AI Apps Like Chat Gpt

AI Apps Like Chat Gpt — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Message queuing service

A message queueing service is a message-oriented middleware or MOM deployed in a compute cloud using software as a service model. Service subscribers access queues and or topics to exchange data using point-to-point or publish and subscribe patterns. It's important to differentiate between event-driven and message-driven (aka queue driven) services: Event-driven services (e.g. AWS SNS) are decoupled from their consumers. Whereas queue / message driven services (e.g. AWS SQS) are coupled with their consumers. Message queues can be a good buffer to handle spiky workloads but they have a finite capacity. According to Gregor Hohpe, message queues require proper mechanisms (aka flow controls) to avoid filling the queue beyond its manageable capacity and to keep the system stable. == Ordering Guarantees in Message Queues == Amazon SQS FIFO and Azure Service Bus sessions are queue-based messaging systems that provide ordering guarantees within a message group or session attempt but do not necessarily guarantee ordered delivery in cases of retries or failures. In SQS FIFO, messages in the same message group are processed in order, with subsequent messages held until the preceding message is successfully processed or moved to the dead-letter queue (DLQ). Once a message is placed in the DLQ, it is no longer retried, creating a gap in the sequence. However, the remaining messages continue to be delivered in order. Azure Service Bus sessions function similarly by maintaining ordering within a session, provided a single consumer processes messages sequentially. The implementation differs from SQS FIFO but follows the same fundamental ordering principle. In contrast, Apache Kafka is a distributed log-based messaging system that guarantees ordering within individual partitions rather than across the entire topic. Unlike queue-based systems, Kafka retains messages in a durable, append-only log, allowing multiple consumers to read at different offsets. Kafka uses manual offset management, giving consumers control over retries and failure handling. If a consumer fails to process a message, it can delay committing the offset, preventing further progress in that partition while other partitions remain unaffected. This partition-based design enables fault isolation and parallel processing while allowing ordering to be maintained within partitions, depending on consumer handling. == Vendors == Apache Kafka Apache Kafka is a distributed system consisting of servers that store and forward messages between producer client and consumer applications. IBM MQ IBM MQ offers a managed service that can be used on IBM Cloud and Amazon Web Services. Microsoft Azure Service Bus Service Bus offers queues, topics & subscriptions, and rules/actions in order to support publish-subscribe, temporal decoupling, and load balancing scenarios. Azure Service Bus is built on AMQP allowing any existing AMQP 1.0 client stack to interact with Service Bus directly or via existing .Net, Java, Node, and Python clients. Standard and Premium tiers allow for pay as you go or isolated resources at massive scale. Oracle Messaging Cloud Service This service provides a messaging solution for applications for asynchronous communication and is influenced by the Java Message Service (JMS) API specification. Any application platform that understands HTTP can also use Oracle Messaging Cloud Service through the REST interface. For Java applications, Oracle Messaging Cloud Service provides a Java library that implements and extends the JMS 1.1 interface. The Java library implements the JMS API by acting as a client of the REST API. Amazon Simple Queue Service Supports messages natively up to 256K, or up to 2GB by transmitting payload via S3. Highly scalable, durable and resilient. Provides loose-FIFO and 'at least once' delivery in order to provide massive scale. Supports REST API and optional Java Message Service client. Low latency. Utilizes Amazon Web Services. IronMQ Supports messages up to 64k; guarantees order; guarantees once only delivery; no delays retrieving messages. Supports REST API and beanstalkd open source protocol. Runs on multiple clouds including AWS and Rackspace. Scaling must be managed by user. RabbitMQ RabbitMQ is a reliable and mature messaging and streaming broker, which is easy to deploy on cloud environments, on-premises, and on your local machine. Supports AMQP, STOMP, MQTT StormMQ Open platform supports messages up to 50Mb. Uses AMQP to avoid vendor lock-in and provide language neutrality. Locate-It Option allows customers to audit the location of their data at all times and satisfy data protection principles. AnypointMQ An enterprise multi-tenant, cloud messaging service that performs advanced asynchronous messaging scenarios between applications. Anypoint MQ is fully integrated with Anypoint Platform, offering role based access control, client application management, and connectors.
Read more →
Rob Fergus

Rob Fergus is a British-American computer scientist working primarily in the fields of machine learning, deep learning, representational learning, and generative models. He is a professor of computer science at Courant Institute of Mathematical Sciences at New York University (NYU) and a research scientist at DeepMind. Fergus developed ZFNet in 2013 together with M.D. Zeiler, his PhD student in NYU. Fergus co-founded Meta AI (then known as Facebook Artificial Intelligence Research (FAIR)) along with Yann Le Cun in September 2013. In 2009, Rob Fergus co-founded the Computational Intelligence, Learning, Vision, and Robotics (CILVR) Lab at NYU along with Yann Le Cun. == Awards and recognition == Rob Fergus has been recognized in academia and received the following awards: NSF Faculty Early Career Development Program (CAREER) Sloan Research Fellowship Test-of-time awards at ECCV, CVPR and ICLR == Notable PhD students == Matt Zeiler (Clarifai founder) Wojciech Zaremba (OpenAI co-founder) Denis Yarats (Perplexity co-founder) Alex Rives (EvolutionaryScale co-founder; faculty at MIT)
Read more →
Best AI Coding Assistants in 2026

Curious about the best AI coding assistant? An AI coding assistant is software that uses machine learning to help you get more done — it combines speed, accuracy, and an interface that just works. Hands-on testing shows real-world results vary, so a short free trial is the smartest way to decide. Whether you are a beginner or a pro, the right AI coding assistant slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
Read more →
Lorien Pratt

Lorien Pratt is an American computer scientist known for contributions to transfer learning and for her work in promoting and developing the concept of decision intelligence. She is chief scientist and founder of Quantellia. Since 1988, she has conducted research on the use of machine learning as an academic, professor, industry analyst, and practicing data scientist. Pratt received her AB degree in computer science from Dartmouth College and her master's and doctorate degrees in computer science from Rutgers University. == Learning to Learn == She is best known for her book "Learning to Learn," co-edited with Sebastian Thrun, which provided an overview on how to use machine learning to better understand bias and generalization of discrete subjects. This approach, still largely theoretical when the book was published in 1998, is also called metalearning and is now a foundational underpinning of machine learning algorithms such as GPT-3 and DALL-E. == Research == === Transfer learning === Pratt's research includes early work in transfer learning where she developed the discriminability-based transfer (DBT) algorithm in 1993 during her tenure as a professor of computer science at Colorado School of Mines. This paper is considered one of the earliest academic works referring to the use of transfer in machine learning and has been cited over 400 times as foundational research for deep neural networks. === Decision intelligence === Since then, Pratt's research has continued to explore the relationships between machine learning and human cognition with the concept of decision intelligence, an emerging field of machine learning guided analytics designed to support human decision. Pratt introduced this concept in 2008, and this term has since been used by a number of vendors providing machine learning-guided analytics including Diwo, Peak AI, Sisu, and Tellius as the technologies used to support machine learning at scale have become easier to deploy, manage, and embed into software platforms. Pratt's work is cited as a core starting point for defining modern aspects of decision intelligence. Pratt's work at Quantellia since 2020 has focused on the use of decision intelligence to improve COVID-19-based outcomes.
Read more →
List of Ada software and tools

This is a list of software and programming tools for the Ada programming language, including IDEs, compilers, libraries, verification and debugging tools, numerical and scientific computing libraries, and related projects. == Compilers == GNAT — GCC Ada compiler and toolchain, maintained by AdaCore AdaCore GNAT Pro — commercial Ada compiler with advanced tooling for high-integrity and real-time systems Green Hills compiler for Ada — Ada compiler for embedded and safety-critical systems ObjectAda — Ada development environment for safety-critical and embedded systems == Integrated development environments (IDEs) and editors == GNAT Studio — IDE developed by AdaCore Emacs — supports Ada editing with Ada mode and syntax checking Eclipse — supports Ada through GNATbench plugin Visual Studio Code — Ada support via Ada Language Server extensions == Libraries and frameworks == See also: Ada Libraries on Wikibooks Ada.Calendar — date and time library Ada Web Services (AWS) — support for RESTful and SOAP web services Ada.Text_IO — standard library for text input/output Florist (POSIX Ada binding) – open-source implementation of the POSIX Ada bindings GNAT – Ada compiler part of GCC, which also provides an extensive runtime and library package hierarchy. GtkAda – Ada bindings for the GTK+ graphical user interface toolkit Matreshka – multipurpose Ada framework supporting Unicode, XML, JSON, and more. XML/Ada – XML and Unicode processing library == Real-time and embedded systems == Ada tasking — built-in concurrency support with tasks, protected objects, and rendezvous. Ada.Real_Time — real-time clocks, delays, and scheduling. ARINC 653 Ada profiles — for avionics real-time applications OpenMP Ada bindings — parallel programming for multi-core embedded systems Ravenscar profile — subset of Ada tasking for real-time and deterministic execution == Numerical and scientific computing == Ada.Numerics — libraries for numerical methods, linear algebra, and mathematical functions. SPARK math libraries — formal-methods-compliant numerical routines == Verification, debugging, and analysis == GNATprove — formal verification and static analysis tool for Ada and SPARK GNATstack — runtime stack analysis and checking GNATcoverage — code coverage measurement for Ada projects AdaControl — style checking and metrics for Ada == Testing frameworks == AUnit — unit testing framework for Ada GNATtest — automated testing framework for Ada == Documentation and code generation == GNATdoc — generates HTML documentation from Ada source code
Read more →
Deepset

deepset is an enterprise software vendor that provides developers with the tools to build production-ready Artificial Intelligence (AI) and natural language processing (NLP) systems, using architectures such as agents, retrieval augmented generation (RAG) and multimodal AI. It was founded in 2018 in Berlin by Milos Rusic, Malte Pietsch, and Timo Möller. deepset authored and maintains the open source software Haystack and its commercial SaaS and self-hosted (VPC, on-prem, air gapped) offering, Haystack Enterprise Platform. (formerly known as deepset Cloud and deepset AI Platform) == History == In June 2018, Milos Rusic, Malte Pietsch, and Timo Möller co-founded deepset in Berlin, Germany. In the same year, the company served first customers who wanted to implement NLP services by tailoring BERT language models to their domain. In July 2019, the company released the initial version of the open source software FARM. In November 2019, the company released the initial version of the open source software Haystack. Throughout 2020 and 2021 deepset published several applied research papers at EMNLP, COLING and ACL, the leading conferences in the area of NLP. In 2020, the research contributions comprised German language models named GBERT and GELECTRA, and a question answering dataset addressing the COVID-19 pandemic called COVID-QA, which was created in collaboration with Intel and has been annotated by biomedical experts. In 2021, the research contributions comprised German models and datasets for question answering and passage retrieval named GermanQuAD and GermanDPR, a semantic answer similarity metric, and an approach for multimodal retrieval of texts and tables to enable question answering on tabular data. Haystack contains implementations of all three contributions, enabling the use of the research through the open source framework. In November 2021, the development of the FARM framework was discontinued and its main features were integrated into the Haystack framework. In April 2022, the company announced its commercial SaaS offering deepset Cloud, which was rebranded in 2025 as Haystack Enterprise Platform supporting SaaS and on-premise deployment options. As of August 2023, the most popular finetuned language model created by deepset was downloaded more than 52 million times. In 2024, deepset was named a Gartner Cool Vendor in AI Engineering. In 2025, deepset was recognized for its growth by WirtschaftsWoche and Sifted and shared partnership integrations and announcements with Meta Llama Stack, MongoDB, NVIDIA, Amazon Web Services (AWS), and PwC. As of September 2025, the Haystack open source AI orchestration framework has more than 24,000 GitHub stars. == Products and applications == Haystack is an open source Python AI Orchestration framework for building custom AI agents and applications with large language models. With its modular building block components, software developers and AI engineers can implement pipelines to build and customize various AI architectures over large document and multimodal data collections, such as agents, retrieval augmented generation (RAG), intelligent document processing (IDP), text-to-SQL as well as document retrieval, semantic search, text generation, question answering, or summarization. Haystack emphasizes context engineering, an approach to AI system design that focuses on explicit control over how contextual information is retrieved, structured, routed to language models, and evaluated after generation. This allows developers to build AI systems with transparent data flow, tool usage, and configurable reasoning processes. Haystack integrates with 90+ model and technology providers including Hugging Face Transformers, Elasticsearch, OpenSearch, OpenAI, Cohere, Anthropic, Mistral and others. Developers can extend these integrations with their own custom components. The framework has an active community on Discord with more than 4k members and GitHub, where so far more than 300 people have contributed to its continuous development, and engage on Meetup. Thousands of organizations use the framework, including public sector leaders like the European Commission and Global 500 enterprises like Airbus, Intel, NVIDIA, Lufthansa, Netflix, Apple, Infineon, Alcatel-Lucent Enterprise, BetterUp, Etalab, Sooth.ai, and Lego. On top of the Haystack open source framework, deepset offers two enterprise offerings to organizations. Haystack Enterprise Starter provides enterprise support on the open source framework from the Haystack engineering team as well as a private GitHub repository with production use case templates and Kubernetes deployment guides. The Haystack Enterprise Platform supports customers at building scalable AI applications by covering the entire process of prototyping, experimentation, deployment, monitoring, and governance. It is built on the Haystack open source framework and is available for hosting in the cloud and self-hosted via VPC, on-premise, or air gapped environments. deepset's enterprise tools are used by organizations including The European Commission, The Economist, Oxford University Press, the German Federal Ministry of Research, Technology, and Space (BMFTR), Manz Verlag, and the German Armed Forces. FARM was an earlier framework for adapting representation models. One of its core concepts was the implementation of adaptive models, which comprised language models and an arbitrary number of prediction heads. FARM supported domain-adaptation and finetuning of these models with advanced options, for example gradient accumulation, cross-validation or automatic mixed-precision training. Its main features were integrated into Haystack in November 2021, and its development was discontinued at that time. == Funding == On August 9, 2023, deepset announced a Series B investment round of $30 million led by Balderton Capital and including participation from existing investors GV, System.One, Lunar Ventures and Harpoon Ventures. On April 28, 2022, deepset announced a Series A investment round of $14 million led by GV, with the participation of Harpoon Ventures, Acequia Capital and a team of experienced commercial open source software and machine learning founders, such as Alex Ratner (Snorkel AI), Mustafa Suleyman (Deepmind), Spencer Kimball (Cockroach Labs), Jeff Hammerbacher (Cloudera) and Emil Eifrem (Neo4j). A previous pre-seed investment round of $1.6 million on March 8, 2021, was led by System.One and Lunar Ventures, who also participated in the subsequent Series A round.
Read more →
A Comprehensive Grammar of the English Language

A Comprehensive Grammar of the English Language is a descriptive grammar of English written by Randolph Quirk, Sidney Greenbaum, Geoffrey Leech, and Jan Svartvik. It was first published by Longman in 1985. In 1991, it was called "The greatest of contemporary grammars, because it is the most thorough and detailed we have," and "It is a grammar that transcends national boundaries." The book relies on elicitation experiments as well as three corpora: a corpus from the Survey of English Usage, the Lancaster-Oslo-Bergen Corpus (UK English), and the Brown Corpus (US English). == Reviews == In 1988, Rodney Huddleston published a very critical review. He wrote:[T]here are some respects in which it is seriously flawed and disappointing. A number of quite basic categories and concepts do not seem to have been thought through with sufficient care; this results in a remarkable amount of unclarity and inconsistency in the analysis, and in the organization of the grammar. Aarts, F. G. A. M. (April 1988). "A Comprehensive Grammar of the English Language: The great tradition continued". English Studies. 69 (2): 163–173. doi:10.1080/00138388808598565.
Read more →
MedSLT

MedSLT is a medium-ranged open source spoken language translator developed by the University of Geneva. It is funded by the Swiss National Science Foundation. The system has been designed for the medical domain. It currently covers the doctor-patient diagnosis dialogues for the domains of headache, chest and abdominal pain in English, French, Japanese, Spanish, Catalan and Arabic. The vocabulary used ranges from 350 to 1000 words depending on the domain and language pair. == Motivation for creating MedSLT == With more than 6000 languages worldwide, language barriers become an increasing problem for healthcare. The lack of medical interpreters can lead to disastrous consequences. These range from prolonged hospital stays to wrong diagnosis and medication. A study found that only about half of the 23 million people with limited proficiency in English in the United States had been provided with a medical interpreter. Millions of refugees and immigrants worldwide face similar problems, although not always as severe. The gap between need and availability of language services might be closed with speech translation systems. == Challenges == The biggest challenge is and was to develop an ideal system, though it is not possible to do so at this moment. This system would fit the needs of doctors and the patients alike, and would provide accurate and flexible translation. A realisation of an ideal translation tool is impossible without the use of unrestricted language and a large vocabulary. Medical professionals demand high reliability from translation. This favours rule-based architectures over data-driven. The latter are more suitable for inexperienced users. Rule-based architectures achieve higher accuracy especially if used by experts. Though it is highly desirable to build a bidirectional system supporting a two-way dialogue, which concentrates on patient-centered communication, the patients will have difficult access to the system. Most patients have no experience with such systems. Less reliable results for translation from the patient-to-doctor direction are the outcome. To overcome this the system needs to provide either easy access or an integrated help tool to guide the users through the process. Although controlled rule-based systems achieve good results, they are brittle. To receive good translations the user needs to be familiar with the system and has to know what is covered by the grammar. Covering different sub-domains (headache, chest and abdominal pain) and language pairs presents additional problems. A shared structure and grammar for all subdomains and language pairs minimises development and maintenance costs. The integration of new doctor and patient languages is also a key challenge. Adding new languages should be quick and rather simple, because he system has to be used in many countries to cover multiple language pairs. Direct translation from source to target language proves to be rather difficult. Using interlingua for unidirectional translation instead of a bidirectional approach helps to simplify the translation process. On top of this, the system has to run on different platforms, because mobility is a key issue for many attending physicians. A portable version addresses these issues, but has to deal with the heavy load of the translation process. == The MedSLT system == The system's speech recognition is based on the Nuance 8.5 platform that supports grammar-based language models. All grammars used for recognition, analysis and generation are compiled from a small set of unification grammars. These core grammars are created by the open-source Regulus Grammar Compiler and are automatically specialised using corpus-driven methods. The specialisation considers both the task (recognition, analysis and generation) and the sub-domain (headache, chest and abdominal pain). The specialisation uses the explanation-based learning algorithm to create a treebank from the training corpus. These examples are divided into sets of subtrees by using domain- and grammar-specific rules (also known as "operationality criteria" in machine translation). The subtree rules are combined into a single rule, creating a specialised unification grammar. The grammar is compiled to an executable form, for analysis and generation by a parser or generator, and for recognition of a CFG grammar. A CFG grammar is required for the Nuance engine. Compilation by Nuance-specific criteria turns the grammar into speech recognition packages. The final step uses the training corpus again for statistical tuning of the language model. MedSLT translation processes are based on a rule-based interlingua. The interlingua is treated as an actual language (it is a very simple version of English) and is specified by a Regulus grammar. This grammar does not take account of complex surface syntax phenomena of real languages like movement or agreement. A set of rules is the base for translating the source language semantic representation to interlingua. Another set of rules covers the translation from interlingua to the target language. The semantic representations are converted to surface words using a target language grammar. Defining semantics for a specific domain enables the developers to specify interlingua with a small, tightly constraint semantic grammar. The translations based on interlingua match direct translations almost perfectly, because the development shifts to a decoupled monolingual architecture. A set of combined interlingua corpora, with one corpus per sub-domain, is the core of this architecture. All source language development corpora are translated to interlingua. These are sorted and grouped together with the corresponding source language examples. The interlingua forms are then translated into each target language, and the results are attached together. This organisation improves the translation process. There is no duplicated effort for multilingual regression testing, because each parsing and generation step is performed once. This allows more frequent testing. The representation language used for all forms is Almost Flat Functional semantics. AFF is derived from the Spoken Language Translator, the precursor of MEdSLT. SLT uses Quasi Logical Form, a logical based representation language. QLF is an expressive yet very complex language, causing high development and maintenance costs. A minimal solution was planned for the medical translator. Early versions of the system utilised a language using simple feature-value lists. These lists were supplemented with an optional level of nesting to represent subordinate clauses (i.e. embedded clauses). Determiners were not included, because they are hard to translate and it is difficult to reliably distinguish and recognise them. This way, translation rules became a lot simpler, because only a list of feature-value pairs had to be mapped to another list of pairs. The language turned out to be underconstrained. Adding natural sortal constraints to the grammar solved this problem, but also returned the language to a more expressive formalism. The newly created AFF combines elements of QLF and the feature-value list semantics. This version of flat semantics is enhanced with additional functional markings. This together with a relatively small vocabulary solved the ambiguity problem of the original flat representation language without creating overly complex rules. In addition, the syntactic structures are treated carefully by a compromise of linguistic and engineering traditions. The grammars are in fact retrieved from linguistically motivated resource, using corpus-based methods. They are driven by small sets of examples. This results in simpler and flatter domain-specific grammars. The semantics are less sophisticated and represent a minimal approach in the engineering tradition. Each lexical item contributes a set of feature-value pairs. This leads to simple-to-write translation rules. There are only lists of features-value pairs to map to other feature-value pairs. However, as a result the machine translation channel model becomes underspecified and is weakened, whereas the target language model is strengthened. An intelligent help module is integrated into the system to support users in utilising the full coverage of the grammars. This tool provides the user with examples as close as possible to the users original utterance. The output is based on a library. Each sub-domain and language pair has its own library. The contents are extracted from the combined interlingua corpora. The help module scans the corpus for the tagged source language form mapped with the corresponding target language form. Additionally a second statistical recogniser is used as backup. The results are used to select similar examples from the library. According to the generation preferences, one of the derived strings is picked and the target language string is realised as spoken language. Some statistical corpus based meth
Read more →
ShareMethods

ShareMethods is a Web 2.0 document management and collaboration service with a focus on sales, marketing, and the extended selling network. It offers a software as a service (SaaS) subscription to companies and is available as a stand-alone application or as an integrated program with CRM tools such as Oracle CRM On Demand or salesforce.com. == History == ShareMethods was launched in 2004 to provide collaboration and communication services for sales and marketing teams, business partners, and customers. The founders have a background of building software-as-a-service applications and creating digital media applications. In September 2005, ShareMethods launched "ShareNow" as one of the first applications on the salesforce.com AppExchange. In September 2006, ShareMethods moved its operations into a SAS 70 Type II data center owned by SunGard. In March 2009, ShareMethods launched "ShareSpaces" to provide on-demand portals or workspaces. In 2013, ShareMethods announced that its platform is available in a private cloud (on-premises) version. == Products == ShareMethods: Combines document management, collaboration, analytics, and CRM integration into a single solution. Key content can be centrally managed and delivered to sales channels, while providing feedback to marketing. ShareMethods is often used as a sales portal for internal sales and a partner portal for external partners. ShareNow: Integrates ShareMethods with salesforce.com providing Single Sign On for salesforce.com users and access to files related to accounts opportunities, etc. including custom objects. Also facilitates collaboration between salesforce.com users and non-users. ShareMethods for Oracle CRM On Demand: Integrates ShareMethods with Oracle CRM On Demand providing Single Sign On for Oracle users and easy access to files related to accounts opportunities, etc. ShareOffice: An on-demand intranet/extranet solution. Features include full-text search, version history, server sync-up, email updates, audit trail/analytics, check-in/check-out, multilingual user interface. ShareSpaces: Independent workspaces or portals where users can collaborate with business partners, teammates, or individuals to work together on content and documents. == Integration and interoperability == ShareMethods is available on Salesforce.com's AppExchange platform. ShareMethods also integrates with Oracle CRM On Demand to provide document management within the CRM application. Customers also can integrate proprietary systems via single-sign-on and self-registration. In addition, developers can make use of the ShareMethods API based on WebDAV to integrate document management functionality.
Read more →
Ω-automaton

In automata theory, a branch of theoretical computer science, an ω-automaton (or stream automaton) is a variation of a finite automaton that runs on infinite, rather than finite, strings as input. Since ω-automata do not stop, they have a variety of acceptance conditions rather than simply a set of accepting states. ω-automata are useful for specifying behavior of systems that are not expected to terminate, such as hardware, operating systems and control systems. For such systems, one may want to specify a property such as "for every request, an acknowledge eventually follows", or its negation "there is a request that is not followed by an acknowledge". The former is a property of infinite words: one cannot say of a finite sequence that it satisfies this property. Classes of ω-automata include the Büchi automata, Rabin automata, Streett automata, parity automata and Muller automata, each deterministic or non-deterministic. These classes of ω-automata differ only in terms of acceptance condition. They all recognize precisely the regular ω-languages except for the deterministic Büchi automata, which is strictly weaker than all the others. Although all these types of automata recognize the same set of ω-languages, they nonetheless differ in succinctness of representation for a given ω-language. == Deterministic ω-automata == Formally, a deterministic ω-automaton is a tuple A = ( Q , Σ , δ , q 0 , A a c c ) {\textstyle A=(Q,\Sigma ,\delta ,q_{0},A_{acc})} , that consists of the following components: Q {\textstyle Q} , is a finite set. The elements of Q {\textstyle Q} are called the states of A {\textstyle A} . Σ {\textstyle \Sigma } , is a finite set called the alphabet of A {\textstyle A} . δ : Q × Σ → Q {\textstyle \delta \colon Q\times \Sigma \rightarrow Q} is a function, called the transition function of A {\textstyle A} . Q 0 {\textstyle Q_{0}} is an element of Q {\textstyle Q} , called the initial state. A a c c {\textstyle A_{acc}} is a set of accepting states of A {\textstyle A} , formally a subset of Q ω {\textstyle Q^{\omega }} . An input for A {\textstyle A} is an infinite string over the alphabet Σ {\textstyle \Sigma } , i.e. it is an infinite sequence α = ( a 1 , a 2 , a 3 , … ) {\textstyle \alpha =(a_{1},a_{2},a_{3},\ldots )} . The run of A {\textstyle A} on such an input is an infinite sequence ρ = ( r 0 , r 1 , r 2 , … ) {\textstyle \rho =(r_{0},r_{1},r_{2},\ldots )} of states, defined as follows: r 0 = q 0 {\textstyle r_{0}=q_{0}} . r 1 = δ ( r 0 , a 1 ) {\textstyle r_{1}=\delta (r_{0},a_{1})} . r 2 = δ ( r 1 , a 2 ) {\textstyle r_{2}=\delta (r_{1},a_{2})} . ... that is, for every i {\textstyle i} : r i = δ ( r i − 1 , a i ) {\textstyle r_{i}=\delta (r_{i-1},a_{i})} . The main purpose of an ω-automaton is to define a subset of the set of all inputs: The set of accepted inputs. Whereas in the case of an ordinary finite automaton every run ends with a state r n {\textstyle r_{n}} and the input is accepted if and only if r n {\textstyle r_{n}} is an accepting state, the definition of the set of accepted inputs is more complicated for ω-automata. Here we must look at the entire run ρ {\textstyle \rho } . The input is accepted if the corresponding run is in Acc {\textstyle {\text{Acc}}} . The set of accepted input ω-words is called the recognized ω-language by the automaton, which is denoted as L ( A ) {\textstyle L(A)} . The definition of Acc {\textstyle {\text{Acc}}} as a subset of Q ω {\textstyle Q^{\omega }} is purely formal and not suitable for practice because normally such sets are infinite. The difference between various types of ω-automata (Büchi, Rabin etc.) consists in how they encode certain subsets Acc {\textstyle {\text{Acc}}} of Q ω {\textstyle Q^{\omega }} as finite sets, and therefore in which such subsets they can encode. == Nondeterministic ω-automata == Formally, a nondeterministic ω-automaton is a tuple A = ( Q , Σ , Δ , Q 0 , Acc ) {\textstyle A=(Q,\Sigma ,\Delta ,Q_{0},{\text{Acc}})} that consists of the following components: Q {\textstyle Q} is a finite set. The elements of Q {\textstyle Q} are called the states of A {\textstyle A} . Σ {\textstyle \Sigma } is a finite set called the alphabet of A {\textstyle A} . Δ {\textstyle \Delta } is a subset of Q × Σ × Q {\textstyle Q\times \Sigma \times Q} and is called the transition relation of A {\textstyle A} . Q 0 {\textstyle Q_{0}} is a subset of Q {\textstyle Q} , called the initial set of states. Acc {\textstyle {\text{Acc}}} is the acceptance condition, a subset of Q ω {\textstyle Q^{\omega }} . Unlike a deterministic ω-automaton, which has a transition function δ {\textstyle \delta } , the non-deterministic version has a transition relation Δ {\textstyle \Delta } . Note that Δ {\textstyle \Delta } can be regarded as a function Q × Σ → P ( Q ) {\textstyle Q\times \Sigma \rightarrow {\mathcal {P}}(Q)} from Q × Σ {\textstyle Q\times \Sigma } to the power set P ( Q ) {\textstyle {\mathcal {P}}(Q)} . Thus, given a state q n {\textstyle q_{n}} and a symbol a n {\textstyle a_{n}} , the next state q n + 1 {\textstyle q_{n+1}} is not necessarily determined uniquely, rather there is a set of possible next states. A run of A {\textstyle A} on the input α = ( a 1 , a 2 , a 3 , … ) {\textstyle \alpha =(a_{1},a_{2},a_{3},\ldots )} is any infinite sequence ρ = ( r 0 , r 1 , r 2 , … ) {\textstyle \rho =(r_{0},r_{1},r_{2},\ldots )} of states that satisfies the following conditions: r 0 {\textstyle r_{0}} is an element of Q 0 {\textstyle Q_{0}} . r 1 {\textstyle r_{1}} is an element of Δ ( r 0 , a 1 ) {\textstyle \Delta (r_{0},a_{1})} . r 2 {\textstyle r_{2}} is an element of Δ ( r 1 , a 2 ) {\textstyle \Delta (r_{1},a_{2})} . ... that is, for every i {\textstyle i} : r i {\textstyle r_{i}} is an element of Δ ( r i − 1 , a i ) {\textstyle \Delta (r_{i-1},a_{i})} . A nondeterministic ω-automaton may admit many different runs on any given input, or none at all. The input is accepted if at least one of the possible runs is accepting. Whether a run is accepting depends only on Acc {\textstyle {\text{Acc}}} , as for deterministic ω-automata. Every deterministic ω-automaton can be regarded as a nondeterministic ω-automaton by taking Δ {\textstyle \Delta } to be the graph of δ {\textstyle \delta } . The definitions of runs and acceptance for deterministic ω-automata are then special cases of the nondeterministic cases. == Acceptance conditions == Acceptance conditions may be infinite sets of ω-words. However, people mostly study acceptance conditions that are finitely representable. The following lists a variety of popular acceptance conditions. Before discussing the list, let's make the following observation. In the case of infinitely running systems, one is often interested in whether certain behavior is repeated infinitely often. For example, if a network card receives infinitely many ping requests, then it may fail to respond to some of the requests but should respond to an infinite subset of received ping requests. This motivates the following definition: For any run ρ {\textstyle \rho } , let Inf ( ρ ) {\textstyle {\text{Inf}}(\rho )} be the set of states that occur infinitely often in ρ {\textstyle \rho } . This notion of certain states being visited infinitely often will be helpful in defining the following acceptance conditions. A Büchi automaton is an ω-automaton A {\textstyle A} that uses the following acceptance condition, for some subset F {\textstyle F} of Q {\textstyle Q} : Büchi condition A {\textstyle A} accepts exactly those runs ρ {\textstyle \rho } for which Inf ( ρ ) ∩ F ≠ ∅ {\textstyle {\text{Inf}}(\rho )\cap F\neq \emptyset } , i.e. there is an accepting state that occurs infinitely often in ρ {\textstyle \rho } . A Rabin automaton is an ω-automaton A {\textstyle A} that uses the following acceptance condition, for some set Ω {\textstyle \Omega } of pairs ( B i , G i ) {\textstyle (B_{i},G_{i})} of sets of states: Rabin condition A {\textstyle A} accepts exactly those runs ρ {\textstyle \rho } for which there exists a pair ( B i , G i ) {\textstyle (B_{i},G_{i})} in Ω {\textstyle \Omega } such that B i ∩ Inf ( ρ ) = ∅ {\textstyle B_{i}\cap {\text{Inf}}(\rho )=\emptyset } and G i ∩ Inf ( ρ ) ≠ ∅ {\textstyle G_{i}\cap {\text{Inf}}(\rho )\neq \emptyset } . A Streett automaton is an ω-automaton A {\textstyle A} that uses the following acceptance condition, for some set Ω {\textstyle \Omega } of pairs ( B i , G i ) {\textstyle (B_{i},G_{i})} of sets of states: Streett condition A {\textstyle A} accepts exactly those runs ρ {\textstyle \rho } such that for all pairs ( B i , G i ) {\textstyle (B_{i},G_{i})} in Ω {\textstyle \Omega } , B i ∩ Inf ( ρ ) ≠ ∅ {\textstyle B_{i}\cap {\text{Inf}}(\rho )\neq \emptyset } or G i ∩ Inf ( ρ ) = ∅ {\textstyle G_{i}\cap {\text{Inf}}(\rho )=\emptyset } . A parity automaton is an automaton A {\textstyle A} whose set of states is Q = { 0 , 1 , 2 , … , k } {\textstyle Q=\{0,1,2,\ldots ,k\}} for some natural number k {\textst
Read more →
FastText

fastText is a library for learning of word embeddings and text classification created by Facebook's AI Research (FAIR) lab. The model allows one to create an unsupervised learning or supervised learning algorithm for obtaining vector representations for words. Facebook makes available pretrained models for 294 languages. Several papers describe the techniques used by fastText. The GitHub repository was archived on March 19, 2024.
Read more →
Best AI Bug Finders in 2026

In search of the best AI bug finder? An AI bug finder is software that uses machine learning to help you get more done — it turns a rough idea into a polished result in seconds. When choosing one, weigh output quality, pricing, export formats, and how well it fits the tools you already use. Whether you are a beginner or a pro, the right AI bug finder slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.
Read more →
The Outliner of Giants

The Outliner of Giants was commercial outlining software. Like other outliners, it allowed the user to create a document consisting of a series of nested lists. It was one of a number of browser-based outliners that are delivered as a web application, used through a web browser, rather than being installed as a stand-alone application. The Outliner of Giants was released in 2009. The service was shut down on December 31, 2017 and only exports are allowed at this time. == Feature set == Unlike most other browser-based outliners - which often focus on providing a minimum viable product - the Outliner of Giants had much of the functionality typically associated with a desktop outliner, such as the ability to use of columns to structure information. However, The Outliner of Giants did not support offline editing, requiring an active internet connection in order to make changes to an outline document. === Outlining === Like all outliners, The Outliner of Giants supported the creation of a hierarchy of items, with users modifying the parent-child relationship between items in order to structure a document. This included the ability to promote or demote items up or down the hierarchy, or move an item up or down a list of siblings on the same level. The Outliner of Giants did not support the true cloning of items (where an item can appear to be in multiple places within the hierarchy at the same time), although it did support the copying of single or multiple nodes. === Import === The Outliner of Giants could import both plain text and the OPML XML format, which is commonly used to transfer data between outlining applications. === Editing === Outline documents could be edited using a WYSIWYG editor, as well as the Markdown, and Textile markup languages. === Annotation === The Outliner of Giants supported functions to annotate an outline, such as the ability to add colored labels, highlights and text, as well as tags and hashtags. === Collaboration === The Outliner of Giants supported real-time collaboration, where multiple users could edit the same document, and can see the changes made by another user as they happened. === Publication === Outlines created through The Outliner of Giants could be published directly online through the service, either as outlines, pages or in a blog format. === Export === The Outliner of Giants can export outline data as plain text, HTML, as well as directly to the Google Docs word processor.
Read more →
AI Sales Assistants: Free vs Paid (2026)

Trying to pick the best AI sales assistant? An AI sales assistant is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI sales assistant slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
Read more →
Top 10 AI Headshot Generators Compared (2026)

Trying to pick the best AI headshot generator? An AI headshot generator is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI headshot generator slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
Read more →