AI Grammar Paraphrase Generator

AI Grammar Paraphrase Generator — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Actifsource

    Actifsource

    Actifsource is a domain-specific modeling workbench. It is realized as plug-in for the software development environment Eclipse. Actifsource supports the creation of multiple domain models which can be linked together. It comes with a UML-like graphical editor to create domain-specific languages and a general graphical editor to edit structures in the created languages. It supports code generation using user-defined generic code templates which are directly linked to the domain models. Code generation is integrated into Eclipse's incremental build process. == Interoperability == Actifsource can use models from other modelling tools by importing and exporting the ecore format which is defined by the Eclipse Modeling Framework. == Licensing policy == There are two versions of actifsource available: The free community edition which can be used freely for non-commercial projects and the enterprise edition which contains additional features. The enterprise edition comes with customer support and maintenance for a limited period of time. This package allows the customers to upgrade to new versions and maintenance releases during their support period.

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  • Best AI Content Generators in 2026

    Best AI Content Generators 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. This guide breaks down the top picks, their pros and cons, and who each one is best for.

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  • Monica S. Lam

    Monica S. Lam

    Monica Sin-Ling Lam is an American computer scientist. She is a professor in the Computer Science Department at Stanford University. == Education == Monica Lam received a B.Sc. from University of British Columbia in 1980 and a Ph.D. in computer science from Carnegie Mellon University in 1987. == Career == Lam joined the faculty of Computer Science at Stanford University in 1988. She has contributed to the research of a wide range of computer systems topics including compilers, program analysis, operating systems, security, computer architecture, and high-performance computing. More recently, she is working in natural language processing, and virtual assistants with an emphasis on privacy protection. She is the faculty director of the Open Virtual Assistant Lab, which organized the first workshop for the World Wide Voice Web. The lab developed the open-source Almond voice assistant, which is sponsored by the National Science Foundation. Almond received Popular Science's Best of What's New award in 2019. Previously, Lam led the SUIF (Stanford University Intermediate Format) Compiler project, which produced a widely used compiler infrastructure known for its locality optimizations and interprocedural parallelization. Many of the compiler techniques she developed have been adopted by industry. Her other research projects included the architecture and compiler for the CMU Warp machine, a systolic array of VLIW processors, and the Stanford DASH distributed shared memory machine. In 1998, she took a sabbatical leave from Stanford to help start Tensilica Inc., a company that specializes in configurable processor cores. In another research project, her program analysis group developed a collection of tools for improving software security and reliability. They developed the first scalable context-sensitive inclusion-based pointer analysis and a freely available tool called BDDBDDB, that allows programmers to express context-sensitive analyses simply by writing Datalog queries. Other tools developed include Griffin, static and dynamic analysis for finding security vulnerabilities in Web applications such as SQL injection, a static and dynamic program query language called QL, a static memory leak detector called Clouseau, a dynamic buffer overrun detector called CRED, and a dynamic error diagnosis tool called DIDUCE. In the Collective project, her research group and she developed the concept of a livePC: subscribers of the livePC will automatically run the latest of the published PC virtual images with each reboot. This approach allows computers to be managed scalably and securely. In 2005, the group started a company called MokaFive to transfer the technology to industry. She also directed the MobiSocial laboratory at Stanford, as part of the Programmable Open Mobile Internet 2020 initiative. Lam is also the cofounder of Omlet, which launched in 2014. Omlet is the first product from MobiSocial. Omlet is an open, decentralized social networking tool, based on an extensible chat platform. Lam chaired the ACM SIGPLAN Programming Languages Design and Implementation Conference in 2000, served on the Editorial Board of ACM Transactions on Computer Systems and numerous program committees for conferences on languages and compilers (PLDI, POPL), operating systems (SOSP), and computer architecture (ASPLOS, ISCA). == Awards and honors == National Academy of Engineering member, 2019 University of British Columbia Computer Science 50th Anniversary Research Award, 2018 Fellow of the ACM, 2007 ACM Programming Language Design and Implementation Best Paper Award in 2004 ACM SIGSOFT Distinguished Paper Award in 2002 ACM Most Influential Programming Language Design and Implementation Paper Award in 2001 NSF Young Investigator award in 1992 Two of her papers were recognized in "20 Years of PLDI--a Selection (1979-1999)" One of her papers was recognized in the "25 Years of the International Symposia on Computer Architecture", 1988. == Selected works == Compilers: Principles, Techniques and Tools (2d Ed) (2006) (the "Dragon Book") by Alfred V. Aho, Monica S. Lam, Ravi Sethi, and Jeffrey D. Ullman (ISBN 0-321-48681-1) A Systolic Array Optimizing Compiler (1989) (ISBN 0-89838-300-5) Monica Lam, Dissertation

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  • Deepset

    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.

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  • Eyes of Things

    Eyes of Things

    Eyes of Things (EoT) is the name of a project funded by the European Union’s Horizon 2020 Research and Innovation Programme under grant agreement number 643924. The purpose of the project, which is funded under the Smart Cyber-physical systems topic, is to develop a generic hardware-software platform for embedded, efficient (i.e. battery-operated, wearable, mobile), computer vision, including deep learning inference. On November 29, 2018, the European Space Agency announced that it was testing the suitability of the device for space applications in advance of a flight in a Cubesat. == Motivation == EoT is based on the following tenets: Future embedded systems will have more intelligence and cognitive functionality. Vision is paramount to such intelligent capacity Unlike other sensors, vision requires intensive processing. Power consumption must be optimized if vision is to be used in mobile and wearable applications Cloud processing of edge-captured images is not sustainable. The sheer amount of visual data generated cannot be transferred to the cloud. Bandwidth is not sufficient and cloud servers cannot cope with it. == Partners == VISILAB group at University of Castilla–La Mancha (Coordinator) Movidius Awaiba Thales Security Solutions & Systems DFKI Fluxguide Evercam nVISO == Awards == 2019 Electronic Component and Systems Innovation Award by the European Commission 2018 HiPEAC Tech Transfer Award 2018 EC Innovation Radar - highlighting excellent innovations Award 2018 Internet of Things (IoT) Technology Research Award Pilot by Google 2016 Semifinalist "THE VISION SHOW STARTUP COMPETITION", Global Association for Vision Information, Boston US

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  • Volker Markl

    Volker Markl

    Volker Markl (born 1971) is a German computer scientist and database systems researcher. == Career == In 1999, Markl received his PhD in computer science under the direction of Rudolf Bayer at the Technical University of Munich. His doctoral research led to the development of the UB-Tree. From 1997 to 2000, he was research group leader at FORWISS, the Bavarian research center for knowledge-based systems. From 2001 to 2008, he was project leader at the IBM Almaden Research Center, Silicon Valley. Since 2008, he has been full professor and Chair of the Database Systems and Information Management Group at Technische Universität Berlin. Since 2014, he is head of the Intelligent Analytics for Massive Data Research Department at the German Research Centre for Artificial Intelligence (DFKI), Berlin. From 2014 to 2020, he was director of the Berlin Big Data Center (BBDC). From 2018 to 2020, he was co-director of the Berlin Machine Learning Center (BZML). Together with Klaus-Robert Müller he became director of the new Berlin Institute for the Foundations of Learning and Data (BIFOLD), after both BBDC and the BZML merged into BIFOLD in 2020. From 2010 through 2019, he led the DFG funded Stratosphere project, which led to the establishment of Apache Flink. In 2018, he was elected president of the VLDB Endowment for a six years period that ended in 2024. == Research == Markl’s research interests lie at the intersection of distributed systems, scalable data processing, and machine learning. == Awards and honors == Markl was elected member of the Berlin-Brandenburg Academy of Sciences and Humanities in 2021. Since 2026 he is member of the German National Academy of Sciences Leopoldina. His work was honoured with several awards, including: 2025 ICDE Best Paper Award 2021 ICDE Best Paper Award 2021 BTW Best Paper Award 2020 ACM SIGMOD Best Paper Award 2020 ACM Fellow 2019 EDBT Best Paper Award 2017 BTW Best Paper Award 2017 EDBT Best Demonstration Award 2016 ACM SIGMOD Research Highlight Award 2014 VLDB Best Paper Award 2012 IBM Faculty Award 2012 IBM Shared University Research Grant 2010 Hewlett Packard Open Innovation Award 2005 IBM Outstanding Technological Achievement Award 2005 IBM Pat Goldberg Best Paper Award

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  • Top 10 AI Customer-support Bots Compared (2026)

    Top 10 AI Customer-support Bots Compared (2026)

    Trying to pick the best AI customer-support bot? An AI customer-support bot 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 customer-support bot 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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  • Top 10 AI Content Generators Compared (2026)

    Top 10 AI Content Generators Compared (2026)

    Comparing the best AI content generator? An AI content generator 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 content 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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  • Bag-of-words model

    Bag-of-words model

    The bag-of-words (BoW) model is a model of text which uses an unordered collection (a "bag") of words. It is used in natural language processing and information retrieval (IR). It disregards word order (and thus most of syntax or grammar) but captures multiplicity. The bag-of-words model is commonly used in methods of document classification where, for example, the (frequency of) occurrence of each word is used as a feature for training a classifier. It has also been used for computer vision. An early reference to "bag of words" in a linguistic context can be found in Zellig Harris's 1954 article on Distributional Structure. == Definition == The following models a text document using bag-of-words. Here are two simple text documents: Based on these two text documents, a list is constructed as follows for each document: Representing each bag-of-words as a JSON object, and attributing to the respective JavaScript variable: Each key is the word, and each value is the number of occurrences of that word in the given text document. The order of elements is free, so, for example {"too":1,"Mary":1,"movies":2,"John":1,"watch":1,"likes":2,"to":1} is also equivalent to BoW1. It is also what we expect from a strict JSON object representation. Note: if another document is like a union of these two, its JavaScript representation will be: So, as we see in the bag algebra, the "union" of two documents in the bags-of-words representation is, formally, the disjoint union, summing the multiplicities of each element. === Word order === The BoW representation of a text removes all word ordering. For example, the BoW representation of "man bites dog" and "dog bites man" are the same, so any algorithm that operates with a BoW representation of text must treat them in the same way. Despite this lack of syntax or grammar, BoW representation is fast and may be sufficient for simple tasks that do not require word order. For instance, for document classification, if the words "stocks" "trade" "investors" appears multiple times, then the text is likely a financial report, even though it would be insufficient to distinguish between Yesterday, investors were rallying, but today, they are retreating.andYesterday, investors were retreating, but today, they are rallying.and so the BoW representation would be insufficient to determine the detailed meaning of the document. == Implementations == Implementations of the bag-of-words model might involve using frequencies of words in a document to represent its contents. The frequencies can be "normalized" by the inverse of document frequency, or tf–idf. Additionally, for the specific purpose of classification, supervised alternatives have been developed to account for the class label of a document. Lastly, binary (presence/absence or 1/0) weighting is used in place of frequencies for some problems (e.g., this option is implemented in the WEKA machine learning software system). == Hashing trick == A common alternative to using dictionaries is the hashing trick, where words are mapped directly to indices with a hash function. When using a hash function, no memory is required to store a dictionary. In practice, hashing simplifies the implementation of bag-of-words models and improves scalability. Collisions can occur when two words are hashed to the same index, but this happens infrequently and may function as a form of regularization.

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  • Li Sheng (computer scientist)

    Li Sheng (computer scientist)

    Li Sheng (Chinese: 李生; born 1943), is a professor at the School of Computer Science and Engineering, Harbin Institute of Technology (HIT), China. He began his research on Chinese-English machine translation in 1985, making himself one of the earliest Chinese scholars in this field. After that, he pursued in vast topics of natural language processing, including machine translation, information retrieval, question answering and applied artificial intelligence. He was the final review committee member for computer area in NSF China. Born and raised in Heilongjiang province, he graduated in 1965 from the computer specialty of HIT, which is one of the earliest computer specialties in Chinese universities. Then he started to work as a staff in the Computer specialty of HIT, which was finally granted as a department in 1985. Also from 1985, he was appointed to undertake a series administrative positions in HIT, e.g. Dean of Computer Department(1987–1988), Director of R&D Division (1988–1990), Chief R&D Officer and several other key leading positions in HIT. Resigned all his administrative positions in 2004, Li devoted himself as the director of MOE-Microsoft Join Key Lab of NLP& Speech (HIT), making it a leading NLP research group with more than 100 staffs and students working on various aspects of NLP. So far, the lab has already been granted for dozens of technology awards by the ministries of central government and local provincial government of China. Its research progresses are reported annually in top tier conferences including ACL, IJCAI, SIGIR etc. As one of the pioneers in NLP research in China, he contributes NLP in China not only in technology innovations but also in talents education. So far, his research group has graduated more than 60 Ph.D. and almost 200 M.E with NLP major. Most of them are now working as the chief researcher in various NLP groups of universities and companies in China, including several world-known NLP scholars, such as Wang Haifeng of Baidu, Zhou Ming of Microsoft Research, Zhang Min (张民) of Soochow University (China), and Zhao Tiejun (赵铁军) and Liu Ting (刘挺) of HIT. Owing to his contributions in Chinese language processing, Li was elected as the President of Chinese Information Processing Society of China (CIPSC) in 2011. He scaled this top level academic organization in China up to more than 3000 registered members, and promoted NLP into several national projects for research or industry development. In addition, the CIPSC is now enhancing its co-operations with world NLP organizations including ACL. == Machine Intelligence & Translation Laboratory (MI&TLAB) == Originates from Machine Translation Research Group of Computer Science Department, Harbin Institute of Technology, which was started Li in 1985. It is one of the earliest institutions engaged in MT research in China, featured by its investigations into Chinese-English machine translation. It is now running under the Research Center on Language Technology, School of Computer Science and Technology, HIT. Details for staffs and publications can be found at https://mitlab.hit.edu.cn. == MOE-MS Joint Key Lab of Natural Language Processing and Speech (HIT) == In June, 2000, the Joint HIT-Microsoft Machine Translation Lab was founded by MI&T Lab and Microsoft Research (China). It was the third joint lab established by Microsoft Research (China) with Chinese universities, and the only one focusing on Machine Translation. Based on this jointly lab, the cooperation between HIT and Microsoft gradually extended to the areas of machine translation, information retrieval, speech recognition and processing, natural language understanding. In Oct, 2004, the joint key lab was granted as one of the 10 joint key labs supported by the Microsoft Research of Asia and Ministry of Education in China. In July 2006, the Shenzhen extension of the lab was launched. More than 200 staff and students have undertaken research projects, including some sponsored by the National Natural Science Foundation of China and the National 863 program of China. Since 2005, the lab has also been organizing a summer camp in Harbin Institute of Technology, and approximately 150 faculty members and students from universities in China have participated. This summer workshop was organized annually until 2014, when it was organized formally as the summer school series by Chinese Information Processing Society, China. Through the lab, a Microsoft Research of Asia-HIT joint PhD program was implemented in 2012. == CEMT-I MT System == In May 1989, CEMT-I passed the formal project appraisal in Harbin, China. Capable of translating technical paper titles from Chinese to English, it is not only the first MT system completed by Li and his group, but also the first Chinese-English Translation system that passed the technical appraisal by Chinese government according to the public reports. It was then awarded the Second Prize of Ministry Level Technology Innovation by the former National Aerospace Industry Corporation in 1990. == Daya Translation Workstation == Owing to the technical achievements by Li's group in Chinese-English machine translation, the former National Aerospace Industry Corporation of China sponsored a commercial system development of "Daya Translation Station (MT)" in 1993. Designed as a comprehensive English composition aid for Chinese users, this system was finished and put into the market in 1995. And in 1997, this system was awarded the Second Prize of Ministry Level Technology Innovation by the former National Aerospace Industry Corporation. == BT863 MT System == From 1994, the researches in Li's lab were supported by National 863 Hi-tech Research and Development Program. During this period, the BT863 system was explored to employ one engine for both Chinese-English and English-Chinese translation. This system was proved to be the best performance among Chinese-English MT systems in the formal technical evaluation of National 863 program, yielding the Third Prize of Ministry Level Technology Innovation by the former National Aerospace Industry Corporation in 1997. == Next Generation IR == This is a key project granted by NSF China (with a joint sponsorship from MSRA) started form 2008. In contrast to his previous NSF grants for different NLP issues, Li explored in his last PI project on key technologies in personalized IR, together with researchers from Tsinghua University and Institute of Software, Chinese Academy of Science. With impressive publications in top tier journals and conferences (including breakthrough publications in SIGIR of his own group), this projected was approved "A-level" achievements by the NSF China office in 2012.

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  • Krohn–Rhodes theory

    Krohn–Rhodes theory

    In mathematics and computer science, the Krohn–Rhodes theory (or algebraic automata theory) is an approach to the study of finite semigroups and automata that seeks to decompose them in terms of elementary components. These components correspond to finite aperiodic semigroups and finite simple groups that are combined in a feedback-free manner (called a "wreath product" or "cascade"). Krohn and Rhodes found a general decomposition for finite automata. The authors discovered and proved an unexpected major result in finite semigroup theory, revealing a deep connection between finite automata and semigroups. Decidability of Krohn-Rhodes complexity long motivated much work in semigroup theory. In June 2024, Stuart Margolis, John Rhodes, and Anne Schilling announced a proof that the complexity is decidable. == Definitions and description of the Krohn–Rhodes theorem == Let T {\displaystyle T} be a semigroup. A semigroup S {\displaystyle S} that is a homomorphic image of a subsemigroup of T {\displaystyle T} is said to be a divisor of T {\displaystyle T} . The Krohn–Rhodes theorem for finite semigroups states that every finite semigroup S {\displaystyle S} is a divisor of a finite alternating wreath product of finite simple groups, each a divisor of S {\displaystyle S} , and finite aperiodic semigroups (which contain no nontrivial subgroups). In the automata formulation, the Krohn–Rhodes theorem for finite automata states that given a finite automaton A {\displaystyle A} with states Q {\displaystyle Q} and input alphabet I {\displaystyle I} , output alphabet U {\displaystyle U} , then one can expand the states to Q ′ {\displaystyle Q'} such that the new automaton A ′ {\displaystyle A'} embeds into a cascade of "simple", irreducible automata: In particular, A {\displaystyle A} is emulated by a feed-forward cascade of (1) automata whose transformation semigroups are finite simple groups and (2) automata that are banks of flip-flops running in parallel. The new automaton A ′ {\displaystyle A'} has the same input and output symbols as A {\displaystyle A} . Here, both the states and inputs of the cascaded automata have a very special hierarchical coordinate form. Moreover, each simple group (prime) or non-group irreducible semigroup (subsemigroup of the flip-flop monoid) that divides the transformation semigroup of A {\displaystyle A} must divide the transformation semigroup of some component of the cascade, and only the primes that must occur as divisors of the components are those that divide A {\displaystyle A} 's transformation semigroup. == Group complexity == The Krohn–Rhodes complexity (also called group complexity or just complexity) of a finite semigroup S is the least number of groups in a wreath product of finite groups and finite aperiodic semigroups of which S is a divisor. All finite aperiodic semigroups have complexity 0, while non-trivial finite groups have complexity 1. In fact, there are semigroups of every non-negative integer complexity. For example, for any n greater than 1, the multiplicative semigroup of all (n+1) × (n+1) upper-triangular matrices over any fixed finite field has complexity n (Kambites, 2007). A major open problem in finite semigroup theory is the decidability of complexity: is there an algorithm that will compute the Krohn–Rhodes complexity of a finite semigroup, given its multiplication table? Upper bounds and ever more precise lower bounds on complexity have been obtained (see, e.g. Rhodes & Steinberg, 2009). Rhodes has conjectured that the problem is decidable. In June 2024, Stuart Margolis, John Rhodes, and Anne Schilling announced a proof in the affirmative of the conjecture, though as of 2025 the result has yet to be confirmed. == History and applications == At a conference in 1962, Kenneth Krohn and John Rhodes announced a method for decomposing a (deterministic) finite automaton into "simple" components that are themselves finite automata. This joint work, which has implications for philosophy, comprised both Krohn's doctoral thesis at Harvard University and Rhodes' doctoral thesis at MIT. Simpler proofs, and generalizations of the theorem to infinite structures, have been published since then (see Chapter 4 of Rhodes and Steinberg's 2009 book The q-Theory of Finite Semigroups for an overview). In the 1965 paper by Krohn and Rhodes, the proof of the theorem on the decomposition of finite automata (or, equivalently sequential machines) made extensive use of the algebraic semigroup structure. Later proofs contained major simplifications using finite wreath products of finite transformation semigroups. The theorem generalizes the Jordan–Hölder decomposition for finite groups (in which the primes are the finite simple groups), to all finite transformation semigroups (for which the primes are again the finite simple groups plus all subsemigroups of the "flip-flop" (see above)). Both the group and more general finite automata decomposition require expanding the state-set of the general, but allow for the same number of input symbols. In the general case, these are embedded in a larger structure with a hierarchical "coordinate system". One must be careful in understanding the notion of "prime" as Krohn and Rhodes explicitly refer to their theorem as a "prime decomposition theorem" for automata. The components in the decomposition, however, are not prime automata (with prime defined in a naïve way); rather, the notion of prime is more sophisticated and algebraic: the semigroups and groups associated to the constituent automata of the decomposition are prime (or irreducible) in a strict and natural algebraic sense with respect to the wreath product (Eilenberg, 1976). Also, unlike earlier decomposition theorems, the Krohn–Rhodes decompositions usually require expansion of the state-set, so that the expanded automaton covers (emulates) the one being decomposed. These facts have made the theorem difficult to understand and challenging to apply in a practical way—until recently, when computational implementations became available (Egri-Nagy & Nehaniv 2005, 2008). H.P. Zeiger (1967) proved an important variant called the holonomy decomposition (Eilenberg 1976). The holonomy method appears to be relatively efficient and has been implemented computationally by A. Egri-Nagy (Egri-Nagy & Nehaniv 2005). Meyer and Thompson (1969) give a version of Krohn–Rhodes decomposition for finite automata that is equivalent to the decomposition previously developed by Hartmanis and Stearns, but for useful decompositions, the notion of expanding the state-set of the original automaton is essential (for the non-permutation automata case). Many proofs and constructions now exist of Krohn–Rhodes decompositions (e.g., [Krohn, Rhodes & Tilson 1968], [Ésik 2000], [Diekert et al. 2012]), with the holonomy method the most popular and efficient in general (although not in all cases). [Zimmermann 2010] gives an elementary proof of the theorem. Owing to the close relation between monoids and categories, a version of the Krohn–Rhodes theorem is applicable to category theory. This observation and a proof of an analogous result were offered by Wells (1980). The Krohn–Rhodes theorem for semigroups/monoids is an analogue of the Jordan–Hölder theorem for finite groups (for semigroups/monoids rather than groups). As such, the theorem is a deep and important result in semigroup/monoid theory. The theorem was also surprising to many mathematicians and computer scientists since it had previously been widely believed that the semigroup/monoid axioms were too weak to admit a structure theorem of any strength, and prior work (Hartmanis & Stearns) was only able to show much more rigid and less general decomposition results for finite automata. Work by Egri-Nagy and Nehaniv (2005, 2008–) continues to further automate the holonomy version of the Krohn–Rhodes decomposition extended with the related decomposition for finite groups (so-called Frobenius–Lagrange coordinates) using the computer algebra system GAP. Applications outside of the semigroup and monoid theories are now computationally feasible. They include computations in biology and biochemical systems (e.g. Egri-Nagy & Nehaniv 2008), artificial intelligence, finite-state physics, psychology, and game theory (see, for example, Rhodes 2009).

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  • Georgetown–IBM experiment

    Georgetown–IBM experiment

    The Georgetown–IBM experiment was an influential demonstration of machine translation, which was performed on January 7, 1954. Developed jointly by Georgetown University and IBM, the experiment involved completely automatic translation of more than sixty Russian sentences into English. == Background == Conceived and performed primarily in order to attract governmental and public interest and funding by showing the possibilities of machine translation, it was by no means a fully featured system: It had only six grammar rules and 250 lexical items in its vocabulary (of stems and endings). Words in the vocabulary were in the fields of politics, law, mathematics, chemistry, metallurgy, communications and military affairs. Vocabulary was punched onto punch cards. This complete dictionary was never fully shown (only the extended one from Garvin's article). Apart from general topics, the system was specialized in the domain of organic chemistry. The translation was carried out using an IBM 701 mainframe computer (launched in April 1953). The Georgetown-IBM experiment is the best-known result of the MIT conference in June 1952 to which all active researchers in the machine translation field were invited. At the conference, Duncan Harkin from US Department of Defense suggested that his department would finance a new machine translation project. Jerome Weisner supported the idea and offered finance from the Research Laboratory of Electronics at MIT. Leon Dostert had been invited to the project for his previous experience with the automatic correction of translations (back then 'mechanical translation'); his interpretation system had a strong impact on the Nuremberg War Crimes Tribunal. The linguistics part of the demonstration was carried out for the most part by linguist Paul Garvin who had also good knowledge of Russian. Over 60 Romanized Russian statements from a wide range of political, legal, mathematical, and scientific topics were entered into the machine by a computer operator who knew no Russian, and the resulting English translations appeared on a printer. The sentences to be translated were carefully selected. Many operations for the demonstration were fitted to specific words and sentences. In addition, there was no relational or sentence analysis which could recognize the sentence structure. The approach was mostly 'lexicographical' based on a dictionary where a specific word had a connection with specific rules and steps. == Algorithm == The algorithm first translates Russian words into numerical codes, then performs the following case-analysis on each numerical code to choose between possible English word translations, reorder the English words, or omit some English words. The flowchart of the algorithm is reproduced in (see Table 1 for the 6 rules). == Translation examples == How it analyzes Vyelyichyina ugla opryedyelyayetsya otnoshyenyiyem dlyini dugi k radyiusu (figure 2 of ). == Reception == Well publicized by journalists and perceived as a success, the experiment did encourage governments to invest in computational linguistics. The authors claimed that within three or five years, machine translation could well be a solved problem. However, the real progress was much slower, and after the ALPAC report in 1966, which found that the ten years of long research had failed to fulfill the expectations, funding was reduced dramatically. The demonstration was given widespread coverage in the foreign press, but only a small fraction of journalists drew attention to previous machine translation attempts.

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  • Automated storage and retrieval system

    Automated storage and retrieval system

    An automated storage and retrieval system (ASRS or AS/RS) consists of a variety of computer-controlled systems for automatically placing and retrieving loads from defined storage locations. Automated storage and retrieval systems (AS/RS) are typically used in applications where: There is a very high volume of loads being moved into and out of storage Storage density is important because of space constraints No value is added in this process (no processing, only storage and transport) Accuracy is critical because of potential expensive damages to the load An AS/RS can be used with standard loads as well as nonstandard loads, meaning that each standard load can fit in a uniformly-sized volume; for example, the film canisters in the image of the Defense Visual Information Center are each stored as part of the contents of the uniformly sized metal boxes, which are shown in the image. Standard loads simplify the handling of a request of an item. In addition, audits of the accuracy of the inventory of contents can be restricted to the contents of an individual metal box, rather than undergoing a top-to-bottom search of the entire facility, for a single item. They can also be used in self storage places. == Overview == AS/RS systems are designed for automated storage and retrieval of parts and items in manufacturing, distribution, retail, wholesale and institutions. They first originated in the 1960s, initially focusing on heavy pallet loads but with the evolution of the technology the handled loads have become smaller. The systems operate under computerized control, maintaining an inventory of stored items. Retrieval of items is accomplished by specifying the item type and quantity to be retrieved. The computer determines where in the storage area the item can be retrieved from and schedules the retrieval. It directs the proper automated storage and retrieval machine (SRM) to the location where the item is stored and directs the machine to deposit the item at a location where it is to be picked up. A system of conveyors and or automated guided vehicles is sometimes part of the AS/RS system. These take loads into and out of the storage area and move them to the manufacturing floor or loading docks. To store items, the pallet or tray is placed at an input station for the system, the information for inventory is entered into a computer terminal and the AS/RS system moves the load to the storage area, determines a suitable location for the item, and stores the load. As items are stored into or retrieved from the racks, the computer updates its inventory accordingly. The benefits of an AS/RS system include reduced labor for transporting items into and out of inventory, reduced inventory levels, more accurate tracking of inventory, and space savings. Items are often stored more densely than in systems where items are stored and retrieved manually. Within the storage, items can be placed on trays or hang from bars, which are attached to chains/drives in order to move up and down. The equipment required for an AS/RS include a storage & retrieval machine (SRM) that is used for rapid storage and retrieval of material. SRMs are used to move loads vertically or horizontally, and can also move laterally to place objects in the correct storage location. The trend towards Just In Time production often requires sub-pallet level availability of production inputs, and AS/RS is a much faster way of organizing the storage of smaller items next to production lines. The Material Handling Institute of America (MHIA), the non-profit trade association for the material handling world, and its members have categorised AS/RS into two primary segments: Fixed Aisle and Carousels/Vertical Lift Modules (VLMs). Both sets of technologies provide automated storage and retrieval for parts and items, but use different technologies. Each technology has its unique set of benefits and disadvantages. Fixed Aisle systems are characteristically larger systems whereas carousels and Vertical Lift Modules are used individually or grouped, but in small to medium-sized applications. A fixed-aisle AS/R machine (stacker crane) is one of two main designs: single-masted or double masted. Most are supported on a track and ceiling guided at the top by guide rails or channels to ensure accurate vertical alignment, although some are suspended from the ceiling. The 'shuttles' that make up the system travel between fixed storage shelves to deposit or retrieve a requested load (ranging from a single book in a library system to a several ton pallet of goods in a warehouse system). The entire unit moves horizontally within an aisle, while the shuttles are able to elevate up to the necessary height to reach the load, and can extend and retract to store or retrieve loads that are several positions deep in the shelving. A semi-automated system can be achieved by utilizing only specialized shuttles within an existing rack system. Another AS/RS technology is known as shuttle technology. In this technology the horizontal movement is made by independent shuttles each operating on one level of the rack while a lift at a fixed position within the rack is responsible for the vertical movement. By using two separate machines for these two axes the shuttle technology is able to provide higher throughput rates than stacker cranes. Storage and Retrieval Machines pick up or drop off loads to the rest of the supporting transportation system at specific stations, where inbound and outbound loads are precisely positioned for proper handling. In addition, there are several types of Automated Storage & Retrieval Systems (AS/RS) devices called Unit-load AS/RS, Mini-load AS/RS, Mid-Load AS/RS, Vertical Lift Modules (VLMs), Horizontal Carousels and Vertical Carousels. These systems are used either as stand-alone units or in integrated workstations called pods or systems. These units are usually integrated with various types of pick to light systems and use either a microprocessor controller for basic usage or inventory management software. These systems are ideal for increasing space utilization up to 90%, productivity levels by 90%, accuracy to 99.9%+ levels and throughput up to 750 lines per hour/per operator or more depending on the configuration of the system. == Horizontal carousels == Robotic Inserter/Extractor devices can be used for horizontal carousels. The robotic device is positioned in the front or rear of up to three horizontal carousels tiered high. The robot grabs the tote required in the order and often replenishes at the same time to speed up throughput. The tote(s) are then delivered to a conveyor, which routes it to a work station for picking or replenishing. Up to eight transactions per minute per unit can be done. Totes or containers up to 36" x 36" x 36" can be used in a system. On a simplistic level, horizontal carousels are also often used as "rotating shelving". With simple "fetch" command, items are brought to the operator and otherwise wasted space is eliminated. AS/RS Applications: Most applications of AS/RS technology have been associated with warehousing and distribution operations. An AS/RS can also be used to store raw materials and work in process in manufacturing. Three application areas can be distinguished for AS/RS: (1) Unit load storage and handling, (2) Order picking, and (3) Work in process storage. Unit load storage and retrieval applications are represented by unit load AS/RS and deep-lane storage systems. These kinds of applications are commonly found in warehousing for finishing goods in a distribution center, rarely in manufacturing. Deep-lane systems are used in the food industry. As described above, order picking involves retrieving materials in less than full unit load quantities. Minilpass, man-on board, and items retrieval systems are used for this second application area. Work in process storage is a more recent application of automated storage technology. While it is desirable to minimize the amount of work in process, WIP is unavoidable and must be effectively managed. Automated storage systems, either automated storage/retrieval systems or carousel systems, represent an efficient way to store materials between processing steps, particularly in batch and job shop production. In high production, work in process is often carried between operations by conveyor system, which this serve both storage and transport functions. === Inventory Category-specific AS/RS === Each inventory category—raw materials, work-in-process, and finished goods—requires its own specialized Automated Storage and Retrieval System (AS/RS). Particularly for work-in-process (WIP) inventories, due to variations in manufacturing processes, the AS/RS systems are significantly different in design and function, tailored specifically to match unique handling, storage, and retrieval requirements === Installed applications === Installed applications of this technology can be wide-ranging. In some librarie

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  • AI Subtitle Generators: Free vs Paid (2026)

    AI Subtitle Generators: Free vs Paid (2026)

    Looking for the best AI subtitle generator? An AI subtitle generator is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI subtitle generator 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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  • Best AI Presentation Makers in 2026

    Best AI Presentation Makers in 2026

    In search of the best AI presentation maker? An AI presentation maker 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 presentation maker 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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