AI Chat List

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

  • Co–Star

    Co–Star

    Co–Star is an American astrological social networking service founded in 2017, and headquartered in New York City. Users enter the date, time and place they were born to generate an astrological chart and daily horoscopes, which can be compared with those of other users. == History == The concept for Co-Star began in 2015 when Banu Guler created an astrological chart as a gift. The idea later developed into a mobile application with collaborators Anna Kopp and Ben Weitzman. The app publicly launched in 2017. The app includes astrological readings, charts, and daily push notifications that have been noted for their unconventional tone. In early 2018, the company raised a $750,000 pre-seed round from Female Founders Fund. In 2019, Co–Star raised a $5.2 million seed round from Maveron, Aspect, and 14W. In January 2020, Co–Star for Android was launched to a 120,000-person waitlist—two years after their iOS version. In April 2021, the company announced a $15 million Series A, led by Spark Capital. As of that date, Co–Star reported more than 20 million downloads and increased adoption among young women in the United States. == Features == Co–Star employs artificial intelligence to analyze publicly accessible NASA JPL data and find patterns in a user's transits. Co–Star's algorithm maps human-written snippets of text to planetary movements to display personalized content for each user. That content has been called “slightly robotic,” “wildly beautiful,” “truly insane," “brutally honest,” and compared to “a free therapy session.” In July 2023, Co–Star released an in-app service called The Void that allows users to ask open-ended questions and receive answers informed by Co–Star's astrological database.

    Read more →
  • METEO System

    METEO System

    The METEO System is a machine translation system specifically designed for the translation of the weather forecasts issued daily by Environment Canada. The system was used from 1981 to 30 September 2001 by Environment Canada to translate forecasts issued in French in the province of Quebec into English and those issued in English in other Canadian provinces into French. Since then, a competitor program has replaced METEO System after an open governmental bid. The system was developed by John Chandioux and was often mentioned as one of the few success stories in the field of machine translation. == History == The METEO System was in operational use at Environment Canada from 1982 to 2001. It stems from a prototype developed in 1975–76 by the TAUM Group, known as TAUM-METEO. The initial motivation to develop that prototype was that a junior translator came to TAUM to ask for help in translating weather bulletins at Environment Canada. Since all official communications emanating from the Canadian government must be available in French and English, because of the Official Languages Act of 1969, and weather bulletins represent a large amount of translation in real time, junior translators had to spend several months producing first draft translations, which were then revised by seniors. That was a difficult and tedious job, because of the specificities of the English and French sublanguages used, and not very rewarding, as the lifetime of a bulletin is only 4 hours. TAUM proposed to build a prototype MT system, and Environment Canada agreed to fund the project. A prototype was ready after a few months, with basic integration in the workflow of translation (source and target bulletins travelled over telex lines at the time and MT happened on a mainframe computer). The first version of the system (METEO 1) went into operation on a Control Data CDC 7600 supercomputer in March 1977. Chandioux then left the TAUM group to manage its operation and improve it, while the TAUM group embarked on a different project (TAUM-aviation, 1977–81). Benoit Thouin made improvements to the initial prototype over the subsequent year, and turned it into an operational system. After three years, METEO 1 had demonstrated the feasibility of microcomputer-based machine translation to the satisfaction of the Canadian government's Translation Bureau of Public Works and Government Services Canada. METEO 1 was formally adopted in 1981, replacing the junior translators in the workflow. Because of the need for high-quality translation, the revision step, done by senior translators, was maintained. The quality, measured as the percentage of edit operations (inserting or deleting a word counts as 1, replacing as 2) on the MT results, reached 85% in 1985. Until that time, the MT part was still implemented as a sequence of Q-systems. The Q-systems formalism is a rule-based SLLP (Specialized Language for Linguistic Programming) invented by Alain Colmerauer in 1967 as he was a postdoc coopérant at the TAUM group. He later invented the Prolog language in 1972 after returning to France and becoming a university professor in Marseille-Luminy. As the engine of the Q-systems is highly non-deterministic, and the manipulated data structures are in some ways too simple, without any types such as string or number, Chandioux encountered limitations in his efforts to raise translation quality and lower computation time to the point he could run it on microcomputers. In 1981, Chandioux created a new SLLP, or metalanguage for linguistic applications, based on the same basic algorithmic ideas as the Q-systems, but more deterministic, and offering typed labels on tree nodes. Following the advice of Bernard Vauquois and Colmerauer, he created GramR, and developed it for microcomputers. In 1982, he could start developing in GramR a new system for translating the weather bulletins on a high-end Cromemco microcomputer. METEO 2 went into operation in 1983. The software then ran in 48Kb of central memory with a 5Mb hard disk for paging. METEO 2 was the first MT application to run on a microcomputer. In 1985, the system had nothing left of the initial prototype, and was officially renamed METEO. It translated about 20 million words per year from English into French, and 10 million words from French into English, with a quality of 97%. Typically, it took 4 minutes for a bulletin in English to be sent from Winnipeg and come back in French after MT and human revision. In 1996, Chandioux developed a special version of his system (METEO 96) which was used to translate the weather forecasts (different kinds of bulletins) issued by the US National Weather Service during the 1996 Summer Olympics in Atlanta. The last known version of the system, METEO 5, dates from 1997 and ran on an IBM PC network under Windows NT. It translated 10 pages per second, but was able to fit into a 1.44Mb floppy disk.

    Read more →
  • The Best Free AI Voice Assistant for Beginners

    The Best Free AI Voice Assistant for Beginners

    Looking for the best AI voice assistant? An AI voice assistant 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 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.

    Read more →
  • Cortana (virtual assistant)

    Cortana (virtual assistant)

    Cortana is a discontinued virtual assistant developed by Microsoft that used the Bing search engine to perform tasks such as setting reminders and answering questions for users. Cortana was available in English, Portuguese, French, German, Italian, Spanish, Chinese, and Japanese language editions, depending on the software platform and region in which it was used. In 2019, Microsoft began reducing the prevalence of Cortana and converting it from an assistant into different software integrations. It was split from the Windows 10 search bar in April 2019. In January 2020, the Cortana mobile app was removed from certain markets, and on March 31, 2021, the Cortana mobile app was shut down globally. On June 2, 2023, Microsoft announced that support for the Cortana standalone app on Microsoft Windows would end in late 2023 and would be replaced by Microsoft Copilot, an AI chatbot. Support for Cortana in the Microsoft Outlook and Microsoft 365 mobile apps was discontinued in fall of 2023. == History == === Beginnings (2009–2014) === The development of Cortana started in 2009 in the Microsoft Speech products team with general manager Zig Serafin and Chief Scientist Larry Heck. Heck and Serafin established the vision, mission, and long-range plan for Microsoft's digital personal assistant and they built a team with the expertise to create the initial prototypes for Cortana. Some of the key researchers in these early efforts included Microsoft Research researchers Dilek Hakkani-Tür, Gokhan Tur, Andreas Stolcke, and Malcolm Slaney, research software developer Madhu Chinthakunta, and user experience designer Lisa Stifelman. To develop the Cortana digital assistant, the team interviewed human personal assistants. The interviews inspired a number of unique features in Cortana, including the assistant's "notebook" feature. Originally, Cortana was meant to be only a codename, but a petition on Windows Phone's UserVoice site proved to be popular and made the codename official. Cortana was demonstrated for the first time at the Microsoft Build developer conference in San Francisco in April 2014. It was launched as a key ingredient of Microsoft's planned "makeover" of future operating systems for Windows Phone and Windows. It was named after Cortana, a synthetic intelligence character in Microsoft's Halo video game franchise originating in Bungie folklore, with Jen Taylor, the character's voice actress, returning to voice the personal assistant's US-specific version. === Expansion (2015–2018) === In January 2015, Microsoft announced the availability of Cortana for Windows 10 desktops and mobile devices as part of merging Windows Phone into the operating system at large. On May 26, 2015, Microsoft announced that Cortana would also be available on other mobile platforms. An Android release was set for July 2015, but the Android APK file containing Cortana was leaked ahead of its release. It was officially released, along with an iOS version, in December 2015. During E3 2015, Microsoft announced that Cortana would come to the Xbox One as part of a universally designed Windows 10 update for the console. Microsoft integrated Cortana into numerous products such as Microsoft Edge. Microsoft's Cortana assistant was deeply integrated into the browser. Cortana was able to find opening hours when on restaurant sites, show retail coupons for websites, or show weather information in the address bar. At the Worldwide Partners Conference 2015 Microsoft demonstrated Cortana integration with products such as GigJam. Conversely, Microsoft announced in late April 2016 that it would block anything other than Bing and Edge from being used to complete Cortana searches, again raising questions of anti-competitive practices by the company. Microsoft's "Windows in the car" concept included Cortana. The concept makes it possible for drivers to make restaurant reservations and see places before they go there. At Microsoft Build 2016, Microsoft announced plans to integrate Cortana into Skype (Microsoft's video-conferencing and instant messaging service) as a bot to allow users to order food, book trips, transcribe video messages and make calendar appointments through Cortana in addition to other bots. As of 2016, Cortana was able to underline certain words and phrases in Skype conversations that relate to contacts and corporations. A writer from Engadget has criticised the Cortana integration in Skype for responding only to very specific keywords, feeling as if she was "chatting with a search engine" due to the impersonal way the bots replied to certain words such as "Hello" causing the Bing Music bot to bring up Adele's song of that name. Microsoft also announced at Microsoft Build 2016 that Cortana would be able to cloud-synchronise notifications between Windows 10 Mobile's and Windows 10's Action Center, as well as notifications from Android devices. In December 2016, Microsoft announced the preview of Calendar.help, a service that enabled people to delegate the scheduling of meetings to Cortana. Users interact with Cortana by including her in email conversations. Cortana would then check people's availability in Outlook Calendar or Google Calendar, and work with others Cc'd on the email to schedule the meeting. The service relied on automation and human-based computation. In May 2017, Microsoft announced INVOKE, a voice-activated speaker featuring Cortana, in collaboration with Harman Kardon. The premium speaker has a cylindrical design and offers 360-degree sound, the ability to make and receive calls with Skype, and all of the other features currently available with Cortana. In 2017, Microsoft partnered with Amazon to integrate Echo and Cortana with each other, allowing users of each smart assistant to summon the other via a command. This feature preview was released in August 2018. Windows 10 users were able to just say "Hey Cortana, open Alexa" and Echo users were able to say "Alexa, open Cortana" to summon the other assistant. === Decreasing focus and discontinuation (2019–2024) === In January 2019, Microsoft CEO Satya Nadella stated that he no longer saw Cortana as a direct competitor against Alexa and Siri. Shortly thereafter, Microsoft began reducing the prevalence of Cortana and converting it from an assistant into different software integrations. It was split from the Windows 10 search bar in April 2019. In January 2020, the Cortana mobile app was removed from certain markets, and then, on July 24, 2020, Cortana was removed from the Xbox dashboard as part of a redesign. On January 31, 2021, Microsoft removed the Cortana mobile application in many markets, including the UK, Australia, Germany, Mexico, China, Spain, Canada, and India. On March 31, 2021, Microsoft shut down the Cortana apps globally for iOS and Android and removed the apps entirely from their corresponding app stores. To access previously recorded content, users had to use Cortana on Windows 10 or other specialized Microsoft applications. Microsoft also reduced emphasis on Cortana in Windows with the 2021 release of Windows 11. Cortana was not used during the device setup process or pinned to the taskbar by default. On June 2, 2023, Microsoft announced the Cortana standalone app on Windows 10 and Windows 11 which would shut down later in the year. In its support article, Microsoft listed several alternatives, most of which have since been rebranded as Microsoft Copilot. They also added that the change would not impact Cortana in Office 365 and Teams environments. On August 11, 2023, Microsoft updated the Cortana standalone app in Windows, informing that it was deprecated and can no longer be used. Microsoft's support article announcing the deprecation of Cortana was updated to reflect this change. Along with the deprecation of the standalone app, it was announced that Cortana support in Teams mobile, Microsoft Teams displays, and Teams rooms would end in late 2023. The support article states that Cortana in the “Play my emails” feature of the Microsoft Outlook mobile app would continue to be available. Later in June 2024, the support article was updated, stating that Cortana in the voice search and the "Play my emails" feature is now removed from the Microsoft Outlook mobile app, officially marking the discontinuation of Cortana across all Microsoft products. On May 22, 2024, Microsoft announced the Windows 11 24H2 update, which removed Cortana, Tips, and WordPad from systems. == Functionality == Cortana was able to set reminders, recognize natural voice without the requirement for keyboard input, and answer questions using information from the Bing search engine. Searches using Windows 10 are made only with the Microsoft Bing search engine, and all links will open with Microsoft Edge, except when a screen reader such as Narrator was being used, where the links will open in Internet Explorer. Windows Phone 8.1's universal Bing SmartSearch features were incorporated into Cortana, which replaced the

    Read more →
  • Clips (software)

    Clips (software)

    Clips is a discontinued mobile video editing software application created by Apple Inc. It was released onto the iOS App Store on April 6, 2017, for free. Initially, it was only available on 64-bit devices running iOS 10.3 or later; as of version 3.1.3, it requires iOS 16.0 or later. Apple describes it as an app for "making and sharing fun videos with text, effects, graphics, and more.". Its final release was on May 9, 2024 before was removed from the App Store on October 10, 2025. == Features == After launching of the app, the user sees the view of the front-facing camera. The app allows the user to create a new clip by tapping on a red record button, or use photos or videos from the device's photo library. Once a clip is recorded, it can be added to a project timeline shown at the bottom of the screen. The user can share their project on social media platforms. The user can also add filters and effects to the project. "Live Titles" (available in several styles) can also be created by dictating to the device.

    Read more →
  • David Horn (Israeli physicist)

    David Horn (Israeli physicist)

    David Horn (Hebrew: דוד הורן; born 10 September 1937) is a Professor (Emeritus) of Physics in the School of Physics and Astronomy at Tel Aviv University (TAU), Israel. He has served as Vice-Rector of TAU, Chairman of the School of Physics and Astronomy and as Dean of the Faculty of Exact Sciences in TAU. He is a fellow of the American Physical Society, nominated for "contributions to theoretical particle physics, including the seminal work on finite energy sum rules, research of the phenomenology of hadronic processes, and investigation of Hamiltonian lattice theories". == Early life and education == David Horn was born and educated in Haifa. He graduated from the Reali School in 1955. He began his academic studies in Physics at the Technion in Haifa in 1957, and received his B.Sc. (Summa Cum Laude) in 1961, and M.Sc. in 1962. He continued his Ph.D. studies at the Hebrew University of Jerusalem until 1965. His thesis on "Some Aspects of the Structure of Weak Interactions" was supervised by Prof. Yuval Ne'eman. == Career == Horn joined the newly founded Tel Aviv University as an assistant in 1962. He became a lecturer in 1965, a senior lecturer in 1967 and an associate professor in 1968. He was promoted to full professor of Physics in 1972. In 1974 he became the incumbent of the Edouard and Francoise Jaupart Chair of Theoretical Physics of Particles and Fields, a position he held until 2007. Horn has supervised 43 graduate students at TAU and authored over 240 scientific publications. He retired as a professor emeritus in 2005, and continues to be an active researcher. Horn spent a significant part of his career holding visiting academic positions at other universities and research institutes, including: Postdoctoral Fellow at Argonne National Lab, ILL, Research Fellow and three times Visiting Associate at California Institute of Technology, Pasadena, CA, Visitor at CERN in Geneva, Visiting Professor at Cornell University, NY, Member of the Institute for Advanced Study, Princeton, NJ, Visiting Professor at SLAC in Stanford University, CA, and Visiting Professor at Kyoto University, Japan. Beginning from 1980, Horn held official positions at Tel Aviv University, starting with tenure as Vice-Rector (1980-1983), a position he left for research at SLAC. After returning he was nominated Chairman of the Department of High Energy Physics (1984-1986), followed by tenures as Chairman of the School of Physics and Astronomy (1986-9), Dean of the Raymond and Beverly Sackler Faculty of Exact Sciences (1990-1995), and first Director of the Adams Super Center for Brain Studies (1993-2000). Horn has also held national and international professional positions. He was Chairman of the Israel Commission for High Energy Physics (1983-2003), and, in this capacity, served as an Israeli observer of the council of CERN (1991-2003). He served as member of the Israel Council for Higher Education (1987-1991), member of the Executive Committee of the European Physical Society (1989-1992) and member of the European Strategy Forum on Research Infrastructures (2005-2017). He chaired the Israeli Committee of Research Infrastructures (2012-2016), issuing roadmaps for scientific RI in 2013 and 2016. == Research == Horn's research work focused on theory and phenomenology of High Energy Physics until 1990. He then shifted his interests to Neural Computation and Machine Learning and, since 2005, he has also published in Bioinformatics. Together with Richard Dolen and Christoph Schmid he discovered the Finite Energy Sum Rules in 1967. It was a realization of the bootstrap approach to hadronic structure, and became known as the Dolen-Horn-Schmid Duality. Together with Richard Silver he investigated a model of coherent production of pions at high energy hadron collisions in 1971, and together with Jeffrey Mandula he undertook the investigation of mesons with constituent gluons in 1978. Moving to lattice gauge theories in 1979, he discovered, together with Shimon Yankielowic and Marvin Weinstein, a non-confining phase in Z(N) theories for large N. In 1981 he demonstrated the existence of finite matrix models with link gauge fields, nowadays known as quantum link models. In 1984 Horn and Weinstein developed the t-expansion methodology. Horn's contributions to neural modeling include a novel mechanism for memory maintenance via neuronal regulation in 1998, developed with Nir Levy and Eytan Ruppin and unsupervised learning of natural languages in 2005, a joint work with Zach Solan, Eytan Ruppin and Shimon Edelman, introducing novel algorithms for motif and grammar extraction from text. Horn has contributed to algorithms of clustering, an important topic in Machine Learning, by developing Support Vector Clustering (SVC) in 2001, together with Asa Ben Hur, Hava Siegelmann and Vladimir Vapnik. This was followed shortly thereafter by a joint work with Assaf Gottlieb on Quantum Clustering (QC). His contributions to Bioinformatics include motif descriptions of function and structure of proteins, as well as motif studies of genomic structures. Together with Erez Persi he studied compositional order of proteomes, and repeat instability of genomes, as evolution markers of organisms and of cancer (a joint work with Persi and others). == Honors == Horn is a Fellow of the American Physical Society (1985) and a Fellow of the Israel Physical Society (2018). == Publications == === Selected articles === R. Dolen, D. Horn and C. Schmid; Prediction of Regge-parameters of rho poles from low-energy pi-N scattering data Phys. Rev. Lett. 19 (1967) 402–407. Finite-Energy Sum Rules and Their Application to pi-N Charge Exchange Phys. Rev. 166 (1968) 1768–1781. D. Horn and R. Silver: Coherent production of pions, Annals Phys. 66 (1971) 509-541 T. Banks, D. Horn and H. Neuberger: Bosonization of the SU(N) Thirring Models, Nucl. Phys. B108, 119 (1976). D. Horn and J. Mandula: Model of Mesons with Constituent Gluons, Phys. Rev. D17, 898 (1978). D. Horn, M. Weinstein and S. Yankielowicz: Hamiltonian Approach to Z(N) Lattice Gauge Theories, Phys. Rev. D19, 3715 (1979). D. Horn: Finite Matrix Models with Continuous Local Gauge Invariance, Phys. Lett. 100B, 149-151 (1981). T. Banks, Y. Dothan and D. Horn: Geometric Fermions, Phys. Lett. 117B, 413 (1982). D. Horn and M. Weinstein: The t expansion: A nonperturbative analytic tool for Hamiltonian systems. Phys. Rev. D 30, 1256-1270 (1984). Ury Naftaly, Nathan Intrator and David Horn: Optimal Ensemble Averaging of Neural Networks. Network, Computation in Neural Systems, 8, 283-296 (1997). David Horn, Nir Levy, Eytan Ruppin: Memory Maintenance via Neuronal Regulation, Neural Computation, 10, 1-18 (1998). Asa Ben-Hur, David Horn, Hava Siegelmann and Vladimir Vapnik: Support Vector Clustering. Journal of Machine Learning Research 2, 125-137 (2001). David Horn and Assaf Gottlieb: Algorithm for data clustering in pattern recognition problems based on quantum mechanics, Phys. Rev. Lett. 88 (2002) 18702 Zach Solan, David Horn, Eytan Ruppin and Shimon Edelman: Unsupervised learning of natural languages, Proc. Natl. Acad. Sc. 102 (2005) 11629–11634. Vered Kunik, Yasmine Meroz, Zach Solan, Ben Sandbank, Uri Weingart, Eytan Ruppin and David Horn: Functional representation of enzymes by specific peptides. PLOS Computational Biology 2007, 3(8):e167. Benny Chor, David Horn, Yaron Levy, Nick Goldman and Tim Massingham: Genomic DNA k-mer spectra: models and modalities. Genome Biology 2009, 10(10):R108 Erez Persi and David Horn. Systematic Analysis of Compositional Order of Proteins Reveals New Characteristics of Biological Functions and a Universal Correlate of Macroevolution. PLoS Comput Biol 9 (2013): e1003346. David Horn. Taxa counting using Specific Peptides of Aminoacyl tRNA Synthetases Encyclopedia of Metagenomics, Springer, 2013. Sagi Shporer, Benny Chor, Saharon Rosset, David Horn. Inversion symmetry of DNA k-mer counts: validity and deviations. BMC Genomics 2016, 17:696 Erez Persi, Davide Prandi, Yuri I. Wolf, Yair Pozniak, Christopher Barbieri, Paola Gasperini, Himisha Beltran, Bishoy M. Faltas, Mark A. Rubin, Tamar Geiger, Eugene V. Koonin, Francesca Demichelis, David Horn. Proteomic and Genomic Signatures of Repeat Instability in Cancer and Adjacent Normal Tissues. PNAS 116, 34, 2019 - 08790 === Book === David Horn and Fredrick Zachariasen: Hadron Physics at Very High Energies. Benjamin 1973. === Patents === Method and Apparatus for Quantum Clustering. USA Patent No. 7,653,646 B2. Method for discovering relationships in data by dynamic quantum clustering USA Patent No 8874412 and USA Patent No. 9,646,074. == Personal life == Horn was married to Nira Fuss since 1963 until her death in 2019. He is a father of three, Yuval, Tamar, and Oded, and grandfather of nine. He lives in Tel Aviv, Israel.

    Read more →
  • 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).

    Read more →
  • How to Choose an AI Logo Maker

    How to Choose an AI Logo Maker

    Trying to pick the best AI logo maker? An AI logo maker 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 logo maker 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.

    Read more →
  • Document classification

    Document classification

    Document classification or document categorization is a problem in library science, information science and computer science. The task is to assign a document to one or more classes or categories. This may be done "manually" (or "intellectually") or algorithmically. The intellectual classification of documents has mostly been the province of library science, while the algorithmic classification of documents is mainly in information science and computer science. The problems are overlapping, however, and there is therefore interdisciplinary research on document classification. The documents to be classified may be texts, images, music, etc. Each kind of document possesses its special classification problems. When not otherwise specified, text classification is implied. Documents may be classified according to their subjects or according to other attributes (such as document type, author, printing year etc.). In the rest of this article only subject classification is considered. There are two main philosophies of subject classification of documents: the content-based approach and the request-based approach. == "Content-based" versus "request-based" classification == Content-based classification is classification in which the weight given to particular subjects in a document determines the class to which the document is assigned. It is, for example, a common rule for classification in libraries, that at least 20% of the content of a book should be about the class to which the book is assigned. In automatic classification it could be the number of times given words appears in a document. Request-oriented classification (or -indexing) is classification in which the anticipated request from users is influencing how documents are being classified. The classifier asks themself: “Under which descriptors should this entity be found?” and “think of all the possible queries and decide for which ones the entity at hand is relevant” (Soergel, 1985, p. 230). Request-oriented classification may be classification that is targeted towards a particular audience or user group. For example, a library or a database for feminist studies may classify/index documents differently when compared to a historical library. It is probably better, however, to understand request-oriented classification as policy-based classification: The classification is done according to some ideals and reflects the purpose of the library or database doing the classification. In this way it is not necessarily a kind of classification or indexing based on user studies. Only if empirical data about use or users are applied should request-oriented classification be regarded as a user-based approach. == Classification versus indexing == Sometimes a distinction is made between assigning documents to classes ("classification") versus assigning subjects to documents ("subject indexing") but as Frederick Wilfrid Lancaster has argued, this distinction is not fruitful. "These terminological distinctions,” he writes, “are quite meaningless and only serve to cause confusion” (Lancaster, 2003, p. 21). The view that this distinction is purely superficial is also supported by the fact that a classification system may be transformed into a thesaurus and vice versa (cf., Aitchison, 1986, 2004; Broughton, 2008; Riesthuis & Bliedung, 1991). Therefore, assigning a subject term to a document in an index is equivalent to assigning that document to the class of documents indexed by that term (all documents indexed or classified as X belong to the same class of documents). == Automatic document classification (ADC) == Automatic document classification tasks can be divided into three sorts: supervised document classification where some external mechanism (such as human feedback) provides information on the correct classification for documents, unsupervised document classification (also known as document clustering), where the classification must be done entirely without reference to external information, and semi-supervised document classification, where parts of the documents are labeled by the external mechanism. There are several software products under various license models available. === Techniques === Automatic document classification techniques include: Artificial neural network Concept Mining Decision trees such as ID3 or C4.5 Expectation maximization (EM) Instantaneously trained neural networks Latent semantic indexing Multiple-instance learning Naive Bayes classifier Natural language processing approaches Rough set-based classifier Soft set-based classifier Support vector machines (SVM) K-nearest neighbour algorithms tf–idf == Applications == Classification techniques have been applied to spam filtering, a process which tries to discern E-mail spam messages from legitimate emails email routing, sending an email sent to a general address to a specific address or mailbox depending on topic language identification, automatically determining the language of a text genre classification, automatically determining the genre of a text readability assessment, automatically determining the degree of readability of a text, either to find suitable materials for different age groups or reader types or as part of a larger text simplification system sentiment analysis, determining the attitude of a speaker or a writer with respect to some topic or the overall contextual polarity of a document. health-related classification using social media in public health surveillance article triage, selecting articles that are relevant for manual literature curation, for example as is being done as the first step to generate manually curated annotation databases in biology

    Read more →
  • How to Choose an AI Virtual Assistant

    How to Choose an AI Virtual Assistant

    In search of the best AI virtual assistant? An AI virtual assistant 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 virtual assistant slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

    Read more →
  • Myhill–Nerode theorem

    Myhill–Nerode theorem

    In the theory of formal languages, the Myhill–Nerode theorem provides a necessary and sufficient condition for a language to be regular. The theorem is named for John Myhill and Anil Nerode, who proved it at the University of Chicago in 1957 (Nerode & Sauer 1957, p. ii). == Statement == Given a language L {\displaystyle L} , and a pair of strings x {\displaystyle x} and y {\displaystyle y} , define a distinguishing extension to be a string z {\displaystyle z} such that exactly one of the two strings x z {\displaystyle xz} and y z {\displaystyle yz} belongs to L {\displaystyle L} . Define a relation ∼ L {\displaystyle \sim _{L}} on strings as x ∼ L y {\displaystyle x\;\sim _{L}\ y} if there is no distinguishing extension for x {\displaystyle x} and y {\displaystyle y} . It is easy to show that ∼ L {\displaystyle \sim _{L}} is an equivalence relation on strings, and thus it divides the set of all strings into equivalence classes. The Myhill–Nerode theorem states that a language L {\displaystyle L} is regular if and only if ∼ L {\displaystyle \sim _{L}} has a finite number of equivalence classes, and moreover, that this number is equal to the number of states in the minimal deterministic finite automaton (DFA) accepting L {\displaystyle L} . Furthermore, every minimal DFA for the language is isomorphic to the canonical one (Hopcroft & Ullman 1979). Generally, for any language, the constructed automaton is a state automaton acceptor. However, it does not necessarily have finitely many states. The Myhill–Nerode theorem shows that finiteness is necessary and sufficient for language regularity. Some authors refer to the ∼ L {\displaystyle \sim _{L}} relation as Nerode congruence, in honor of Anil Nerode. == Use and consequences == The Myhill–Nerode theorem may be used to show that a language L {\displaystyle L} is regular by proving that the number of equivalence classes of ∼ L {\displaystyle \sim _{L}} is finite. This may be done by an exhaustive case analysis in which, beginning from the empty string, distinguishing extensions are used to find additional equivalence classes until no more can be found. For example, the language consisting of binary representations of numbers that can be divided by 3 is regular. Given two binary strings x , y {\displaystyle x,y} , extending them by one digit gives 2 x + b , 2 y + b {\displaystyle 2x+b,2y+b} , so 2 x + b ≡ 2 y + b mod 3 {\displaystyle 2x+b\equiv 2y+b\mod 3} iff x ≡ y mod 3 {\displaystyle x\equiv y\mod 3} . Thus, 00 {\displaystyle 00} (or 11 {\displaystyle 11} ), 01 {\displaystyle 01} , and 10 {\displaystyle 10} are the only distinguishing extensions, resulting in the 3 classes. The minimal automaton accepting our language would have three states corresponding to these three equivalence classes. Another immediate corollary of the theorem is that if for a language L {\displaystyle L} the relation ∼ L {\displaystyle \sim _{L}} has infinitely many equivalence classes, it is not regular. It is this corollary that is frequently used to prove that a language is not regular. == Generalizations == The Myhill–Nerode theorem can be generalized to tree automata.

    Read more →
  • Language and Computers

    Language and Computers

    Language and Computers: Studies in Practical Linguistics (ISSN 0921-5034) is a book series on corpus linguistics and related areas. As studies in linguistics, volumes in the series have, by definition, their foundations in linguistic theory; however, they are not concerned with theory for theory's sake, but always with a definite direct or indirect interest in the possibilities of practical application in the dynamic area where language and computers meet. The book series was founded in 1988, and is published by Brill|Rodopi. == Editors == Christian Mair Charles F. Meyer == Volumes == Volumes include: # 77. English Corpus Linguistics: Variation in Time, Space and Genre. Selected papers from ICAME 32., Edited by Gisle Andersen and Kristin Bech. ISBN 978-90-420-3679-6 E-ISBN 978-94-012-0940-3 # 76. English Corpus Linguistics: Crossing Paths., Edited by Merja Kytö. ISBN 978-90-420-3518-8 E-ISBN 978-94-012-0793-5 # 75. Corpus Linguistics and Variation in English.Theory and Description., Edited by Joybrato Mukherjee and Magnus Huber. ISBN 978-90-420-3495-2 E-ISBN 978-94-012-0771-3 # 74. English Corpus Linguistics: Looking back, Moving forward. Papers from the 30th International Conference on English Language Research on Computerized Corpora (ICAME 30), Lancaster, UK, 27–31 May 2009., Edited by Sebastian Hoffmann, Paul Rayson and Geoffrey Leech. ISBN 978-90-420-3466-2 E-ISBN 978-94-012-0747-8 #73. Corpus-based Studies in Language Use, Language Learning, and Language Documentation., Edited by John Newman, Harald Baayen and Sally Rice. ISBN 978-90-420-3401-3 E-ISBN 978-94-012-0688-4 #72. The Progressive in Modern English. A Corpus-Based Study of Grammaticalization and Related Changes., by Svenja Kranich. ISBN 978-90-420-3143-2 E-ISBN 978-90-420-3144-9 #71. Corpus-linguistic applications. Current studies, new directions, Edited by Stefan Th. Gries, Stefanie Wulff, and Mark Davies.. ISBN 978-90-420-2800-5 #70. A resource-light approach to morpho-syntactic tagging., by Anna Feldman and Jirka Hana. ISBN 978-90-420-2768-8 #69. Corpus Linguistics. Refinements and Reassessments., Edited by Antoinette Renouf and Andrew Kehoe. ISBN 978-90-420-2597-4 #68. Corpora: Pragmatics and Discourse. Papers from the 29th International Conference on English Language Research on Computerized Corpora (ICAME 29). Ascona, Switzerland, 14–18 May 2008., Edited by Andreas H. Jucker, Daniel Schreier and Marianne Hundt. ISBN 978-90-420-2592-9 #67. Modals and Quasi-modals in English., by Peter Collins. ISBN 978-90-420-2532-5 #66. Linking up contrastive and learner corpus research., Edited by Gaëtanelle Gilquin, Szilvia Papp and María Belén Díez-Bedmar. ISBN 978-90-420-2446-5 #64. Language, People, Numbers. Corpus Linguistics and Society., Edited by Andrea Gerbig and Oliver Mason. ISBN 978-90-420-2350-5 #63. Variation and change in the lexicon. A corpus-based analysis of adjectives in English ending in –ic and –ical. , by Mark Kaunisto. ISBN 978-90-420-2233-1 #62. Corpus Linguistics 25 Years on., Edited by Roberta Facchinetti. ISBN 978-90-420-2195-2 #61. Corpora in the Foreign Language Classroom. Selected papers from the Sixth International Conference on Teaching and Language Corpora (TaLC 6), Edited by Encarnación Hidalgo, Luis Quereda and Juan Santana. ISBN 978-90-420-2142-6 #60. Corpus Linguistics Beyond the Word. Corpus Research from Phrase to Discourse, Edited by Eileen Fitzpatrick. ISBN 978-90-420-2135-8 #59. Corpus Linguistics and the Web., Edited by Marianne Hundt, Nadja Nesselhauf and Carolin Biewer. ISBN 978-90-420-2128-0 #58. English mediopassive constructions. A cognitive, corpus-based study of their origin, spread, and current status, by Marianne Hundt. ISBN 978-90-420-2127-3 / ISBN 90-420-2127-6

    Read more →
  • Rendering equation

    Rendering equation

    In computer graphics, the rendering equation is an integral equation that expresses the amount of light leaving a point on a surface as the sum of emitted light and reflected light. It was independently introduced into computer graphics by David Immel et al. and James Kajiya in 1986. The equation is important in the theory of physically based rendering, describing the relationships between the bidirectional reflectance distribution function (BRDF) and the radiometric quantities used in rendering. The rendering equation is defined at every point on every surface in the scene being rendered, including points hidden from the camera. The incoming light quantities on the right side of the equation usually come from the left (outgoing) side at other points in the scene (ray casting can be used to find these other points). The radiosity rendering method solves a discrete approximation of this system of equations. In distributed ray tracing, the integral on the right side of the equation may be evaluated using Monte Carlo integration by randomly sampling possible incoming light directions. Path tracing improves and simplifies this method. The rendering equation can be extended to handle effects such as fluorescence (in which some absorbed energy is re-emitted at different wavelengths) and can support transparent and translucent materials by using a bidirectional scattering distribution function (BSDF) in place of a BRDF. The theory of path tracing sometimes uses a path integral (integral over possible paths from a light source to a point) instead of the integral over possible incoming directions. == Equation form == The rendering equation may be written in the form L o ( x , ω o , λ , t ) = L e ( x , ω o , λ , t ) + L r ( x , ω o , λ , t ) {\displaystyle L_{\text{o}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)=L_{\text{e}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)+L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} L r ( x , ω o , λ , t ) = ∫ Ω f r ( x , ω i , ω o , λ , t ) L i ( x , ω i , λ , t ) ( ω i ⋅ n ) d ⁡ ω i {\displaystyle L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)=\int _{\Omega }f_{\text{r}}(\mathbf {x} ,\omega _{\text{i}},\omega _{\text{o}},\lambda ,t)L_{\text{i}}(\mathbf {x} ,\omega _{\text{i}},\lambda ,t)(\omega _{\text{i}}\cdot \mathbf {n} )\operatorname {d} \omega _{\text{i}}} where L o ( x , ω o , λ , t ) {\displaystyle L_{\text{o}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is the total spectral radiance of wavelength λ {\displaystyle \lambda } directed outward along direction ω o {\displaystyle \omega _{\text{o}}} at time t {\displaystyle t} , from a particular position x {\displaystyle \mathbf {x} } x {\displaystyle \mathbf {x} } is the location in space ω o {\displaystyle \omega _{\text{o}}} is the direction of the outgoing light λ {\displaystyle \lambda } is a particular wavelength of light t {\displaystyle t} is time L e ( x , ω o , λ , t ) {\displaystyle L_{\text{e}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is emitted spectral radiance L r ( x , ω o , λ , t ) {\displaystyle L_{\text{r}}(\mathbf {x} ,\omega _{\text{o}},\lambda ,t)} is reflected spectral radiance ∫ Ω … d ⁡ ω i {\displaystyle \int _{\Omega }\dots \operatorname {d} \omega _{\text{i}}} is an integral over Ω {\displaystyle \Omega } Ω {\displaystyle \Omega } is the unit hemisphere centered around n {\displaystyle \mathbf {n} } containing all possible values for ω i {\displaystyle \omega _{\text{i}}} where ω i ⋅ n > 0 {\displaystyle \omega _{\text{i}}\cdot \mathbf {n} >0} f r ( x , ω i , ω o , λ , t ) {\displaystyle f_{\text{r}}(\mathbf {x} ,\omega _{\text{i}},\omega _{\text{o}},\lambda ,t)} is the bidirectional reflectance distribution function, the proportion of light reflected from ω i {\displaystyle \omega _{\text{i}}} to ω o {\displaystyle \omega _{\text{o}}} at position x {\displaystyle \mathbf {x} } , time t {\displaystyle t} , and at wavelength λ {\displaystyle \lambda } ω i {\displaystyle \omega _{\text{i}}} is the negative direction of the incoming light L i ( x , ω i , λ , t ) {\displaystyle L_{\text{i}}(\mathbf {x} ,\omega _{\text{i}},\lambda ,t)} is spectral radiance of wavelength λ {\displaystyle \lambda } coming inward toward x {\displaystyle \mathbf {x} } from direction ω i {\displaystyle \omega _{\text{i}}} at time t {\displaystyle t} n {\displaystyle \mathbf {n} } is the surface normal at x {\displaystyle \mathbf {x} } ω i ⋅ n {\displaystyle \omega _{\text{i}}\cdot \mathbf {n} } is the weakening factor of outward irradiance due to incident angle, as the light flux is smeared across a surface whose area is larger than the projected area perpendicular to the ray. This is often written as cos ⁡ θ i {\displaystyle \cos \theta _{i}} . Two noteworthy features are: its linearity—it is composed only of multiplications and additions, and its spatial homogeneity—it is the same in all positions and orientations. These mean a wide range of factorings and rearrangements of the equation are possible. It is a Fredholm integral equation of the second kind, similar to those that arise in quantum field theory. Note this equation's spectral and time dependence — L o {\displaystyle L_{\text{o}}} may be sampled at or integrated over sections of the visible spectrum to obtain, for example, a trichromatic color sample. A pixel value for a single frame in an animation may be obtained by fixing t ; {\displaystyle t;} motion blur can be produced by averaging L o {\displaystyle L_{\text{o}}} over some given time interval (by integrating over the time interval and dividing by the length of the interval). Note that a solution to the rendering equation is the function L o {\displaystyle L_{\text{o}}} . The function L i {\displaystyle L_{\text{i}}} is related to L o {\displaystyle L_{\text{o}}} via a ray-tracing operation: The incoming radiance from some direction at one point is the outgoing radiance at some other point in the opposite direction. == Applications == Solving the rendering equation for any given scene is the primary challenge in realistic rendering. One approach to solving the equation is based on finite element methods, leading to the radiosity algorithm. Another approach using Monte Carlo methods has led to many different algorithms including path tracing, photon mapping, and Metropolis light transport, among others. == Limitations == Although the equation is very general, it does not capture every aspect of light reflection. Some missing aspects include the following: Transmission, which occurs when light is transmitted through the surface, such as when it hits a glass object or a water surface, Subsurface scattering, where the spatial locations for incoming and departing light are different. Surfaces rendered without accounting for subsurface scattering may appear unnaturally opaque — however, it is not necessary to account for this if transmission is included in the equation, since that will effectively include also light scattered under the surface, Polarization, where different light polarizations will sometimes have different reflection distributions, for example when light bounces at a water surface, Phosphorescence, which occurs when light or other electromagnetic radiation is absorbed at one moment and emitted at a later moment, usually with a longer wavelength (unless the absorbed electromagnetic radiation is very intense), Interference, where the wave properties of light are exhibited, Fluorescence, where the absorbed and emitted light have different wavelengths, Non-linear effects, where very intense light can increase the energy level of an electron with more energy than that of a single photon (this can occur if the electron is hit by two photons at the same time), and emission of light with higher frequency than the frequency of the light that hit the surface suddenly becomes possible, and Doppler effect, where light that bounces off an object moving at a very high speed will get its wavelength changed: if the light bounces off an object that is moving towards it, the light will be blueshifted and the photons will be packed more closely so the photon flux will be increased; if it bounces off an object moving away from it, it will be redshifted and the photon flux will be decreased. This effect becomes apparent only at speeds comparable to the speed of light, which is not the case for most rendering applications. For scenes that are either not composed of simple surfaces in a vacuum or for which the travel time for light is an important factor, researchers have generalized the rendering equation to produce a volume rendering equation suitable for volume rendering and a transient rendering equation for use with data from a time-of-flight camera.

    Read more →
  • AI Customer-support Bots: Free vs Paid (2026)

    AI Customer-support Bots: Free vs Paid (2026)

    Curious about the best AI customer-support bot? An AI customer-support bot 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 customer-support bot 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.

    Read more →
  • Intelligent character recognition

    Intelligent character recognition

    Intelligent character recognition (ICR) is a method of extracting handwritten text from images. It is a more sophisticated type of OCR technology that recognizes different handwriting styles and fonts to intelligently interpret data from physical documents. ICR is used to organize paper-based unstructured data by scanning documents, extracting information, and adapting extracted data for database storage. ICR algorithms collaborate with OCR to automate data entry from forms by removing the need for keystrokes. It has a high degree of accuracy and is a dependable method for processing various handwritten media quickly. == Capabilities == Most ICR software has a self-learning neural network-based algorithms, which automatically update the recognition database for new handwriting patterns. It extends the usefulness of scanning devices for the purpose of document processing, from printed character recognition (a function of OCR) to hand-written matter recognition. Because this process is involved in recognizing hand writing, accuracy levels may, in some circumstances, not be very good but can achieve 97%+ accuracy rates in reading handwriting in structured forms. Often to achieve these high recognition rates several read engines are used within the software and each is given elective voting rights to determine the true reading of characters. In numeric fields, engines which are designed to read numbers take preference, while in alpha fields, engines designed to read hand written letters have higher elective rights. When used in conjunction with a bespoke interface hub, hand-written data can be automatically populated into a back office system avoiding laborious manual keying and can be more accurate than traditional human data entry. === Automated forms processing === An important development of ICR was the invention of automated forms processing in 1993 by Joseph Corcoran who was awarded a patent on the invention. This involved a three-stage process of capturing the image of the form to be processed by ICR and preparing it to enable the ICR engine to give best results, then capturing the information using the ICR engine and finally processing the results to automatically validate the output from the ICR engine. This application of ICR increased the usefulness of the technology and made it applicable for use with real world forms in normal business applications. Modern software applications use ICR as a technology of recognizing text in forms filled in by hand (hand-printed). == Differences between ICR and OCR == === OCR === Optical character recognition (OCR) is commonly considered to apply to any recognition technique that reads machine printed text. An example of a traditional OCR use case would be to translate the characters from an image of a printed document, such as a book page, newspaper clipping, or legal contract, into a separate file that could be searched and updated with a word processor or document viewer. It's also quite helpful for automating the processing of forms. Information can be swiftly extracted from form fields and entered into another application, like a spreadsheet or database, by zonally applying the OCR engine to those fields. Yet, data is typically manually input rather than typed into form fields. Character identification becomes even more challenging while reading handwritten material. The diversity of more than 700,000 printed font variants is tiny compared to the near unlimited variations in hand-printed characters. The recognition program must take into account not just stylistic differences but also the kind of writing implement used, the standard of the paper, errors, hand stability, and smudges or running ink. === ICR === Intelligent character recognition (ICR) makes use of continuously improving algorithms to collect more information about the variances in hand-printed characters and more precisely identify them. ICR, which was created in the early 1990s to aid in the automation of forms processing, enables the conversion of manually entered data into text that is simple to read, search for, and change. When used to read characters that are obviously divided into distinct areas or zones, such as fixed fields seen on many structured forms, it works best. Both OCR and ICR can be configured to read a variety of languages; however, limiting the expected character set to a smaller number of languages will produce better recognition outcomes. ICR cannot read cursive handwriting since it must still be able to assess each character individually. While writing in cursive, it might be difficult to tell where one character ends and another one begins, and there are more differences across samples than when hand-printing text. A more recent method called intelligent word recognition (IWR) focuses on reading a word in context rather than recognizing individual characters. == Intelligent word recognition == Intelligent word recognition (IWR) can recognize and extract not only printed-handwritten information, cursive handwriting as well. ICR recognizes on the character-level, whereas IWR works with full words or phrases. Capable of capturing unstructured information from every day pages, IWR is said to be more evolved than hand print ICR. Not meant to replace conventional ICR and OCR systems, IWR is optimized for processing real-world documents that contain mostly free-form, hard-to-recognize data fields that are inherently unsuitable for ICR. This means that the highest and best use of IWR is to eliminate a high percentage of the manual entry of handwritten data and run-on hand print fields on documents that otherwise could be keyed only by humans.

    Read more →