multiple terrorist attacks. Knowledge Base Population: Fill a database of facts given a set of documents. Typically the database is in the form of triplets, (entity 1, relation, entity 2), e.g. (Barack Obama, Spouse, Michelle Obama) Named entity recognition: recognition of known entity names (for people and organizations), place names, temporal expressions, and certain types of numerical expressions, by employing existing knowledge of the domain or information extracted from other sentences. Typically the recognition task involves assigning a unique identifier to the extracted entity. A simpler task is named entity detection, which aims at detecting entities without having any existing knowledge about the entity instances. For example, in processing the sentence "M. Smith likes fishing", named entity detection would denote detecting that the phrase "M. Smith" does refer to a person, but without necessarily having (or using) any knowledge about a certain M. Smith who is (or, "might be") the specific person whom that sentence is talking about. Coreference resolution: detection of coreference and anaphoric links between text entities. In IE tasks, this is typically restricted to finding links between previously extracted named entities. For example, "International Business Machines" and "IBM" refer to the same real-world entity. If we take the two sentences "M. Smith likes fishing. But he doesn't like biking", it would be beneficial to detect that "he" is referring to the previously detected person "M. Smith". Relationship extraction: identification of relations between entities, such as: PERSON works for ORGANIZATION (extracted from the sentence "Bill works for IBM.") PERSON located in LOCATION (extracted from the sentence "Bill is in France.") Semi-structured information extraction which may refer to any IE that tries to restore some kind of information structure that has been lost through publication, such as: Table extraction: finding and extracting tables from documents. Table information extraction : extracting information in structured manner from the tables. This task is more complex than table extraction, as table extraction is only the first step, while understanding the roles of the cells, rows, columns, linking the information inside the table and understanding the information presented in the table are additional tasks necessary for table information extraction. Comments extraction : extracting comments from the actual content of articles in order to restore the link between authors of each of the sentences Language and vocabulary analysis Terminology extraction: finding the relevant terms for a given corpus Audio extraction Template-based music extraction: finding relevant characteristic in an audio signal taken from a given repertoire; for instance time indexes of occurrences of percussive sounds can be extracted in order to represent the essential rhythmic component of a music piece. Note that this list is not exhaustive and that the exact meaning of IE activities is not commonly accepted and that many approaches combine multiple sub-tasks of IE in order to achieve a wider goal. Machine learning, statistical analysis and/or natural language processing are often used in IE. IE on non-text documents is becoming an increasingly interesting topic in research, and information extracted from multimedia documents can now be expressed in a high level structure as it is done on text. This naturally leads to the fusion of extracted information from multiple kinds of documents and sources. == World Wide Web applications == IE has been the focus of the MUC conferences. The proliferation of the Web, however, intensified the need for developing IE systems that help people
Argument technology
Argument technology is a sub-field of collective intelligence and artificial intelligence that focuses on applying computational techniques to the creation, identification, analysis, navigation, evaluation and visualisation of arguments and debates. In the 1980s and 1990s, philosophical theories of arguments in general, and argumentation theory in particular, were leveraged to handle key computational challenges, such as modeling non-monotonic and defeasible reasoning and designing robust coordination protocols for multi-agent systems. At the same time, mechanisms for computing semantics of Argumentation frameworks were introduced as a way of providing a calculus of opposition for computing what it is reasonable to believe in the context of conflicting arguments. With these foundations in place, the area was kick-started by a workshop held in the Scottish Highlands in 2000, the result of which was a book coauthored by philosophers of argument, rhetoricians, legal scholars and AI researchers. Since then, the area has been supported by various dedicated events such as the International Workshop on Computational Models of Natural Argument (CMNA) which has run annually since 2001; the International Workshop on Argument in Multi Agent Systems (ArgMAS) annually since 2004; the Workshop on Argument Mining, annually since 2014, and the Conference on Computational Models of Argument (COMMA), biennially since 2006. Since 2010, the field has also had its own journal, Argument & Computation, which was published by Taylor & Francis until 2016 and since then by IOS Press. One of the challenges that argument technology faced was a lack of standardisation in the representation and underlying conception of argument in machine readable terms. Many different software tools for manual argument analysis, in particular, developed idiosyncratic and ad hoc ways of representing arguments which reflected differing underlying ways of conceiving of argumentative structure. This lack of standardisation also meant that there was no interchange between tools or between research projects, and little re-use of data resources that were often expensive to create. To tackle this problem, the Argument Interchange Format set out to establish a common standard that captured the minimal common features of argumentation which could then be extended in different settings. Since about 2018, argument technology has been growing rapidly, with, for example, IBM's Grand Challenge, Project Debater, results for which were published in Nature in March 2021; German research funder, DFG's nationwide research programme on Robust Argumentation Machines, RATIO, begun in 2019; and UK nationwide deployment of The Evidence Toolkit by the BBC in 2019. A 2021 video narrated by Stephen Fry provides a summary of the societal motivations for work in argument technology. Argument technology has applications in a variety of domains, including education, healthcare, policy making, political science, intelligence analysis and risk management and has a variety of sub-fields, methodologies and technologies. == Technologies == === Argument assistant === An argument assistant is a software tool which support users when writing arguments. Argument assistants can help users compose content, review content from one other, including in dialogical contexts. In addition to Web services, such functionalities can be provided through the plugin architectures of word processor software or those of Web browsers. Internet forums, for instance, can be greatly enhanced by such software tools and services. === Argument blogging === ArguBlogging is software which allows its users to select portions of hypertext on webpages in their Web browsers and to agree or disagree with the selected content, posting their arguments to their blogs with linked argument data. It is implemented as a bookmarklet, adding functionality to Web browsers and interoperating with blogging platforms such as Blogger and Tumblr. === Argument mapping === Argument maps are visual, diagrammatic representations of arguments. Such visual diagrams facilitate diagrammatic reasoning and promote one's ability to grasp and to make sense of information rapidly and readily. Argument maps can provide structured, semi-formal frameworks for representing arguments using interactive visual language. One avenue of research and development is the design of online platforms to leverage collective intelligence to populate such maps and to integrate data, optimize and assess arguments. === Argument mining === Argument mining, or argumentation mining, is a research area within the natural language processing field. The goal of argument mining is the automatic extraction and identification of argumentative structures from natural language text with the aid of computer programs. === Argument search === An argument search engine is a search engine that is given a topic as a user query and returns a list of arguments for and against the topic or about that topic. Such engines could be used to support informed decision-making or to help debaters prepare for debates. === Automated argumentative essay scoring === The goal of automated argumentative essay scoring systems is to assist students in improving their writing skills by measuring the quality of their argumentative content. === Debate technology === Debate technology focuses on human-machine interaction and in particular providing systems that support, monitor and engage in debate. One of the most high-profile examples of debating technology is IBM's Project Debater which combines scripted communication with very large-scale processing of news articles to identify and construct arguments on the fly in a competitive debating setting. Debating technology also encompasses tools aimed at providing insight into debates, typically using techniques from data science. These analytics have been developed in both academic and commercial settings. === Decision support system === Argument technology can reduce both individual and group biases and facilitate more accurate decisions. Argument-based decision support systems do so by helping users to distinguish between claims and the evidence supporting them, and express their confidence in and evaluate the strength of evidence of competing claims. They have been used to improve predictions of housing market trends, risk analysis, ethical and legal decision making. ==== Ethical decision support system ==== An ethical decision support system is a decision support system which supports users in moral reasoning and decision-making. ==== Legal decision support system ==== A legal decision support system is a decision support system which supports users in legal reasoning and decision-making. === Explainable artificial intelligence === An explainable or transparent artificial intelligence system is an artificial intelligence system whose actions can be easily understood by humans. === Intelligent tutoring system === An intelligent tutoring system is a computer system that aims to provide immediate and customized instruction or feedback to learners, usually without requiring intervention from a human teacher. The intersection of argument technology and intelligent tutoring systems includes computer systems which aim to provide instruction in: critical thinking, argumentation, ethics, law, mathematics, and philosophy. === Legal expert system === A legal expert system is a domain-specific expert system that uses artificial intelligence to emulate the decision-making abilities of a human expert in the field of law. === Machine ethics === Machine ethics is a part of the ethics of artificial intelligence concerned with the moral behavior of artificially intelligent beings. As humans argue with respect to morality and moral behavior, argument can be envisioned as a component of machine ethics systems and moral reasoning components. === Proof assistant === In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer. === Ethical considerations === Ethical considerations of argument technology include privacy, transparency, societal concerns, and diversity in representation. These factors cut across different levels such as technology, user interface design, user, service context, and society. There is concern about unethical misuse for "generating arguments on controversial topics with specific stances and deploying them on social platforms". Another issue may concern the design of conclusion-making algorithms, such as e.g. enabling such to conclude that certain key data is needed instead of only making lists of best-fit conclusions or enabling the generation of multi
Digital fashion
Digital fashion is a field of fashion design that relies on 3D software or artificial intelligence to produce hyper-realistic, data-intensive digital 3D garment simulations that are digital-only products or digital models for physical products. Digital garments can be worn and presented in virtual environments, social media, online gaming, virtual reality (VR), and augmented reality (AR) platforms. The field aims to contribute to the development of a more sustainable future for the fashion industry. It has been praised as a possible answer to ethical and creative concerns of traditional fashion by promoting innovation, reducing waste, and encouraging conscious consumption. However, empirical research has questioned whether digital fashion communities embody the radical and anti-consumerist values they claim. A 2025 study presented by YeSeung Lee at the FACTUM international conference on fashion communication analysed 88,141 posts across nine platforms over eight months using Pulsar. It found that only 4.8% of author biographies indicated any sociopolitical focus, and that discourse predominantly relied on generic slogans and trending buzzwords, primarily reinforcing existing fashion hierarchies and consumerist frameworks rather than challenging them. Digital fashion is also the interplay between digital technology and couture. Human AI is an intersection of technology and human representation, in which human value is emphasized and enhanced by technology and the possibilities of discovering design. Information and communication technologies (ICTs) have been deeply integrated both into the fashion industry, as well as within the experience of clients and prospects. Such interplay has happened at three main levels. ICTs are used to design and produce fashion products, while the industry organization also leverages digital technologies. ICTs impact marketing, distribution and sales. ICTs are extensively used in communication activities with all relevant stakeholders and contribute to co-create the fashion world. The fashion industry in general has paved the way for digital fashion to be introduced with more technology being in the industry, like virtual dressing rooms and the gamification of the fashion industry. Digital fashion is also seen on many different online fashion retail websites. This evolution in the fashion industry has called for more education and research of digital fashion. == Design, production, and organization == Among the many applications available to fashion designers to model the fusion of creativity with digital avenues, the Digital Textile Printing can be mentioned here. === Digital textile printing === Digital textile printing has brought together the worlds of fashion, technology, art, chemistry, and printing to produce a new process for printing textiles on clothing. Digital printing is a process in which prints are directly applied to fabrics with a printer, reducing 95% of the use of water, 75% of the use of energy and minimizing textile waste. The main advantage of digital printing is the ability to do very small runs of each design (even less than 1 yard). Digital Textile printing also offers other benefits, such as fast printing speeds that help the time and space needed to print different patterns on garments of choice. == Marketing, distribution, and sales == While all digital channels can be used in order to market and sell fashion completely online (eCommerce), they usually are implemented in connection with offline channels (so-called "omni-channel"). Here, virtual and augmented reality play a crucial role. The fashion industry has faced its own problems including pollution and fabric waste, which has resulted in a shift to more sustainable methods like digital fashion. The industry is also constantly being intertwined with digital media and has allowed for the use of digital tools within the business itself and with consumers. Two of the ways digital fashion is utilized with consumers is through virtual dressing rooms and virtual cosmetic counters. Prospects and clients can use ICTs - own computers, tablets and smartphones - to virtually simulate fitting rooms and cosmetics counters and see how they look in specific outfits and makeup. Customers can give any look and decide on what suits them and buy products. Oftentimes, beauty retailers will feature virtual fitting rooms to allow users to experience the look of their product before committing to a purchase. Some examples are color contact retailers Freshlook, which allows users to simulate contact lens wear in their color contacts studio before purchase. Colorful Eyes also offers a virtual color contact lens try-on room. === Virtual dressing room === A virtual dressing room (also often referred to as virtual fitting room and virtual changing room although they do perform different functions) is the online equivalent of the near-ubiquitous in-store changing room – that is, it enables shoppers to try on clothes to check one or more of size, fit or style, but virtually rather than physically. Fashion retailer Topshop installed a Kinect-powered virtual fitting room at its Moscow store. Created by AR Door, the Augmented Fitting Room system overlays 3D augmented reality clothes on the customer. Simple gestures and on-screen buttons let users "try on" different outfits. However, the high variability of virtual fit platforms to predict consumer clothes sizes called into question the accuracy of these systems in their current form. AI-powered Wardrobe and Outfit Planning Beyond virtual fitting rooms, the integration of artificial intelligence has enabled the rise of digital wardrobe management. These platforms use computer vision and machine learning to catalog a user’s physical or digital garments, providing automated outfit recommendations based on weather, occasion, and personal style trends. Fashion-tech startups utilize AI-driven garment simulation to help users plan outfits virtually, bridging the gap between digital-only fashion and physical wardrobe utility. This "smart closet" approach aims to reduce "wardrobe fatigue" and decrease unnecessary consumption by maximizing the use of existing items through digital visualization. === Communication and experience co-creation === Fashion is also a matter of socially negotiating what is "in" or "out", fashionable or not. In other words, fashion items do not only play on the economic market of physical goods but also - and sometimes even more importantly - on the semiotic market of the production of social tastes and customs. Thanks to social media, and to all services offered by the so-called web2.0, laypeople can contribute to co-create the fashion world, shaping tastes, customs, and fashion-related values. Social media, in general, has catapulted the impact fashion has on our everyday lives and values. Fashion has taken a central role in mass production and is constantly evolving due to the ever-lasting digital transformation. Social media has also helped evolve to a point where not only can brands reach consumers, but consumers can reach brands as well. TikTok for example started a trend in 2020 with #GucciModelChallenge. This creates a space where the brand is gaining awareness from their consumers in the ever-changing digital age. === Gamification === Gaming has played an important role in fostering digital aspects of the fashion world, first beginning with dress-up games that used avatars and allowed players to select garments. Nevertheless, it seems it will now move on to the real world and start using avatars of real people. Garments from luxurious brands have been copied and adapted into the aesthetics of games such as Animal Crossing: New Horizons and The Sims. As to the former, during COVID-19 lock-downs players recreated outfits from a variety of fashion brands, including Chanel, Gucci and Versace. It became a platform for users to showcase their costume designs. In April 2019, Moschino collaborated with simulation game The Sims in a capsule collection that featured signature Jeremy Scott garments. The collection was made available to shop and the campaign was set against the backdrop of a Sims-like atmosphere. Furthermore, in May 2019, Nike partnered up with Fortnite to include their iconic Jordan sneakers. In similar fashion, in May 2020, Marc Jacobs designed 6 of the brand's favorite looks for Nintendo's Animal Crossing: New Horizons in a partnership with Instagram user @AnimalCrossingFashionArchive. They were made available to download. Similarly, the other luxury brands mentioned, Louis Vuitton partnered with game League of Legends to create skins for characters within the game. Digital fashion in different video games allows users to express themselves beyond their avatars and combine the self-expression of fashion into the digital gaming realm. == Digital fashion education and research == Nowadays, the fashion industry needs experts in digital fashion, equipped with the above-ske
Fuzzy Control Language
Fuzzy Control Language, or FCL, is a language for implementing fuzzy logic, especially fuzzy control. It was standardized by IEC 61131-7. It is a domain-specific programming language: it has no features unrelated to fuzzy logic, so it is impossible to even print "Hello, world!". Therefore, one does not write a program in FCL, but one may write part of it in FCL. == Example == RULE 0: IF (temperature IS cold) THEN (output IS low) RULE 1: IF (temperature IS very cold) THEN (output IS high) == Limitations == FCL is not an entirely complete fuzzy language, for instance, it does not support "hedges", which are adverbs that modify the set. For instance, the programmer cannot write: RULE 0: If (Temperature is VERY COLD) then (Output is VERY HIGH) However, the programmer can simply define new sets for "very cold" and "very high". FCL also lacks support for higher-order fuzzy sets, subsets, and so on. None of these features are essential to fuzzy control, although they may be nice to have.
C-RAN
C-RAN (Cloud-RAN), also referred to as Centralized-RAN, is an architecture for cellular networks. C-RAN is a centralized, cloud computing-based architecture for radio access networks that supports 2G, 3G, 4G, 5G and future wireless communication standards. Its name comes from the four 'C's in the main characteristics of C-RAN system, "Clean, Centralized processing, Collaborative radio, and a real-time Cloud Radio Access Network". == Background == Traditional cellular, or Radio Access Networks (RAN), consist of many stand-alone base stations (BTS). Each BTS covers a small area, whereas a group BTS provides coverage over a continuous area. Each BTS processes and transmits its own signal to and from the mobile terminal, and forwards the data payload to and from the mobile terminal and out to the core network via the backhaul. Each BTS has its own cooling, back haul transportation, backup battery, monitoring system, and so on. Because of limited spectral resources, network operators 'reuse' the frequency among different base stations, which can cause interference between neighboring cells. There are several limitations in the traditional cellular architecture. First, each BTS is costly to build and operate. Moore's law helps reduce the size and power of an electrical system, but the supporting facilities of the BTS are not improved quite as well. Second, when more BTS are added to a system to improve its capacity, interference among BTS is more severe as BTS are closer to each other and more of them are using the same frequency. Third, because users are mobile, the traffic of each BTS fluctuates (called 'tide effect'), and as a result, the average utilization rate of individual BTS is pretty low. However, these processing resources cannot be shared with other BTS. Therefore, all BTS are designed to handle the maximum traffic, not average traffic, resulting in a waste of processing resources and power at idle times. == Evolution of base station architecture == === All-in-one macro base station === In the 1G and 2G cellular networks, base stations had an all-in-one architecture. Analog, digital, and power functions were housed in a single cabinet as large as a refrigerator. Usually the base station cabinet was placed in a dedicated room along with all necessary supporting facilitates such as power, backup battery, air conditioning, environment surveillance, and backhaul transmission equipment. The RF signal is generated by the base station RF unit and propagates through pairs of RF cables up to the antennas on the top of a base station tower or other mounting points. This all-in-one architecture was mostly found in macro cell deployments. === Distributed base station === For 3G, a distributed base station architecture was introduced by Ericsson, Nokia, Huawei, and other leading telecom equipment vendors. In this architecture the radio function unit, also known as the remote radio head (RRH), is separated from the digital function unit, or baseband unit (BBU) by fiber. Digital baseband signals are carried over fiber, using the Open Base Station Architecture Initiative (OBSAI) or Common Public Radio Interface (CPRI) standard. The RRH can be installed on the top of tower close to the antenna, reducing the loss compared to the traditional base station where the RF signal has to travel through a long cable from the base station cabinet to the antenna at the top of the tower. The fiber link between RRH and BBU also allows more flexibility in network planning and deployment as they can be placed a few hundred meters or a few kilometers away. Most modern base stations now use this decoupled architecture. === C-RAN/Cloud-RAN === C-RAN may be viewed as an architectural evolution of the above distributed base station system. It takes advantage of many technological advances in wireless, optical and IT communications systems. For example, it uses the latest CPRI standard, low cost Coarse or Dense Wavelength Division Multiplexing (CWDM/ DWDM) technology, and mmWave to allow transmission of baseband signal over long distance thus achieving large scale centralised base station deployment. It applies recent Data Centre Network technology to allow a low cost, high reliability, low latency and high bandwidth interconnect network in the BBU pool. It utilizes open platforms and real-time virtualization technology rooted in cloud computing to achieve dynamic shared resource allocation and support multi-vendor, multi-technology environments. == Architecture overview == C-RAN architecture has the following characteristics that are distinct from other cellular architectures: Large scale centralized deployment: Allows many RRHs to connect to a centralized BBU pool. The maximum distance can be 20km in fiber link for 4G (LTE/LTE-A) systems, and even longer distances (40~80km) for 3G (WCDMA/TD-SCDMA) and 2G (GSM/CDMA) systems. Native support to Collaborative Radio technologies: Any BBU can talk with any other BBU within the BBU pool with very high bandwidth (10 Gbit/s and above) and low latency (10 μs level). This is enabled by the interconnection of BBUs in the pool. This is one major difference from BBU Hotelling, or base station Hotelling; in the latter case, the BBUs of different base stations are simply stacked together and have no direct link between them to allow physical layer co-ordination. Real-time virtualization capability based on open platform: This is different from traditional base stations built on proprietary hardware, where the software and hardware are close-sourced and provided by single vendors. In contrast, a C-RAN BBU pool is built on open hardware, like x86/ARM CPU based servers, and interface cards that handle fiber links to RRHs and inter-connections in the pool. Real-time virtualization ensures that resources in the pool can be allocated dynamically to base station software stacks, say 4G/3G/2G function modules from different vendors, according to network load. However, to satisfy the strict timing requirements of wireless communication systems, the real-time performance for C-RAN is at the level of tens of microseconds, which is two orders of magnitude better than the millisecond level 'real-time' performance usually seen in Cloud Computing environments. == Similar architecture and systems == KT, a telecom operator in the Republic of Korea, introduced a Cloud Computing Center (CCC) system in their 3G (WCDMA/HSPA) and 4G (LTE/LTE-A) network in 2011 and 2012. The concept of CCC is basically the same as C-RAN. SK Telecom has also deployed Smart Cloud Access Network (SCAN) and Advanced-SCAN in their 4G (LTE/LTE-A) network in Korea no later than 2012. In 2014, Airvana (now CommScope) introduced OneCell, a C-RAN-based small cell system designed for enterprises and public spaces. == Competing architectures in cellular network evolution == === All-in-one BTS === One major alternative solution that is addressing similar challenges of RAN, is the small size, all-in-one outdoor BTS. Thanks to the achievements in the semiconductor industry, all the functionality of a BTS, including RF, baseband processing, MAC processing and package level processing, can now be implemented in a volume of <50 liters. This makes the system small and weatherproof, reduces the difficulty of BTS site choice and construction, eliminates the air conditioning requirement, and thus reduces operational costs. However, because each BTS is still working on its own, it cannot readily make use of the collaboration algorithms to reduce the interference between neighboring BTSs. It is also relatively hard to upgrade or repair because the all-in-one BTS units are usually mounted near the antenna. More processing units in less-protected environments also implies a higher failure rate compared to C-RAN, which only has the RRU deployed outdoors. The advantage of Cloud RAN lies in its ability to implement LTE-Advanced features such as Coordinated MultiPoint (CoMP) with very low latency between multiple radio heads. However, the economic benefit of improvements such as CoMP can be negated by the higher backhaul costs for some operators. === Small cell === The main competition between small cell and C-RAN occurs in two deployment scenarios: outdoor hotspot coverage and indoor coverage. == Academic research and publications == As one of the promising evolution paths for future cellular network architecture, C-RAN has attracted high academic research interest. Meanwhile, because the native support of cooperative radio capability built into the C-RAN architecture, it also enables many advanced algorithms that were hard to implement in cellular networks, including Cooperative Multi-Point Transmission/Receiving, Network Coding, etc. In October 2011, Wireless World Research Forum 27 was hosted in Germany, when China Mobile was invited to give a C-RAN presentation. In August 2012, IEEE C-RAN 2012 workshop was hosted in Kunming, China. CRC Press published a book, "Green Communications: Theore
BL (logic)
In mathematical logic, basic fuzzy logic (or shortly BL), the logic of the continuous t-norms, is one of the t-norm fuzzy logics. It belongs to the broader class of substructural logics, or logics of residuated lattices; it extends the logic MTL of all left-continuous t-norms. == Syntax == === Language === The language of the propositional logic BL consists of countably many propositional variables and the following primitive logical connectives: Implication → {\displaystyle \rightarrow } (binary) Strong conjunction ⊗ {\displaystyle \otimes } (binary). The sign & is a more traditional notation for strong conjunction in the literature on fuzzy logic, while the notation ⊗ {\displaystyle \otimes } follows the tradition of substructural logics. Bottom ⊥ {\displaystyle \bot } (nullary — a propositional constant); 0 {\displaystyle 0} or 0 ¯ {\displaystyle {\overline {0}}} are common alternative signs and zero a common alternative name for the propositional constant (as the constants bottom and zero of substructural logics coincide in MTL). The following are the most common defined logical connectives: Weak conjunction ∧ {\displaystyle \wedge } (binary), also called lattice conjunction (as it is always realized by the lattice operation of meet in algebraic semantics). Unlike MTL and weaker substructural logics, weak conjunction is definable in BL as A ∧ B ≡ A ⊗ ( A → B ) {\displaystyle A\wedge B\equiv A\otimes (A\rightarrow B)} Negation ¬ {\displaystyle \neg } (unary), defined as ¬ A ≡ A → ⊥ {\displaystyle \neg A\equiv A\rightarrow \bot } Equivalence ↔ {\displaystyle \leftrightarrow } (binary), defined as A ↔ B ≡ ( A → B ) ∧ ( B → A ) {\displaystyle A\leftrightarrow B\equiv (A\rightarrow B)\wedge (B\rightarrow A)} As in MTL, the definition is equivalent to ( A → B ) ⊗ ( B → A ) . {\displaystyle (A\rightarrow B)\otimes (B\rightarrow A).} (Weak) disjunction ∨ {\displaystyle \vee } (binary), also called lattice disjunction (as it is always realized by the lattice operation of join in algebraic semantics), defined as A ∨ B ≡ ( ( A → B ) → B ) ∧ ( ( B → A ) → A ) {\displaystyle A\vee B\equiv ((A\rightarrow B)\rightarrow B)\wedge ((B\rightarrow A)\rightarrow A)} Top ⊤ {\displaystyle \top } (nullary), also called one and denoted by 1 {\displaystyle 1} or 1 ¯ {\displaystyle {\overline {1}}} (as the constants top and zero of substructural logics coincide in MTL), defined as ⊤ ≡ ⊥ → ⊥ {\displaystyle \top \equiv \bot \rightarrow \bot } Well-formed formulae of BL are defined as usual in propositional logics. In order to save parentheses, it is common to use the following order of precedence: Unary connectives (bind most closely) Binary connectives other than implication and equivalence Implication and equivalence (bind most loosely) === Axioms === A Hilbert-style deduction system for BL has been introduced by Petr Hájek (1998). Its single derivation rule is modus ponens: from A {\displaystyle A} and A → B {\displaystyle A\rightarrow B} derive B . {\displaystyle B.} The following are its axiom schemata: ( B L 1 ) : ( A → B ) → ( ( B → C ) → ( A → C ) ) ( B L 2 ) : A ⊗ B → A ( B L 3 ) : A ⊗ B → B ⊗ A ( B L 4 ) : A ⊗ ( A → B ) → B ⊗ ( B → A ) ( B L 5 a ) : ( A → ( B → C ) ) → ( A ⊗ B → C ) ( B L 5 b ) : ( A ⊗ B → C ) → ( A → ( B → C ) ) ( B L 6 ) : ( ( A → B ) → C ) → ( ( ( B → A ) → C ) → C ) ( B L 7 ) : ⊥ → A {\displaystyle {\begin{array}{ll}{\rm {(BL1)}}\colon &(A\rightarrow B)\rightarrow ((B\rightarrow C)\rightarrow (A\rightarrow C))\\{\rm {(BL2)}}\colon &A\otimes B\rightarrow A\\{\rm {(BL3)}}\colon &A\otimes B\rightarrow B\otimes A\\{\rm {(BL4)}}\colon &A\otimes (A\rightarrow B)\rightarrow B\otimes (B\rightarrow A)\\{\rm {(BL5a)}}\colon &(A\rightarrow (B\rightarrow C))\rightarrow (A\otimes B\rightarrow C)\\{\rm {(BL5b)}}\colon &(A\otimes B\rightarrow C)\rightarrow (A\rightarrow (B\rightarrow C))\\{\rm {(BL6)}}\colon &((A\rightarrow B)\rightarrow C)\rightarrow (((B\rightarrow A)\rightarrow C)\rightarrow C)\\{\rm {(BL7)}}\colon &\bot \rightarrow A\end{array}}} The axioms (BL2) and (BL3) of the original axiomatic system were shown to be redundant (Chvalovský, 2012) and (Cintula, 2005). All the other axioms were shown to be independent (Chvalovský, 2012). == Semantics == Like in other propositional t-norm fuzzy logics, algebraic semantics is predominantly used for BL, with three main classes of algebras with respect to which the logic is complete: General semantics, formed of all BL-algebras — that is, all algebras for which the logic is sound Linear semantics, formed of all linear BL-algebras — that is, all BL-algebras whose lattice order is linear Standard semantics, formed of all standard BL-algebras — that is, all BL-algebras whose lattice reduct is the real unit interval [0, 1] with the usual order; they are uniquely determined by the function that interprets strong conjunction, which can be any continuous t-norm.