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AI Cv Keywords — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Oculus Medium

    Oculus Medium

    Oculus Medium is a digital sculpting software that works with virtual reality headsets and 6DoF motion controllers. It is used to create and paint digital sculptures. Medium works only on Oculus Rift. It was released on December 5, 2016, following with a major update in 2018 introducing new features and a revamped UI. On December 9, 2019, Oculus Medium was acquired by Adobe and re-named to "Medium by Adobe".

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  • Madhan Karky

    Madhan Karky

    Madhan Karky Vairamuthu is an Indian lyricist, screenwriter, research associate, software engineer, and entrepreneur. A holder of a doctorate in computer science from the University of Queensland, Karky began his professional career as an assistant professor at the College of Engineering, Guindy, and soon after ventured into the Tamil cinema, working as a lyricist and dialogue writer. He resigned from his teaching profession in early 2013 and began working full-time in the film industry, while also launching the Karky Research Foundation (KaReFo), an educational research organization which primarily focuses on language computing and language literacy. He also founded the Mellinam Education, which develops educational games and story books designed to propagate learning among children, and DooPaaDoo, an online music platform which promotes independent music and serves a distributor for film soundtracks. == Early life == Karky is the eldest son of seven-time National Award winning lyricist Vairamuthu and Ponmani, a Tamil scholar and veteran professor at the Meenakshi College for Women. He has a younger brother, Kabilan, who is a novelist and also works as a lyricist and dialogue writer for Tamil films. === Education === He grew up in Chennai and was educated at the Loyala Matriculation School in Kodambakkam. By his own admission, he was not a good student, excelling primarily only in Tamil and English. During his time in high school, he gained an interest in computer science He got admission in College of Engineering, Guindy which is affiliated with the Anna University. He began his undergraduate education in the field of Computer engineering in the year 1997. While in CEG, as part of his final year project, Karky developed a program called the Tamil Voice Engine, under the supervision of Professor T.V. Geetha. The goal of the project was construction of a text to speech engine for the Tamil language. The research paper on the project was officially selected at the Tamil Internet Conference in Kuala Lumpur, Malaysia. Other projects during his tenure include the Name Generator, which was part of his course on Creativity, Innovation and New Product Development (the objective being to generate random names that are pronounceable with respect to Indian phonetics) and Compiler Design, for which a high level programming language was conceived, with the goal of proper specification and interpretation of lexical rules and grammar rules. For Chennai Kavigal, he created a Spell Checker for a Tamil Word Processor. The project involved a lot of Natural Language Processing elements, based on a root dictionary built as a part of the morphological analyzer for the Tamil Language. The endgame being determining the correctness of words. Following the completion of his bachelor's degree in 2001, Karky began his master's degree at the University of Queensland in the year 2003. In that particular stint, he developed a project based on the theory of computation and strong mathematics (under the supervision of Dr. George Havas). It aimed at analyzing an existing algorithm of reducing any kind of matrix format to a standard format called 'Hermite Normal form', which is a unit upper triangular matrix. Some of his other projects during this course include the Disciplined Software Process Project (whose objective was to introduce and practice the software development process for individuals called Personal Software Process), the On-Line Art Store Website (which involved the creation of a website that trades paintings through the Internet) and the Text Based Voice Chat (for which a Proxy Voice Chat system was designed and developed in Visual Basic that incorporated the predominant computing aspects). In addition to his academics, Karky also served as Academic tutor at the university. He conducted class room tutorials and laboratory sessions on subjects such as Relational Database Systems and Programming Languages. As part of his PhD program on information technology, he developed a Java-based simulation platform called SENSE (Simulated Environment of Networked Sensor Experiments), to test different heuristics. This project was done under the guidance of Dr. Maria Orlowska and Dr. Shazia Sadiq. His thesis is titled "Design considerations for query dissemination in wireless sensor networks". === Teaching career === Upon his return to India following the completion of his post-graduation, Karky returned to CEG Anna University in December 2007. He was a Senior Research Fellow for the next six months, managing research projects as well as multiple student projects at an undergrad and postgrad levels. In addition to those, he handled courses and labs for students who pursued their master's degrees. He also served as a Project Scientist between July 2008 and July 2009, managing projects of research groups as well as ME & MBA students. Starting from August 2009, he began his role as an assistant professor. He lectured Computer Science students who were pursuing their Bachelors and master's degrees as well as coordinated the Tamil Computing Lab at the university. He also served as counsellor for NRI and foreign national students, as well as the Staff treasurer of Computer Science Engineering Association. Some of the subjects he taught include Advanced Databases, Ethics for Engineers, Principles of Programming Languages, Environmental Science and Tamil Computing (for PhD students). === Family and personal life === Karky's been married to Nandini Eswaramoorthy, a fellow alum at Anna University, since June 22, 2008. Nandini Karky now works in the Tamil film industry as a subtitler for feature films and documentaries. They have a son named Haiku Karky, who was born in 2009. == Film career == === Debut === During his teaching stint at Anna University, Karky also began his career in the Tamil film industry with the science-fiction film Enthiran (2010), the magnum opus of director Shankar. Karky had approached the director in 2008 with some of the songs he had written, and was brought him on board to help with the dialogues of the film, especially assisting with technical terminology. He stated that there were three sets of dialogues written for almost every scene of the film; one by Shankar, one by Karky, and the other by the late Sujatha, a frequent collaborator with the director who had died during the early stages of the film's pre-production. Shankar would go through all the three drafts and implement those that fit best. The climax was the only portion that didn't have multiple hands, as it was written solely by Karky. In addition to the dialogue, Karky wrote 2 songs for the film, as well: "Irumbile oru Irudhaiyam" (the first song of his career, which was partially crooned by A.R. Rahman) and "Boom Boom Robo Da". However, Kanden Kadhalai (2009), in which he had written the song "Ododi Poren" (composed by Vidyasagar), became his first release. For his work on Enthiran, Karky was named Best Find of the Year at the 2011 Vijay Awards. === Lyric writer === Following his work on Enthiran, Karky became one of the most sought after lyricists in the Tamil film industry, having multiple collaborations with A.R. Rahman, Harris Jayaraj, G. V. Prakash Kumar, D. Imman, M.M. Keeravani, Yuvan Shankar Raja, S. Thaman, Sanjay Leela Bhansali, Anirudh Ravichander and Sam CS. In addition to his native Tamil, he is known for penning songs in multiple languages; some of which include "Asku Laska" from Nanban (which features 16 different languages), "The Rise of Damo" from 7 Aum Arivu (written in Mandarin) and "Continua" from Nootrenbadhu (in Portuguese). His work is also characterized by infusing uncommon Tamil words that aren't normally used in everyday lexicon, as part of lyrics (like "Kuviyamillaa Kaatchi Paezhai" from Ko and "Panikoozh" from I). He also wrote the first palindrome song in Tamil cinema for the film Vinodhan. As of the end of 2025, he has over one thousand songs to his credit. Some of Karky's most popular songs include "Irumbile oru Irudhaiyam" (Enthiran), "Enamo Edho" (Ko), "Nee Koorinal" (Nootrenbadhu), "Asku Laska" (Nanban), "Google Google" (Thuppakki), "Elay Keechaan" (Kadal), "Osakka" (Vanakkam Chennai), "Selfie Pulla" (Kaththi), "Pookkalae Sattru Oyivedungal" (I), "Mei Nigara" (24), "Azhagiye" (Kaatru Veliyidai), "Endhira Logathu Sundariye" (2.0) and "Kurumba" (Tik Tik Tik). === Dialogue writer === On the heels of the success with Enthiran, Karky once again collaborated as a dialogue writer with director Shankar for Nanban. An adaptation of the Hindi blockbuster 3 Idiots, he infused a twang to the dialogue that aimed to showcase college life in a different manner. He also collaborated as a technical advisor with Shankar with 2.0 (the sequel to Enthiran). Karky's also known for his successful collaboration with Telugu director S.S. Rajamouli, on his two-part magnum opus Baahubali; the second part being the most profitable South Indian film of all time, and RRR. His o

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  • Android Auto

    Android Auto

    Android Auto is a mobile app developed by Google to mirror features of a smartphone (or other Android device) on a car's dashboard information and entertainment head unit. Once an Android device is paired with the car's head unit, the system can mirror some apps on the vehicle's display. Supported apps include GPS mapping and navigation, music playback, SMS, telephone, and Web search. The system supports both touchscreen and button-controlled head units. Hands-free operation through voice commands is available and recommended to reduce driver distraction. Android Auto is part of the Open Automotive Alliance, a joint effort of 28 automobile manufacturers, with Nvidia as tech supplier, available in 36 countries. == History == Android Auto was revealed at Google I/O 2014. The app was released to the public on March 19, 2015. In November 2016, Google implemented an app that would run the Android Auto UI on the mobile device. In July 2019, Android Auto received its first major UI rework, which among other changes, brought an app drawer to Android Auto for the first time. Google also announced that the app's ability to be used on a phone would be discontinued in favor of Google Assistant's drive mode. In December 2020, Google announced the expansion of Android Auto to 36 additional countries in Europe, Indonesia, and more. In April 2021, Android Auto launched in Belgium, Denmark, Netherlands, Norway, Portugal, and Sweden. Google announced in May 2022 a user interface redesign for Android Auto, codenamed CoolWalk, which aims to simplify the app's usage, and make it more adaptable to screens of different orientations and aspect ratios. The redesign incorporates a new split-screen layout, where Google Maps can be displayed alongside a music player. CoolWalk was originally slated to launch in Q3 2022. In June 2022, Android Auto no longer ran directly on a mobile device; the app permitting this was decommissioned, in favor of a Driving Mode built into the Google Assistant app for a similar purpose. In November 2022, the CoolWalk user interface was released in Android Auto's beta program. == Functionality == Android Auto is software that can be utilized from an Android mobile device, acting as a vehicle's dashboard head unit. Once the user's Android device is connected to the vehicle, the head unit will serve as an external display for the Android device, presenting supported software in a car-specific user interface provided by the Android Auto app. In Android Auto's first iterations, the device was required to be connected via USB to the car. For some time, starting in November 2016, Google added the option to run Android Auto as a regular app on an Android device, allowing users to choose whether to use Android Auto on a personal phone or tablet, rather than on a compatible automotive head unit. This app was decommissioned in June 2022 in favor of a Driving Mode built into the Google Assistant app. At CES 2018, Google confirmed that the Google Assistant would be coming to Android Auto later in the year. An Android Auto SDK has been released, allowing third parties to modify their apps to work with Android Auto; initially, only APIs for music and messaging apps were available. == Head unit support == In May 2015, Hyundai became the first manufacturer to offer Android Auto support, making it first available in the 2015 Hyundai Sonata. Automobile manufacturers that will offer Android Auto support in their cars include Abarth, Acura, Alfa Romeo, Aston Martin, Audi, Bentley, Buick, BMW, BYD, Cadillac, Chevrolet, Chrysler, Citroën, Dodge, Ferrari, Fiat, Ford, GMC, Genesis, Holden, Honda, Hyundai, Infiniti, Jaguar Land Rover, Jeep, Kia, Lamborghini, Lexus, Lincoln, Mahindra and Mahindra, Maserati, Maybach, Mazda, Mercedes-Benz, Mitsubishi, Nissan, Opel, Peugeot, Porsche, RAM, Renault, SEAT, Škoda, SsangYong, Subaru, Suzuki, Tata Motors Cars, Toyota, Volkswagen and Volvo. Additionally, aftermarket car-audio systems supporting Android Auto add the technology into host vehicles, including Pioneer, Kenwood, Panasonic, and Sony. == Criticism == In May 2019, Italy filed an antitrust complaint targeting Android Auto, citing a Google policy of allowing third-parties to only offer media and messaging apps on the platform, preventing Enel from offering an app for locating vehicle charging stations. Google announced a new SDK, to be released to select partners in August 2020 and made generally available by the end of the year. == Availability == As of December 2025, Android Auto is available in 46 countries:

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  • Maghi King

    Maghi King

    Margaret (Maghi) Daniel King is a retired British computational linguist known for her work on evaluating the quality of machine translation. She is an honorary professor in the Department of Translation Technology of the University of Geneva in Switzerland, and the former director of the Dalle Molle Institute for Semantic and Cognitive Studies at the University of Geneva. == Education and career == King read classics, Ancient History and Philosophy (Greats) at the University of Oxford, worked as a computer programmer, and became a lecturer in the Department of Computation at the University of Manchester Institute of Science and Technology. She moved to the Dalle Molle Institute for Semantic and Cognitive Studies (ISSCO) in 1974. In 1976, ISSCO became part of the University of Geneva, and she continued there, becoming ISSCO's director in 1978. She remained director until her retirement in 2006. == Recognition == King is a Fellow of the European Association for Artificial Intelligence (formerly ECCAI), elected in 1999.

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  • Structural synthesis of programs

    Structural synthesis of programs

    Structural synthesis of programs (SSP) is a special form of (automatic) program synthesis that is based on propositional calculus. More precisely, it uses intuitionistic logic for describing the structure of a program in such a detail that the program can be automatically composed from pieces like subroutines or even computer commands. It is assumed that these pieces have been implemented correctly, hence no correctness verification of these pieces is needed. SSP is well suited for automatic composition of services for service-oriented architectures and for synthesis of large simulation programs. == History == Automatic program synthesis began in the artificial intelligence field, with software intended for automatic problem solving. The first program synthesizer was developed by Cordell Green in 1969. At about the same time, mathematicians including R. Constable, Z. Manna, and R. Waldinger explained the possible use of formal logic for automatic program synthesis. Practically applicable program synthesizers appeared considerably later. The idea of structural synthesis of programs was introduced at a conference on algorithms in modern mathematics and computer science organized by Andrey Ershov and Donald Knuth in 1979. The idea originated from G. Pólya’s well-known book on problem solving. The method for devising a plan for solving a problem in SSP was presented as a formal system. The inference rules of the system were restructured and justified in logic by G. Mints and E. Tyugu in 1982. A programming tool PRIZ that uses SSP was developed in the 1980s. A recent Integrated development environment that supports SSP is CoCoViLa — a model-based software development platform for implementing domain specific languages and developing large Java programs. == The logic of SSP == Structural synthesis of programs is a method for composing programs from already implemented components (e.g. from computer commands or software object methods) that can be considered as functions. A specification for synthesis is given in intuitionistic propositional logic by writing axioms about the applicability of functions. An axiom about the applicability of a function f is a logical implication X1 ∧ X2 ∧ ... ∧ Xm → Y1 ∧ Y2 ... Yn, where X1, X2, ... Xm are preconditions and Y1, Y2, ... Yn are postconditions of the application of the function f. In intuitionistic logic, the function f is called a realization of this formula. A precondition can be a proposition stating that input data exists, e.g. Xi may have the meaning “variable xi has received a value”, but it may denote also some other condition, e.g. that resources needed for using the function f are available, etc. A precondition may also be an implication of the same form as the axiom given above; then it is called a subtask. A subtask denotes a function that must be available as an input when the function f is applied. This function itself must be synthesized in the process of SSP. In this case, realization of the axiom is a higher order function, i.e., a function that uses another function as an input. For instance, the formula (state → nextState) ∧ initialState → result can specify a higher order function with two inputs and an output result. The first input is a function that has to be synthesized for computing nextState from state, and the second input is initialState. Higher order functions give generality to the SSP – any control structure needed in a synthesized program can be preprogrammed and used then automatically with a respective specification. In particular, the last axiom presented here is a specification of a complex program – a simulation engine for simulating dynamic systems on models where nextState can be computed from state of the system.

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  • Roni Rosenfeld

    Roni Rosenfeld

    Roni Rosenfeld (Hebrew: רוני רוזנפלד) is an Israeli-American computer scientist and computational epidemiologist, currently serving as the head of the Machine Learning Department at Carnegie Mellon University. He is an international expert in machine learning, infectious disease forecasting, statistical language modeling and artificial intelligence. == Education == Rosenfeld received his B.Sc. in mathematics and physics from Tel Aviv University in 1985. He received his Ph.D. in computer science from Carnegie Mellon University in 1994. While a graduate student, he developed and open-sourced a statistical language-modeling toolkit to allow anyone to create statistical language models from their own corpora and experiment with and extend the toolkit's capabilities. The toolkit has been used by more than 100 NLP laboratories in more than 20 countries. Rosenfeld's Ph.D. thesis, A Maximum Entropy Approach to Adaptive Statistical Language Modeling, was advised by Raj Reddy and Xuedong Huang and won the 2001 Computer, Speech and Language award for "Most Influential Paper in the Last 5 Years." == Career == Shortly after receiving his Ph.D., Rosenfeld joined the faculty of the Carnegie Mellon School of Computer Science as an assistant professor. He was promoted to the rank of associate professor in 1999 and received tenure in 2001. In 2005 he was promoted to professor of language technologies, machine learning computer science and computational biology in the School of Computer Science at Carnegie Mellon University. Rosenfeld also holds adjunct appointments at the University of Pittsburgh School of Medicine, department of computational and systems biology. From 2002 to 2003, Rosenfeld was a visiting professor at the University of Hong Kong. Rosenfeld is the director of Carnegie Mellon's Machine Learning for Social Good (ML4SG) program. He has held educational leadership positions in a variety of programs, including the M.S. in computational finance (1997–1999), graduate computational and statistical learning (2001–2003), M.S. in machine learning (2017) and undergraduate minor in machine learning. Rosenfeld was appointed Head of Carnegie Mellon's Machine Learning Department in 2018. == Research == Rosenfeld's research interests include epidemiological forecasting, information and communication technologies for development (ICT4D), and machine learning for social good. === Epidemiological forecasting === Rosenfeld is a world expert in epidemiological forecasting. He founded and directs the Delphi research group, which has won most of the epidemiological forecasting challenges organized by the U.S. CDC and other U.S. government agencies. In December 2016, the CDC named his group the "Most Accurate Forecaster" for 2015–2016, and in October 2017, the Delphi group's two systems took the top two spots in the 2016-2017 flu forecasting challenge. The CDC recognized Rosenfeld's Delphi group at Carnegie Mellon University as having contributed the most accurate national-, regional-, and state-level influenza-like illness forecasts and national-level hospitalization forecasts to the site. In 2019, the CDC recognized forecasts provided by the Delphi group at Carnegie Mellon as having been the most accurate for five seasons in a row, and named the Delphi group an Influenza Forecasting Center of Excellence, a five-year designation that includes $3 million in research funding. Rosenfeld describes his forecasting research goal as "to make epidemiological forecasting as universally accepted and useful as weather forecasting is today." His recent work in the area has focused on selecting high value epidemiological forecasting targets (e.g. Influenza and Dengue); creating baseline forecasting methods for them; establishing metrics for measuring and tracking forecasting accuracy; estimating the limits of forecastability for each target; and identifying new sources of data that could be helpful to the forecasting goal. == Honors and awards == 2017 Joel and Ruth Spira Teaching Award 2017 CDC Influenza Forecasting Challenge "Most Accurate Forecaster" 1992 Allen Newell Medal for Research Excellence

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  • Is an AI Art Generator Worth It in 2026?

    Is an AI Art Generator Worth It in 2026?

    Curious about the best AI art generator? An AI art generator 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 art 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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  • Mirella Lapata

    Mirella Lapata

    Mirella Lapata is a computer scientist and Professor in the School of Informatics at the University of Edinburgh. Working on the general problem of extracting semantic information from large bodies of text, Lapata develops computer algorithms and models in the field of natural language processing (NLP). == Education == Lapata obtained a Master of Arts (MA) degree from Carnegie Mellon University and subsequently earned a doctorate from the University of Edinburgh. Lapata's doctoral research investigated the acquisition of information from polysemous linguistic units using probabilistic methods supervised by Alex Lascarides, Chris Brew and Steve Finch. == Career and research == After her doctorate, Lapata assumed academic positions at Saarland University and at the Department of Computer Science at the University of Sheffield. At the University of Edinburgh she became a reader in the School of Informatics where she is a full Professor and holds a personal chair in natural language processing. Lapata is a member of the Human Communication Research Center and Institute for Language, Cognition and Computation, both in Edinburgh. Between 2015 and 2017, Lapata served as a member of the Royal Society Machine Learning Working Group. Recently Lapata was granted a European Research Council (ERC) Consolidator Grant worth €1.9M to fund five years of her project, TransModal: Translating from Multiple Modalities into Text. === Awards and honours === In 2009 Lapata became the first recipient of the Microsoft British Computer Society (BCS)/BCS IRSG Karen Spärck Jones Award. The award recognises achievement in furthering the progress in information retrieval and natural language processing; the award commemorates the life and work of Karen Spärck Jones. In 2012 Lapata won an Empirical Methods in Natural Language Processing (EMNLP)-CoNLL 2012 Best Reviewer Award. In 2018 Lapata was awarded, alongside Li Dong, an Association for Computational Linguistics (ACL) Best Paper Honorable Mention. In 2019 Lapata was elected a Fellow of the Royal Society of Edinburgh In 2020 Lapata was elected to the Academia Europaea. In 2025 Lapata was awarded the BCS Lovelace Medal for Computing Research.

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  • Alice AI (AI model family)

    Alice AI (AI model family)

    Alice AI is a neural network family developed by the Russian company Yandex LLC. Alice AI can create and revise texts, generate new ideas and capture the context of the conversation with the user. Alice AI is trained using a dataset which includes information from books, magazines, newspapers and other open sources available on the internet. The neural network may get facts wrong and hallucinate, but as it learns, it will produce increasingly accurate answers. == Usage == YandexGPT is integrated into virtual assistant Alice (an analog of Siri and Alexa) and is available in Yandex services and applications. The company gives businesses access to the neural network’s API through the public cloud platform Yandex Cloud and develops its own B2B solutions on its basis. Since July 2023, 800 companies have participated in the closed testing of YandexGPT. IT developers, banks, retail businesses, and companies from other industries can use the technology in two modes — API and Playground (an interface in the Yandex Cloud console for testing models and hypotheses). Two model versions are available to businesses: one works in asynchronous mode and is better able to handle complex tasks, while the other is suitable for creating quick responses in real time. As a result, YandexGPT has been tested in dozens of scenarios such as content tasks, tech support, creating chatbots, virtual assistants, etc. == History == In February 2023, Yandex announced that it was working on its own version of the ChatGPT generative neural network while developing a language model from the YaLM (Yet another Language Model) family. The project was tentatively named YaLM 2.0, which was later changed to YandexGPT. On May 17, the company unveiled a neural network called YandexGPT (YaGPT) and enabled its virtual assistant Alice to interact with the new language model. On June 15, 2023, Yandex added the YandexGPT language model to the image generation application Shedevrum. This enabled its users to create fully-fledged posts complete with a title, text, and relevant illustration. In July 2023, YandexGPT launched new features enabling businesses to create virtual assistants and chatbots, as well as generate and structure texts. On September 7, 2023, Yandex presented a new version of the language model, YandexGPT 2, at the Practical ML Conf. Compared to the previous one, the new version is able to perform more types of tasks, and the quality of answers has improved. The developers claimed that YandexGPT 2 answered user questions better than the first version in 67% of cases. From October 6, 2023, YandexGPT can create short retellings of online Russian-language videos on the Internet. It can summarize videos that are from two minutes to four hours long and contain speech.

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  • Top 10 AI Marketing Tools Compared (2026)

    Top 10 AI Marketing Tools Compared (2026)

    Comparing the best AI marketing tool? An AI marketing tool is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI marketing tool slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  • Two-way finite automaton

    Two-way finite automaton

    In computer science, in particular in automata theory, a two-way finite automaton is a finite automaton that is allowed to re-read its input. == Two-way deterministic finite automaton == A two-way deterministic finite automaton (2DFA) is an abstract machine, a generalized version of the deterministic finite automaton (DFA) which can revisit characters already processed. As in a DFA, there are a finite number of states with transitions between them based on the current character, but each transition is also labelled with a value indicating whether the machine will move its position in the input to the left, right, or stay at the same position. Equivalently, 2DFAs can be seen as read-only Turing machines with no work tape, only a read-only input tape. 2DFAs were introduced in a seminal 1959 paper by Rabin and Scott, who proved them to have equivalent power to one-way DFAs. That is, any formal language which can be recognized by a 2DFA can be recognized by a DFA which only examines and consumes each character in order. Since DFAs are obviously a special case of 2DFAs, this implies that both kinds of machines recognize precisely the class of regular languages. However, the equivalent DFA for a 2DFA may require exponentially many states, making 2DFAs a much more practical representation for algorithms for some common problems. 2DFAs are also equivalent to read-only Turing machines that use only a constant amount of space on their work tape, since any constant amount of information can be incorporated into the finite control state via a product construction (a state for each combination of work tape state and control state). == Formal description == Formally, a two-way deterministic finite automaton can be described by the following 8-tuple: M = ( Q , Σ , L , R , δ , s , t , r ) {\displaystyle M=(Q,\Sigma ,L,R,\delta ,s,t,r)} where Q {\displaystyle Q} is the finite, non-empty set of states Σ {\displaystyle \Sigma } is the finite, non-empty set of input symbols L {\displaystyle L} is the left endmarker R {\displaystyle R} is the right endmarker δ : Q × ( Σ ∪ { L , R } ) → Q × { l e f t , r i g h t } {\displaystyle \delta :Q\times (\Sigma \cup \{L,R\})\rightarrow Q\times \{\mathrm {left,right} \}} s {\displaystyle s} is the start state t {\displaystyle t} is the end state r {\displaystyle r} is the reject state In addition, the following two conditions must also be satisfied: For all q ∈ Q {\displaystyle q\in Q} δ ( q , L ) = ( q ′ , r i g h t ) {\displaystyle \delta (q,L)=(q^{\prime },\mathrm {right} )} for some q ′ ∈ Q {\displaystyle q^{\prime }\in Q} δ ( q , R ) = ( q ′ , l e f t ) {\displaystyle \delta (q,R)=(q^{\prime },\mathrm {left} )} for some q ′ ∈ Q {\displaystyle q^{\prime }\in Q} It says that there must be some transition possible when the pointer reaches either end of the input word. For all symbols σ ∈ Σ ∪ { L } {\displaystyle \sigma \in \Sigma \cup \{L\}} δ ( t , σ ) = ( t , R ) {\displaystyle \delta (t,\sigma )=(t,R)} δ ( r , σ ) = ( r , R ) {\displaystyle \delta (r,\sigma )=(r,R)} δ ( t , R ) = ( t , L ) {\displaystyle \delta (t,R)=(t,L)} δ ( r , R ) = ( r , L ) {\displaystyle \delta (r,R)=(r,L)} It says that once the automaton reaches the accept or reject state, it stays in there forever and the pointer goes to the right most symbol and cycles there infinitely. == Two-way nondeterministic finite automaton == A two-way nondeterministic finite automaton (2NFA) may have multiple transitions defined in the same configuration. Its transition function is δ : Q × ( Σ ∪ { L , R } ) → 2 Q × { l e f t , r i g h t } {\displaystyle \delta :Q\times (\Sigma \cup \{L,R\})\rightarrow 2^{Q\times \{\mathrm {left,right} \}}} . Like a standard one-way NFA, a 2NFA accepts a string if at least one of the possible computations is accepting. Like the 2DFAs, the 2NFAs also accept only regular languages. == Two-way alternating finite automaton == A two-way alternating finite automaton (2AFA) is a two-way extension of an alternating finite automaton (AFA). Its state set is Q = Q ∃ ∪ Q ∀ {\displaystyle Q=Q_{\exists }\cup Q_{\forall }} where Q ∃ ∩ Q ∀ = ∅ {\displaystyle Q_{\exists }\cap Q_{\forall }=\emptyset } . States in Q ∃ {\displaystyle Q_{\exists }} and Q ∀ {\displaystyle Q_{\forall }} are called existential resp. universal. In an existential state a 2AFA nondeterministically chooses the next state like an NFA, and accepts if at least one of the resulting computations accepts. In a universal state 2AFA moves to all next states, and accepts if all the resulting computations accept. == State complexity tradeoffs == Two-way and one-way finite automata, deterministic and nondeterministic and alternating, accept the same class of regular languages. However, transforming an automaton of one type to an equivalent automaton of another type incurs a blow-up in the number of states. Christos Kapoutsis determined that transforming an n {\displaystyle n} -state 2DFA to an equivalent DFA requires n ( n n − ( n − 1 ) n ) {\displaystyle n(n^{n}-(n-1)^{n})} states in the worst case. If an n {\displaystyle n} -state 2DFA or a 2NFA is transformed to an NFA, the worst-case number of states required is ( 2 n n + 1 ) = O ( 4 n n ) {\displaystyle {\binom {2n}{n+1}}=O\left({\frac {4^{n}}{\sqrt {n}}}\right)} . Ladner, Lipton and Stockmeyer. proved that an n {\displaystyle n} -state 2AFA can be converted to a DFA with 2 n 2 n {\displaystyle 2^{n2^{n}}} states. The 2AFA to NFA conversion requires 2 Θ ( n log ⁡ n ) {\displaystyle 2^{\Theta (n\log n)}} states in the worst case, see Geffert and Okhotin. It is an open problem whether every 2NFA can be converted to a 2DFA with only a polynomial increase in the number of states. The problem was raised by Sakoda and Sipser, who compared it to the P vs. NP problem in the computational complexity theory. Berman and Lingas discovered a formal relation between this problem and the L vs. NL open problem, see Kapoutsis for a precise relation. == Sweeping automata == Sweeping automata are 2DFAs of a special kind that process the input string by making alternating left-to-right and right-to-left sweeps, turning only at the endmarkers. Sipser constructed a sequence of languages, each accepted by an n-state NFA, yet which is not accepted by any sweeping automata with fewer than 2 n {\displaystyle 2^{n}} states. == Two-way quantum finite automaton == The concept of 2DFAs was in 1997 generalized to quantum computing by John Watrous's "On the Power of 2-Way Quantum Finite State Automata", in which he demonstrates that these machines can recognize nonregular languages and so are more powerful than DFAs. == Two-way pushdown automaton == A pushdown automaton that is allowed to move either way on its input tape is called two-way pushdown automaton (2PDA); it has been studied by Hartmanis, Lewis, and Stearns (1965). Aho, Hopcroft, Ullman (1968) and Cook (1971) characterized the class of languages recognizable by deterministic (2DPDA) and non-deterministic (2NPDA) two-way pushdown automata; Gray, Harrison, and Ibarra (1967) investigated the closure properties of these languages.

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  • Ellen Voorhees

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    Ellen Marie Voorhees (born March 13, 1958) is an American computer scientist known for her work in document retrieval, information retrieval, and natural language processing. She works in the retrieval group at the National Institute of Standards and Technology (NIST). == Education and career == Voorhees was born in Bensalem Township, Pennsylvania, and was the 1976 valedictorian at Bensalem High School. She completed her undergraduate studies at Pennsylvania State University, graduating in 1979 with a bachelor's degree in computer science. She attended Cornell University, where she received her master's degree and then went on to complete her Ph.D. in 1985. Her dissertation, The Effectiveness and Efficiency of Agglomerative Hierarchic Clustering in Document Retrieval, was supervised by Gerard Salton. Prior to joining NIST, she was a senior member of the technical staff at Siemens Corporate Research in Princeton, New Jersey. == Recognition == Voorhees was elected as an ACM Fellow in 2018 for "contributions in evaluation of information retrieval, question answering, and other language technologies". In 2023, Voorhees was awarded an honorary Doctor of Science degree from the University of Glasgow in recognition of her body of work in the evaluation of information retrieval, question answering, and other language technologies. In 2024, Voorhees received the Gerard Salton Award, a lifetime achievement award given by ACM's Special Interest Group on Information Retrieval (SIGIR).

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