AI Detector No Character Limit

AI Detector No Character Limit — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

EnQuire

Enquire is a web-based software application used as a platform for project, contract and grant management, as well as reporting and planning. Initially designed for the specific business requirements of the Australian Government, Queensland Government and Queensland Regional Bodies to manage natural resource projects, Enquire has since seen adoption outside of this industry and user segment. The use of Enquire by Natural Resource Management bodies within Queensland has been cited as a reason for the improved efficiency, quantity and quality of reporting. Technically, Enquire is implemented as a Java application built on a MySQL database. Enquire is hosted and supported under the software as a service model by Tactiv Pty Ltd. == History == The system was first released in 2005 under the name ViSTA NRM Online, proactively changing its name to Enquire in 2007 to avoid possible confusion with Windows Vista, which was being released at the time. In 2012, the Enquire project and support team was commercialized as its own company called Tactiv Pty Ltd. Tactiv is based predominantly in Brisbane, Australia. Tactiv has continued to develop and grow the Enquire Grant, Contract and Project management solution, releasing a new platform in 2017. Since commercialization, Tactiv has grown its client base to include government and non-government organizations such as foundations and not-for-profit organizations. == Functionality == The functionality of Enquire can be broken down into 5 key lifecycle solutions, all fully integrated and supported by over 40 feature rich and configurable modules: Grant Management Contract Management Project Portfolio Management Procurement Management Relationship Management The system provides its platform to meet the needs of "off the shelf" customers looking for a ready to use best practice option as well as a fully configurable option for specific requirements. The system offers a client supplier portal for external applicants or suppliers, a management portal for internal team usage and an administration portal for clients to manage access, roles, information, and other configurations. Key functional modules include: Online authoring and publishing for forms and applications Workflows Project Tracking Performance Reporting Financial Reporting Stakeholder Communication Budget management Document Management Milestone tracking Payments and Variations Management KPI tracking and Impact reporting The Enquire system is used to report against the Queensland Government's Q2 Coast and Country Program and parts of the Australian Government's Caring for our Country program. There is also a strategic planning module, which provides functionality to manage core-business administration and reporting requirements, whilst providing visibility of key activities and their alignment against organizational goals and strategic objectives. The systems architecture supports a range of implementation models with the capacity to manage one-to-one, one-to-many and many-to-many relationships between investors and investees. Under the usage model within Queensland, Regional Bodies use Enquire to load project contracts and report against these online. The regional bodies also record output, target and financial information in Enquire, which can then be used for operational purposes including financial, performance and target reporting. == External Audit == The Australian National Audit Office Audit Report No.21 2007–08 undertook a case study on Enquire. It noted: "The Queensland Department of Environment and Resource Management has developed the first integrated web-based system [Enquire] to manage performance information about Natural Resource Management activities in Queensland." Four of Queensland's 14 regional bodies commented on Enquire through the ANAO's survey. These four regional bodies indicated that Enquire offers a means of consistent reporting at the State level.
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Sinkov statistic

Sinkov statistics, also known as log-weight statistics, is a specialized field of statistics that was developed by Abraham Sinkov, while working for the small Signal Intelligence Service organization, the primary mission of which was to compile codes and ciphers for use by the U.S. Army. The mathematics involved include modular arithmetic, a bit of number theory, some linear algebra of two dimensions with matrices, some combinatorics, and a little statistics. Sinkov did not explain the theoretical underpinnings of his statistics, or characterized its distribution, nor did he give a decision procedure for accepting or rejecting candidate plaintexts on the basis of their S1 scores. The situation becomes more difficult when comparing strings of different lengths because Sinkov does not explain how the distribution of his statistics changes with length, especially when applied to higher-order grams. As for how to accept or reject a candidate plaintext, Sinkov simply said to try all possibilities and to pick the one with the highest S1 value. Although the procedure works for some applications, it is inadequate for applications that require on-line decisions. Furthermore, it is desirable to have a meaningful interpretation of the S1 values.
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The Best Free AI Headshot Generator for Beginners

Shopping for the best AI headshot generator? An AI headshot generator is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI headshot generator slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
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Top 10 AI Chatbots Compared (2026)

Shopping for the best AI chatbot? An AI chatbot is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI chatbot slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.
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GitHub Codespaces

GitHub Codespaces is a cloud-based online integrated development environment developed by GitHub. It allows users to create and manage development environments directly within the browser or through Visual Studio Code desktop. Codespaces is tightly integrated with GitHub repositories and enables on-demand coding, debugging, and testing in a full-featured development container hosted in the cloud. == Features == Instant development environments integrated with GitHub Browser-based and desktop access via Visual Studio Code Configurable Dockerfile or devcontainer.json environments Built-in support for GitHub Copilot, extensions, snippets, and SSH. == Licensing == GitHub Codespaces is proprietary software and available to GitHub users under various subscription plans. Codespaces includes a monthly usage quota for free tier users of 120 hours, and expanded access for GitHub education, Pro, Team, and GitHub Enterprise plans. == GitHub Classroom == GitHub Classroom is an educational tool developed by GitHub to streamline the process of managing programming assignments and coursework. Integrated with GitHub repositories, it allows instructors to distribute starter code, automate grading workflows, and track student progress. GitHub Classroom is widely used in computer science education and supports integration with GitHub Codespaces for cloud-based development environments. == Programming languages supported == == Extensions == Some of the popular extensions include:
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Co-Büchi automaton

In automata theory, a co-Büchi automaton is a variant of Büchi automaton. The only difference is the accepting condition: a Co-Büchi automaton accepts an infinite word w {\displaystyle w} if there exists a run, such that all the states occurring infinitely often in the run are in the final state set F {\displaystyle F} . In contrast, a Büchi automaton accepts a word w {\displaystyle w} if there exists a run, such that at least one state occurring infinitely often in the final state set F {\displaystyle F} . (Deterministic) Co-Büchi automata are strictly weaker than (nondeterministic) Büchi automata. == Formal definition == Formally, a deterministic co-Büchi automaton is a tuple A = ( Q , Σ , δ , q 0 , F ) {\displaystyle {\mathcal {A}}=(Q,\Sigma ,\delta ,q_{0},F)} that consists of the following components: Q {\displaystyle Q} is a finite set. The elements of Q {\displaystyle Q} are called the states of A {\displaystyle {\mathcal {A}}} . Σ {\displaystyle \Sigma } is a finite set called the alphabet of A {\displaystyle {\mathcal {A}}} . δ : Q × Σ → Q {\displaystyle \delta :Q\times \Sigma \rightarrow Q} is the transition function of A {\displaystyle {\mathcal {A}}} . q 0 {\displaystyle q_{0}} is an element of Q {\displaystyle Q} , called the initial state. F ⊆ Q {\displaystyle F\subseteq Q} is the final state set. A {\displaystyle {\mathcal {A}}} accepts exactly those words w {\displaystyle w} with the run ρ ( w ) {\displaystyle \rho (w)} , in which all of the infinitely often occurring states in ρ ( w ) {\displaystyle \rho (w)} are in F {\displaystyle F} . In a non-deterministic co-Büchi automaton, the transition function δ {\displaystyle \delta } is replaced with a transition relation Δ {\displaystyle \Delta } . The initial state q 0 {\displaystyle q_{0}} is replaced with an initial state set Q 0 {\displaystyle Q_{0}} . Generally, the term co-Büchi automaton refers to the non-deterministic co-Büchi automaton. For more comprehensive formalism see also ω-automaton. == Acceptance Condition == The acceptance condition of a co-Büchi automaton is formally ∃ i ∀ j : j ≥ i ρ ( w j ) ∈ F . {\displaystyle \exists i\forall j:\;j\geq i\quad \rho (w_{j})\in F.} The Büchi acceptance condition is the complement of the co-Büchi acceptance condition: ∀ i ∃ j : j ≥ i ρ ( w j ) ∈ F . {\displaystyle \forall i\exists j:\;j\geq i\quad \rho (w_{j})\in F.} == Properties == Co-Büchi automata are closed under union, intersection, projection and determinization.
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Is an AI Content Generator Worth It in 2026?

Trying to pick the best AI content generator? An AI content 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 content generator slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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Mona Diab

Mona Talat Diab (Arabic: منى طلعت دياب) is a computer science professor and director of Carnegie Mellon University's Language Technologies Institute. Previously, she was a professor at George Washington University and a research scientist with Facebook AI. Her research focuses on natural language processing, computational linguistics, cross lingual/multilingual processing, computational socio-pragmatics, Arabic language processing, and applied machine learning. == Education == Diab completed her M.Sc. in computer science with a major in machine learning and artificial intelligence at The George Washington University (1997) and her Ph.D. in computational linguistics at the University of Maryland, Linguistics Department and University of Maryland Institute for Advanced Computer Studies (UMIACS) in 2003, under the supervision of Philip Resnik. She was also a postdoctoral research scientist at Stanford University (2003–2005) under the mentorship of Dan Jurafsky, where she was a part of the Stanford NLP Group. == Career == After her postdoc at Stanford, Diab took a position as research scientist (principal investigator) at the Center for Computational Learning Systems (CCLS) in Columbia University, where she was also adjunct professor in the computer science department. In 2013 she joined the George Washington University as an associate professor, where she was promoted to full professor in 2017. Diab is the founder and director of the GW NLP lab CARE4Lang. Diab served as an elected faculty senator at Columbia University for 6 years (2007–2012) and an elected faculty senator at GW (2013–2014). She served the computational linguistics community as elected member, secretary and president of ACL SIGLEX (2005–2016) and elected president of ACL SIGSemitic. She currently serves as the elected VP-elect for ACL SIGDAT. In 2017 Diab joined Amazon AWS AI Deep Learning Group for Human Language Technologies, where she led the AWS Lex project for task oriented dialogue systems for enterprises. A couple of years later, she moved to Facebook AI as a research scientist. In the fall of 2023, she became the director of CMU's Language Technologies Institute -- the first full time director since the passing of its founder Jaime Carbonell. == Research == Diab's research interests include several areas in computational linguistics/natural language processing, like conversational AI, computational lexical semantics, multilingual and cross lingual processing, social media processing with an emphasis on computational socio- pragmatics, information extraction & text analytics, machine translation. Besides this, she also has special interests in Arabic NLP and low resource scenarios. Diab co-established two research trends in the computational linguistics field, computational approaches to linguistic code switching in 2007 and semantic textual similarity in 2010. Diab together with Nizar Habash and Owen Rambow, co-founded CADIM in 2005, a global reference point in Arabic dialect processing. In 2012, Diab together with Eneko Agirre and Johan Bos, brought together two ACL communities SIGLEX and SIGSEM and established the 1st tier conference SEM. == Awards and recognition == Selected as one of top 150 leaders and visionaries in AI nationwide to participate in White House AI Summit in Government, Washington, D.C., US, September 2019 March 2017: 3 Muslim Women in STEM You Should Know About, Teen Vogue, March 2017 May 2017: Behind Every Strong Woman Is...Another Strong Woman: Ten women give thanks to the women who supported them on the way up. Elle, May 2017. Google Faculty Research Award – Tharwa++: Building a multidialectal Arabic Lexical Repository, (PI), 09.2015 –12.2016. Google Faculty Research Award – Nuanced Sentiment and Perspective Analysis for Arabic Social Media Text, (PI), 12.2014 –12.2015 QNRF Best Poster Award – Ossama Obeid, Houda Bouamor, Wajdi Zaghouani, Mahmoud Ghoneim, Abdelati Hawwari, Mona Diab, Kemal Oflazer. (2016) MANDIAC: A Web-based Annotation System For Manual Arabic Diacritization. Proceedings of the 2nd Workshop on Arabic Corpora and Processing Tools, LREC 2016. Best Paper Award – Aminian, Maryam, Mahmoud Ghoneim, Mona Diab. (2015) Unsupervised False Friend Disambiguation Using Contextual Word Clusters and Parallel Word Alignments. In Proceedings of Workshop 9th Semantics Syntax Statistical Translation, NAACL 2015, Denver CO, US. == Publications == Diab has over 250 publications, and she is an acting editor for several scientific journals. === Selected publications === Semeval-2012 task 6: A pilot on semantic textual similarity. E. Agirre, D. Cer, M. Diab, A. Gonzalez-Agirre. SEM 2012: The First Joint Conference on Lexical and Computational Semantics–Volume 1: Proceedings of the main conference and the shared task, and Volume 2: Proceedings of the Sixth International Workshop on Semantic Evaluation (SemEval 2012) Predictive linguistic features of schizophrenia. ES Kayi, M Diab, L Pauselli, M Compton, G Coppersmith. arXiv preprint arXiv:1810.09377 Ideological perspective detection using semantic features. H Elfardy, M Diab, C Callison-Burch – Proceedings of SEM 2015 DeSePtion: Dual sequence prediction and adversarial examples for improved fact-checking. Christopher Hidey, Tuhin Chakrabarty, Tariq Alhindi, Siddharth Varia, Kriste Krstovski, Mona Diab, Smaranda Muresan, 2020 Does Causal Coherence Predict Online Spread of Social Media? Pedram Hosseini, Mona Diab, David A Broniatowski. Proceedings of International Conference on Social Computing, Behavioral-Cultural Modeling and Prediction and Behavior Representation in Modeling and Simulation, 2019. Diversity, Density, and Homogeneity: Quantitative Characteristic Metrics for Text Collections. YA Lai, X Zhu, Y Zhang, M Diab, arXiv preprint arXiv:2003.08529, 2020 Readability of written medicine information materials in Arabic language: expert and consumer evaluation. S Al Aqeel, N Abanmy, A Aldayel, H Al-Khalifa, M Al-Yahya, M Diab. BMC health services research 18 (1), 1–7, 2019 Unsupervised word mapping using structural similarities in monolingual embeddings. H Aldarmaki, M Mohan, M Diab – Transactions of the Association for Computational Linguistics, 2018 An unsupervised method for word sense tagging using parallel corpora M Diab, P Resnik. Proceedings of ACL 2002 Overview for the first shared task on language identification in code-switched data. Thamar Solorio, Elizabeth Blair, Suraj Maharjan, Steven Bethard, Mona Diab, Mahmoud Ghoneim, Abdelati Hawwari, Fahad AlGhamdi, Julia Hirschberg, Alison Chang, Pascale Fung. Proceedings of the First Workshop on Computational Approaches to Code Switching, 2014 Modeling sentences in the latent space. W Guo, M Diab – ACL 20 12 Task-based evaluation of multiword expressions: a pilot study in statistical machine translation. M Carpuat, M Diab – NAACL-HLT 2010 Rumor detection and classification for twitter data. S Hamidian, MT Diab – arXiv preprint arXiv:1912.08926, 2019 Subgroup detection in ideological discussions. A Abu-Jbara, P Dasigi, M Diab, D Radev – ACL 2012 Madamira: A fast, comprehensive tool for morphological analysis and disambiguation of arabic. A. Pasha, M. Al-Badrashiny, M. Diab, A. El Kholy, R. Eskander, N. Habash, M. Pooleery, O. Rambow, R. Roth. LREC 14, 1094–1101. 2014 Context-Aware Self-Attentive Natural Language Understanding for Task-Oriented Chatbots. A. Gupta, P. Zhang, G. Lalwani, M. Diab. EMNLP 2019 A multitask learning approach for diacritic restoration. S. Alqahtani, A. Mishra, M. Diab. ACL 2020
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Confusion network

A confusion network (sometimes called a word confusion network or informally known as a sausage) is a natural language processing method that combines outputs from multiple automatic speech recognition or machine translation systems. Confusion networks are simple linear directed acyclic graphs with the property that each a path from the start node to the end node goes through all the other nodes. The set of words represented by edges between two nodes is called a confusion set. In machine translation, the defining characteristic of confusion networks is that they allow multiple ambiguous inputs, deferring committal translation decisions until later stages of processing. This approach is used in the open source machine translation software Moses and the proprietary translation API in IBM Bluemix Watson.
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Janyce Wiebe

Janyce Marbury Wiebe (1959–2018) was an American computer science specializing in natural language processing and known for her work on subjectivity, sentiment analysis, opinion mining, discourse processing, and word-sense disambiguation. == Early life and education == Wiebe was born in 1959, in Albany, New York. She majored in English at the Binghamton University, graduating in 1981, and completed a Ph.D. in computer science in 1990, at the University at Buffalo. Her dissertation, Recognizing Subjective Sentences: A Computational Investigation of Narrative Text, was supervised by philosopher William J. Rapaport. == Career == After postdoctoral research at the University of Toronto, she became an assistant professor at New Mexico State University in 1992. In 2000, she moved to the University of Pittsburgh, where she became a professor of computer science and director of the Intelligent Systems Program. == Recognition == Wiebe was named a Fellow of the Association for Computational Linguistics in 2015. == Death == She died of leukemia on December 10, 2018.
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Karen Spärck Jones

Karen Ida Boalth Spärck Jones (26 August 1935 – 4 April 2007) was a self-taught programmer and a pioneering British computer and information scientist responsible for the concept of inverse document frequency (IDF), a technology that underlies most modern search engines. She was an advocate for women in computer science, her slogan being, "Computing is too important to be left to men." In 2019, The New York Times published her belated obituary in its series Overlooked, calling her "a pioneer of computer science for work combining statistics and linguistics, and an advocate for women in the field." From 2008, to recognise her achievements in the fields of information retrieval (IR) and natural language processing (NLP), the Karen Spärck Jones Award is awarded annually to a recipient for outstanding research in one or both of her fields. == Early life and education == Karen Ida Boalth Spärck Jones was born in Huddersfield, Yorkshire, England. Her parents were Alfred Owen Jones, a chemistry lecturer, and Ida Spärck, a Norwegian who worked for the Norwegian government while in exile in London during World War II. Spärck Jones was educated at a grammar school in Huddersfield and then from 1953 to 1956 at Girton College, Cambridge, studying history, with an additional final year in Moral Sciences (philosophy). While at Cambridge, Spärck Jones joined the organisation known as the Cambridge Language Research Unit (CLRU) and met the head of CLRU Margaret Masterman, who would inspire her to go into computer science. While working at the CLRU, Spärck Jones began pursuing her PhD. At the time of submission, her PhD thesis was cast aside as uninspired and lacking original thought, but was later published in its entirety as a book. She briefly became a school teacher before moving into computer science. Spärck Jones married fellow Cambridge computer scientist Roger Needham in 1958. Spärck Jones's mother, Ida Spärck, had fled Norway on one of the last boats out after the German invasion in April 1940, going on to serve the Norwegian government in exile in London throughout the war. This background of displacement and resilience shaped the household in which Spärck Jones grew up. She later kept her mother's Norwegian surname professionally after marrying, stating that "it maintains a permanent existence of your own." Spärck Jones described her entry into computing as almost accidental. She had been working as a schoolteacher when she began visiting the CLRU out of curiosity about her husband's work. It was Margaret Masterman — whom she later described as "a very strange and interesting woman" — who offered her a research position and drew her fully into the field. == Career == Spärck Jones worked at the Cambridge Language Research Unit from the late 1950s, then at Cambridge University Computer Laboratory from 1974 until her retirement in 2002. From 1999, she held the post of Professor of Computers and Information. She had been given a permanent position only in 1993, and earlier in her career had been employed on a series of short-term contracts. She continued to work in the Computer Laboratory until shortly before her death. Her publications include nine books and numerous papers. A full list of her publications is available from the Cambridge Computer Laboratory. Spärck Jones' main research interests, since the late 1950s, were natural language processing and information retrieval. In 1964, Spärck Jones published "Synonymy and Semantic Classification", which is now seen as a foundational paper in the field of natural language processing. One of her most important contributions was the concept of inverse document frequency (IDF) weighting in information retrieval, which she introduced in a 1972 paper. IDF is used in most search engines today, usually as part of the term frequency–inverse document frequency (TF–IDF) weighting scheme. In the 1980s, Spärck Jones began her work on early speech recognition systems. In 1982 she became involved in the Alvey Programme which was an initiative to motivate more computer science research across the country. == Significance of inverse document frequency == At the time Spärck Jones was working, most computer scientists were focused on making people adapt to machines — learning precise codes and commands to retrieve information. Spärck Jones was working in the opposite direction: teaching computers to understand human language as it is actually used. Her 1972 paper introduced the concept of inverse document frequency (IDF) by observing that not all words carry equal informational value. A word like "the" appears in virtually every document and tells a retrieval system almost nothing about what any specific document is about. A rare word like "photosynthesis," by contrast, is highly specific and informative. IDF assigns each word a statistical weight based on how rarely it occurs across a document collection — the rarer the word, the higher its weight. When combined with term frequency (TF), which measures how often a word appears within a single document, the resulting TF–IDF score gives every word a relevance rating that can be used to rank documents in response to a search query. By 2007, Spärck Jones noted that "pretty much every web engine uses those principles." Her colleague John Tait remarked that "a lot of the stuff she was working on until five or ten years ago seemed like mad nonsense, and now we take it for granted." The 1972 paper remains among the most cited works in information retrieval research, with over 4,500 citations recorded in Google Scholar at the time of her death. The conceptual foundation of TF–IDF — that word meaning is statistical and contextual — has also informed later developments in machine learning and natural language processing, including transformer-based language models such as BERT. == Impact on artificial intelligence == Even though Spärck Jones' views on artificial intelligence (AI) were rather pessimistic in regard to the perceived limitations of AI in information retrieval, her work in natural language processing, information retrieval, and introducing the concept of inverse document frequency (IDF) contributed to the future technological development of AI. Her statistical and ranking methods shifted the direction of the development of AI towards being more expandable and led by data. Her work had a more indirect and conceptual impact on AI, compared to the current and direct impact it has had on search engines. == Gender and advocacy == Spärck Jones spent the majority of her career at Cambridge on short-term contracts without permanent employment, a situation she attributed directly to gender. In her 2001 IEEE oral history interview she stated that Cambridge was "in many ways not user-friendly, in the sense of women-friendly." She was frequently the only woman present in professional meetings throughout her career. She channelled this experience into active advocacy. She was a founding member of the women@cl network at Cambridge's Computer Laboratory, worked on outreach programmes aimed at encouraging girls into computing, and became widely known for her slogan: "Computing is too important to be left to men." She was the first woman ever to receive the BCS Lovelace Medal. === Honours and awards === These include: Gerard Salton Award (1988) Elected a Fellow of Association for the Advancement of Artificial Intelligence (AAAI) in 1993 President of the Association for Computational Linguistics (ACL) in 1994 Honorary degree of Doctor of Science from The City University in 1997. Elected a Fellow of the British Academy (FBA), where she also served as Vice-President in 2000–2002 Fellow of European Association for Artificial Intelligence (ECCAI) Association for Information Science and Technology (ASIS&T) Award of Merit (2002) Association for Computational Linguistics (ACL) Lifetime Achievement Award (2004) ACM - AAAI Allen Newell Award (2006) BCS Lovelace Medal (2007) Association for Computing Machinery (ACM) Women's Group Athena Award (2007) == Death and legacy == Spärck Jones died on 4 April 2007, due to cancer at the age of 71. In 2008, the BCS Information Retrieval Specialist Group (BCS IRSG) in conjunction with the British Computer Society established an annual Karen Spärck Jones Award in her honour, to encourage and promote research that advances understanding of Natural Language Processing or Information Retrieval. The Karen Spärck Jones lecture sponsored by BCS recognises the contribution that women have made to computing. In August 2017, the University of Huddersfield renamed one of its campus buildings in her honour. Formerly known as Canalside West, the Spärck Jones building houses the University's School of Computing and Engineering. When Spärck Jones died in 2007, The Times did not publish an obituary for her, despite having published one for her husband Roger Needham in 2003. In 2019, The New York Times included her in its Overlooked series under the title "Ove
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Thompson's construction

In computer science, Thompson's construction algorithm, also called the McNaughton–Yamada–Thompson algorithm, is a method of transforming a regular expression into an equivalent nondeterministic finite automaton (NFA). This NFA can be used to match strings against the regular expression. This algorithm is credited to Ken Thompson. Regular expressions and nondeterministic finite automata are two representations of formal languages. For instance, text processing utilities use regular expressions to describe advanced search patterns, but NFAs are better suited for execution on a computer. Hence, this algorithm is of practical interest, since it can compile regular expressions into NFAs. From a theoretical point of view, this algorithm is a part of the proof that they both accept exactly the same languages, that is, the regular languages. An NFA can be made deterministic by the powerset construction and then be minimized to get an optimal automaton corresponding to the given regular expression. However, an NFA may also be interpreted directly. To decide whether two given regular expressions describe the same language, each can be converted into an equivalent minimal deterministic finite automaton via Thompson's construction, powerset construction, and DFA minimization. If, and only if, the resulting automata agree up to renaming of states, the regular expressions' languages agree. == The algorithm == The algorithm works recursively by splitting an expression into its constituent subexpressions, from which the NFA will be constructed using a set of rules. More precisely, from a regular expression E, the obtained automaton A with the transition function Δ respects the following properties: A has exactly one initial state q0, which is not accessible from any other state. That is, for any state q and any letter a, Δ ( q , a ) {\displaystyle \Delta (q,a)} does not contain q0. A has exactly one final state qf, which is not co-accessible from any other state. That is, for any letter a, Δ ( q f , a ) = ∅ {\displaystyle \Delta (q_{f},a)=\emptyset } . Let c be the number of concatenation of the regular expression E and let s be the number of symbols apart from parentheses — that is, |, , a and ε. Then, the number of states of A is 2s − c (linear in the size of E). The number of transitions leaving any state is at most two. Since an NFA of m states and at most e transitions from each state can match a string of length n in time O(emn), a Thompson NFA can do pattern matching in linear time, assuming a fixed-size alphabet. === Rules === The following rules are depicted according to Aho et al. (2007), p. 122. In what follows, N(s) and N(t) are the NFA of the subexpressions s and t, respectively. The empty-expression ε is converted to A symbol a of the input alphabet is converted to The union expression s|t is converted to State q goes via ε either to the initial state of N(s) or N(t). Their final states become intermediate states of the whole NFA and merge via two ε-transitions into the final state of the NFA. The concatenation expression st is converted to The initial state of N(s) is the initial state of the whole NFA. The final state of N(s) becomes the initial state of N(t). The final state of N(t) is the final state of the whole NFA. The Kleene star expression s is converted to An ε-transition connects initial and final state of the NFA with the sub-NFA N(s) in between. Another ε-transition from the inner final to the inner initial state of N(s) allows for repetition of expression s according to the star operator. The parenthesized expression (s) is converted to N(s) itself. With these rules, using the empty expression and symbol rules as base cases, it is possible to prove with structural induction that any regular expression may be converted into an equivalent NFA. == Example == Two examples are now given, a small informal one with the result, and a bigger with a step by step application of the algorithm. === Small Example === The picture below shows the result of Thompson's construction on (ε|ab). The purple oval corresponds to a, the teal oval corresponds to a, the green oval corresponds to b, the orange oval corresponds to ab, and the blue oval corresponds to ε. === Application of the algorithm === As an example, the picture shows the result of Thompson's construction algorithm on the regular expression (0|(1(01(00)0)1)) that denotes the set of binary numbers that are multiples of 3: { ε, "0", "00", "11", "000", "011", "110", "0000", "0011", "0110", "1001", "1100", "1111", "00000", ... }. The upper right part shows the logical structure (syntax tree) of the expression, with "." denoting concatenation (assumed to have variable arity); subexpressions are named a-q for reference purposes. The left part shows the nondeterministic finite automaton resulting from Thompson's algorithm, with the entry and exit state of each subexpression colored in magenta and cyan, respectively. An ε as transition label is omitted for clarity — unlabelled transitions are in fact ε transitions. The entry and exit state corresponding to the root expression q is the start and accept state of the automaton, respectively. The algorithm's steps are as follows: An equivalent minimal deterministic automaton is shown below. == Relation to other algorithms == Thompson's is one of several algorithms for constructing NFAs from regular expressions; an earlier algorithm was given by McNaughton and Yamada. Converse to Thompson's construction, Kleene's algorithm transforms a finite automaton into a regular expression. Glushkov's construction algorithm is similar to Thompson's construction, once the ε-transitions are removed. == Use in string pattern matching == Regular expressions are often used to specify patterns that software is then asked to match. Generating an NFA by Thompson's construction, and using an appropriate algorithm to simulate it, it is possible to create pattern-matching software with performance that is ⁠ O ( m n ) {\displaystyle O(mn)} ⁠, where m is the length of the regular expression and n is the length of the string being matched. This is much better than is achieved by many popular programming-language implementations; however, it is restricted to purely regular expressions and does not support patterns for non-regular languages like backreferences.
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Sample (graphics)

In computer graphics, a sample is an intersection of a channel and a pixel. The diagram below depicts a 24-bit pixel, consisting of 3 samples for Red, Green, and Blue. In this particular diagram, the Red sample occupies 9 bits, the Green sample occupies 7 bits and the Blue sample occupies 8 bits, totaling 24 bits per pixel. Note that the samples do not have to be equal size and not all samples are mandatory in a pixel. Also, a pixel can consist of more than 3 samples (e.g. 4 samples of the RGBA color space). A sample is related to a subpixel on a physical display.
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AI Paragraph Rewriters: Free vs Paid (2026)

Curious about the best AI paragraph rewriter? An AI paragraph rewriter 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 paragraph rewriter slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.
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Best AI Voice Assistants in 2026

Trying to pick the best AI voice assistant? An AI voice 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 voice assistant slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
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