AI For Business Escp

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  Artificial Inventor Project

  The Artificial Inventor Project (AIP) is a global legal initiative headed by Professor Ryan Abbott dedicated to pursuing intellectual property (IP) rights for inventions and creative works generated autonomously by artificial intelligence (AI) systems without traditional human inventorship or authorship. The project coordinates a series of pro bono test cases worldwide, aiming to prompt law reform and public debate on how IP law should accommodate non-human creators. == History == In 2019, AIP filed patent applications in multiple jurisdictions, including the United States, United Kingdom, European Patent Office, Australia, Switzerland, and South Africa, naming the AI system DABUS (Device for the Autonomous Bootstrapping of Unified Sentience), created by Stephen Thaler, as the inventor. The aim was to challenge legal norms that require inventors to be natural persons and highlight pressing policy questions about AI-generated innovation and IP regimes. == Legal proceedings by jurisdiction == === Australia === In July 2021, a Federal Court of Australia judge (Beach J) ruled that AI can be considered an inventor under the Patents Act 1990, ordering IP Australia to reinstate the relevant patent. However, the full court then overturned this ruling on appeal and denied further review. === European Patent Office === The EPO Board of Appeal determined in 2022 that only a human inventor may be named, rendering DABUS‑based applications unacceptable. === South Africa === In 2021, a patent was granted listing DABUS as the inventor. As South Africa’s procedural system does not involve substantive inventorship review, the grant proceeded on formal grounds alone. === Switzerland === On 26 June 2025, the Swiss Federal Administrative Court ruled that artificial intelligence systems such as DABUS cannot be listed as inventors on patent applications. The court upheld the existing practice of the Swiss Federal Institute of Intellectual Property (IPI), affirming that only natural persons may be recognized as inventors under Swiss patent law. === United Kingdom === In December 2023, the UK Supreme Court unanimously held that AI systems cannot be legally recognized as inventors, affirming that "an inventor must be a person" under current British law. === United States === In Thaler v. Hirshfeld (2021), a U.S. federal court agreed with the USPTO that inventors must be natural persons, rejecting the DABUS application and setting a precedent consistent with existing statute and administrative policy. == Criticism and impact == The project has fueled substantial discourse. Critics caution that allowing AI inventorship may complicate notions of accountability and ownership. Proponents argue that legal recognition must evolve to avoid disincentivizing innovation produced by AI and to maintain honesty about the true source of invention.

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  Top 10 Conversational AI Platforms Compared (2026)

  In search of the best conversational AI platform? An conversational AI platform 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 conversational AI platform slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  Is an AI Pair Programmer Worth It in 2026?

  Shopping for the best AI pair programmer? An AI pair programmer is software that uses machine learning to help you get more done — it keeps getting smarter as the underlying models improve. Pricing, accuracy, and the size of the model behind the tool are the three factors that most affect daily usefulness. Whether you are a beginner or a pro, the right AI pair programmer slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  Is an AI Customer-support Bot Worth It in 2026?

  In search of the best AI customer-support bot? An AI customer-support bot 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 customer-support bot slots into your workflow and pays for itself fast. We tested the leading options and ranked them by quality, value, and ease of use.

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  Dynamic epistemic logic

  Dynamic epistemic logic (DEL) is a logical framework dealing with knowledge and information change. Typically, DEL focuses on situations involving multiple agents and studies how their knowledge changes when events occur. These events can change factual properties of the actual world (they are called ontic events): for example a red card is painted in blue. They can also bring about changes of knowledge without changing factual properties of the world (they are called epistemic events): for example, a card is revealed publicly (or privately) to be red. Originally, DEL focused on epistemic events. Only some of the basic ideas are present in this entry of the original DEL framework; more details about DEL in general can be found in the references. Due to the nature of its object of study and its abstract approach, DEL is related and has applications to numerous research areas, such as computer science (artificial intelligence), philosophy (formal epistemology), economics (game theory) and cognitive science. In computer science, DEL is for example very much related to multi-agent systems, which are systems where multiple intelligent agents interact and exchange information. As a combination of dynamic logic and epistemic logic, dynamic epistemic logic is a young field of research. It really started in 1989 with Plaza's logic of public announcement. Independently, Gerbrandy and Groeneveld proposed a system dealing moreover with private announcement and that was inspired by the work of Veltman. Another system was proposed by van Ditmarsch whose main inspiration was the Cluedo game. But the most influential and original system was the system proposed by Baltag, Moss and Solecki. This system can deal with all the types of situations studied in the works above and its underlying methodology is conceptually grounded. This entry will present some of its basic ideas. Formally, DEL extends ordinary epistemic logic by the inclusion of event models to describe actions, and a product update operator that defines how epistemic models are updated as the consequence of executing actions described through event models. Epistemic logic will first be recalled. Then, actions and events will enter into the picture and we will introduce the DEL framework. == Epistemic logic == Epistemic logic is a modal logic dealing with the notions of knowledge and belief. As a logic, it is concerned with understanding the process of reasoning about knowledge and belief: which principles relating the notions of knowledge and belief are intuitively plausible? Like epistemology, it stems from the Greek word ϵ π ι σ τ η μ η {\displaystyle \epsilon \pi \iota \sigma \tau \eta \mu \eta } or ‘episteme’ meaning knowledge. Epistemology is nevertheless more concerned with analyzing the very nature and scope of knowledge, addressing questions such as “What is the definition of knowledge?” or “How is knowledge acquired?”. In fact, epistemic logic grew out of epistemology in the Middle Ages thanks to the efforts of Burley and Ockham. The formal work, based on modal logic, that inaugurated contemporary research into epistemic logic dates back only to 1962 and is due to Hintikka. It then sparked in the 1960s discussions about the principles of knowledge and belief and many axioms for these notions were proposed and discussed. For example, the interaction axioms K p → B p {\displaystyle Kp\rightarrow Bp} and B p → K B p {\displaystyle Bp\rightarrow KBp} are often considered to be intuitive principles: if an agent Knows p {\displaystyle p} then (s)he also Believes p {\displaystyle p} , or if an agent Believes p {\displaystyle p} , then (s)he Knows that (s)he Believes p {\displaystyle p} . More recently, these kinds of philosophical theories were taken up by researchers in economics, artificial intelligence and theoretical computer science where reasoning about knowledge is a central topic. Due to the new setting in which epistemic logic was used, new perspectives and new features such as computability issues were then added to the research agenda of epistemic logic. === Syntax === In the sequel, A G T S = { 1 , … , n } {\displaystyle AGTS=\{1,\ldots ,n\}} is a finite set whose elements are called agents and P R O P {\displaystyle PROP} is a set of propositional letters. The epistemic language is an extension of the basic multi-modal language of modal logic with a common knowledge operator C A {\displaystyle C_{A}} and a distributed knowledge operator D A {\displaystyle D_{A}} . Formally, the epistemic language L EL C {\displaystyle {\mathcal {L}}_{\textsf {EL}}^{C}} is defined inductively by the following grammar in BNF: L EL C : ϕ ::= p ∣ ¬ ϕ ∣ ( ϕ ∧ ϕ ) ∣ K j ϕ ∣ C A ϕ ∣ D A ϕ {\displaystyle {\mathcal {L}}_{\textsf {EL}}^{C}:\phi ~~::=~~p~\mid ~\neg \phi ~\mid ~(\phi \land \phi )~\mid ~K_{j}\phi ~\mid ~C_{A}\phi ~\mid ~D_{A}\phi } where p ∈ P R O P {\displaystyle p\in PROP} , j ∈ A G T S {\displaystyle j\in {AGTS}} and A ⊆ A G T S {\displaystyle A\subseteq {AGTS}} . The basic epistemic language L E L {\displaystyle {\mathcal {L}}_{EL}} is the language L E L C {\displaystyle {\mathcal {L}}_{EL}^{C}} without the common knowledge and distributed knowledge operators. The formula ⊥ {\displaystyle \bot } is an abbreviation for ¬ p ∧ p {\displaystyle \neg p\land p} (for a given p ∈ P R O P {\displaystyle p\in PROP} ), ⟨ K j ⟩ ϕ {\displaystyle \langle K_{j}\rangle \phi } is an abbreviation for ¬ K j ¬ ϕ {\displaystyle \neg K_{j}\neg \phi } , E A ϕ {\displaystyle E_{A}\phi } is an abbreviation for ⋀ j ∈ A K j ϕ {\displaystyle \bigwedge \limits _{j\in A}K_{j}\phi } and C ϕ {\displaystyle C\phi } an abbreviation for C A G T S ϕ {\displaystyle C_{AGTS}\phi } . Group notions: general, common and distributed knowledge. In a multi-agent setting there are three important epistemic concepts: general knowledge, distributed knowledge and common knowledge. The notion of common knowledge was first studied by Lewis in the context of conventions. It was then applied to distributed systems and to game theory, where it allows to express that the rationality of the players, the rules of the game and the set of players are commonly known. General knowledge. General knowledge of ϕ {\displaystyle \phi } means that everybody in the group of agents A G T S {\displaystyle {AGTS}} knows that ϕ {\displaystyle \phi } . Formally, this corresponds to the following formula: E ϕ := ⋀ j ∈ A G T S K j ϕ . {\displaystyle E\phi :={\underset {j\in {AGTS}}{\bigwedge }}K_{j}\phi .} Common knowledge. Common knowledge of ϕ {\displaystyle \phi } means that everybody knows ϕ {\displaystyle \phi } but also that everybody knows that everybody knows ϕ {\displaystyle \phi } , that everybody knows that everybody knows that everybody knows ϕ {\displaystyle \phi } , and so on ad infinitum. Formally, this corresponds to the following formula C ϕ := E ϕ ∧ E E ϕ ∧ E E E ϕ ∧ … {\displaystyle C\phi :=E\phi \land EE\phi \land EEE\phi \land \ldots } As we do not allow infinite conjunction the notion of common knowledge will have to be introduced as a primitive in our language. Before defining the language with this new operator, we are going to give an example introduced by Lewis that illustrates the difference between the notions of general knowledge and common knowledge. Lewis wanted to know what kind of knowledge is needed so that the statement p {\displaystyle p} : “every driver must drive on the right” be a convention among a group of agents. In other words, he wanted to know what kind of knowledge is needed so that everybody feels safe to drive on the right. Suppose there are only two agents i {\displaystyle i} and j {\displaystyle j} . Then everybody knowing p {\displaystyle p} (formally E p {\displaystyle Ep} ) is not enough. Indeed, it might still be possible that the agent i {\displaystyle i} considers possible that the agent j {\displaystyle j} does not know p {\displaystyle p} (formally ¬ K i K j p {\displaystyle \neg K_{i}K_{j}p} ). In that case the agent i {\displaystyle i} will not feel safe to drive on the right because he might consider that the agent j {\displaystyle j} , not knowing p {\displaystyle p} , could drive on the left. To avoid this problem, we could then assume that everybody knows that everybody knows that p {\displaystyle p} (formally E E p {\displaystyle EEp} ). This is again not enough to ensure that everybody feels safe to drive on the right. Indeed, it might still be possible that agent i {\displaystyle i} considers possible that agent j {\displaystyle j} considers possible that agent i {\displaystyle i} does not know p {\displaystyle p} (formally ¬ K i K j K i p {\displaystyle \neg K_{i}K_{j}K_{i}p} ). In that case and from i {\displaystyle i} ’s point of view, j {\displaystyle j} considers possible that i {\displaystyle i} , not knowing p {\displaystyle p} , will drive on the left. So from i {\displaystyle i} ’s point of view, j {\displaystyle j} might drive on the left as well (by the same argument as abov

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  Karen Spärck Jones

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

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  DFA minimization

  In automata theory (a branch of theoretical computer science), DFA minimization is the task of transforming a given deterministic finite automaton (DFA) into an equivalent DFA that has a minimum number of states. Here, two DFAs are called equivalent if they recognize the same regular language. Several different algorithms accomplishing this task are known and described in standard textbooks on automata theory. == Minimal DFA == For each regular language, there also exists a minimal automaton that accepts it, that is, a DFA with a minimum number of states and this DFA is unique (except that states can be given different names). The minimal DFA ensures minimal computational cost for tasks such as pattern matching. There are three classes of states that can be removed or merged from the original DFA without affecting the language it accepts. Unreachable states are the states that are not reachable from the initial state of the DFA, for any input string. These states can be removed. Dead states are the states from which no final state is reachable. These states can be removed unless the automaton is required to be complete. Nondistinguishable states are those that cannot be distinguished from one another for any input string. These states can be merged. DFA minimization is usually done in three steps: remove dead and unreachable states (this will accelerate the following step), merge nondistinguishable states, optionally, re-create a single dead state ("sink" state) if the resulting DFA is required to be complete. == Unreachable states == The state p {\displaystyle p} of a deterministic finite automaton M = ( Q , Σ , δ , q 0 , F ) {\displaystyle M=(Q,\Sigma ,\delta ,q_{0},F)} is unreachable if no string w {\displaystyle w} in Σ ∗ {\displaystyle \Sigma ^{}} exists for which p = δ ∗ ( q 0 , w ) {\displaystyle p=\delta ^{}(q_{0},w)} . In this definition, Q {\displaystyle Q} is the set of states, Σ {\displaystyle \Sigma } is the set of input symbols, δ {\displaystyle \delta } is the transition function (mapping a state and an input symbol to a set of states), δ ∗ {\displaystyle \delta ^{}} is its extension to strings (also known as extended transition function), q 0 {\displaystyle q_{0}} is the initial state, and F {\displaystyle F} is the set of accepting (also known as final) states. Reachable states can be obtained with the following algorithm: Assuming an efficient implementation of the state sets (e.g. new_states) and operations on them (such as adding a state or checking whether it is present), this algorithm can be implemented with time complexity O ( n + m ) {\displaystyle O(n+m)} , where n {\displaystyle n} is the number of states and m {\displaystyle m} is the number of transitions of the input automaton. Unreachable states can be removed from the DFA without affecting the language that it accepts. == Nondistinguishable states == The following algorithms present various approaches to merging nondistinguishable states. === Hopcroft's algorithm === One algorithm for merging the nondistinguishable states of a DFA, due to Hopcroft (1971), is based on partition refinement, partitioning the DFA states into groups by their behavior. These groups represent equivalence classes of the Nerode congruence, whereby every two states are equivalent if they have the same behavior for every input sequence. That is, for every two states p1 and p2 that belong to the same block of the partition P, and every input word w, the transitions determined by w should always take states p1 and p2 to either states that both accept or states that both reject. It should not be possible for w to take p1 to an accepting state and p2 to a rejecting state or vice versa. The following pseudocode describes the form of the algorithm as given by Xu. Alternative forms have also been presented. The algorithm starts with a partition that is too coarse: every pair of states that are equivalent according to the Nerode congruence belong to the same set in the partition, but pairs that are inequivalent might also belong to the same set. It gradually refines the partition into a larger number of smaller sets, at each step splitting sets of states into pairs of subsets that are necessarily inequivalent. The initial partition is a separation of the states into two subsets of states that clearly do not have the same behavior as each other: the accepting states and the rejecting states. The algorithm then repeatedly chooses a set A from the current partition and an input symbol c, and splits each of the sets of the partition into two (possibly empty) subsets: the subset of states that lead to A on input symbol c, and the subset of states that do not lead to A. Since A is already known to have different behavior than the other sets of the partition, the subsets that lead to A also have different behavior than the subsets that do not lead to A. When no more splits of this type can be found, the algorithm terminates. Lemma. Given a fixed character c and an equivalence class Y that splits into equivalence classes B and C, only one of B or C is necessary to refine the whole partition. Example: Suppose we have an equivalence class Y that splits into equivalence classes B and C. Suppose we also have classes D, E, and F; D and E have states with transitions into B on character c, while F has transitions into C on character c. By the Lemma, we can choose either B or C as the distinguisher, let's say B. Then the states of D and E are split by their transitions into B. But F, which doesn't point into B, simply doesn't split during the current iteration of the algorithm; it will be refined by other distinguisher(s). Observation. All of B or C is necessary to split referring classes like D, E, and F correctly—subsets won't do. The purpose of the outermost if statement (if Y is in W) is to patch up W, the set of distinguishers. We see in the previous statement in the algorithm that Y has just been split. If Y is in W, it has just become obsolete as a means to split classes in future iterations. So Y must be replaced by both splits because of the Observation above. If Y is not in W, however, only one of the two splits, not both, needs to be added to W because of the Lemma above. Choosing the smaller of the two splits guarantees that the new addition to W is no more than half the size of Y; this is the core of the Hopcroft algorithm: how it gets its speed, as explained in the next paragraph. The worst case running time of this algorithm is O(ns log n), where n is the number of states and s is the size of the alphabet. This bound follows from the fact that, for each of the ns transitions of the automaton, the sets drawn from Q that contain the target state of the transition have sizes that decrease relative to each other by a factor of two or more, so each transition participates in O(log n) of the splitting steps in the algorithm. The partition refinement data structure allows each splitting step to be performed in time proportional to the number of transitions that participate in it. This remains the most efficient algorithm known for solving the problem, and for certain distributions of inputs its average-case complexity is even better, O(n log log n). Once Hopcroft's algorithm has been used to group the states of the input DFA into equivalence classes, the minimum DFA can be constructed by forming one state for each equivalence class. If S is a set of states in P, s is a state in S, and c is an input character, then the transition in the minimum DFA from the state for S, on input c, goes to the set containing the state that the input automaton would go to from state s on input c. The initial state of the minimum DFA is the one containing the initial state of the input DFA, and the accepting states of the minimum DFA are the ones whose members are accepting states of the input DFA. === Moore's algorithm === Moore's algorithm for DFA minimization is due to Edward F. Moore (1956). Like Hopcroft's algorithm, it maintains a partition that starts off separating the accepting from the rejecting states, and repeatedly refines the partition until no more refinements can be made. At each step, it replaces the current partition with the coarsest common refinement of s + 1 partitions, one of which is the current one and the rest of which are the preimages of the current partition under the transition functions for each of the input symbols. The algorithm terminates when this replacement does not change the current partition. Its worst-case time complexity is O(n2s): each step of the algorithm may be performed in time O(ns) using a variant of radix sort to reorder the states so that states in the same set of the new partition are consecutive in the ordering, and there are at most n steps since each one but the last increases the number of sets in the partition. The instances of the DFA minimization problem that cause the worst-case behavior are the same as for Hopcroft's algorithm. The number of steps th

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  Best AI Clip Makers in 2026

  Trying to pick the best AI clip maker? An AI clip 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 clip maker 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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  ArcSoft ShowBiz

  ShowBiz is a video editor by ArcSoft for the Windows operating system. It can create VCD and DVDs and can also export to the formats AVI, MPEG, WMV, and MOV. ShowBiz also contains a DVD burning and menu building feature. As of 2003, it was one of the three most dominant bundled titles. == Reception == PC Magazine reviewer Jan Ozer states: "ArcSoft's ShowBiz has evolved into a competent editor that's generally more usable than Dazzle's MovieStar program, providing more configuration controls, better preview features, and a much greater range of fun effects." John Virata, senior editor of Digital Media Online, says in his three page review of ShowBiz DVD 2, "It is an easy editor to work with and has a logically laid out interface that takes you step by step through the video creation and DVD creation process"

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  Jürgen Schmidhuber

  Jürgen Schmidhuber (born 17 January 1963) is a German computer scientist noted for his work in the field of artificial intelligence, specifically artificial neural networks. He has been described by media outlets as a leading pioneer of modern artificial intelligence. He is a scientific director of the Dalle Molle Institute for Artificial Intelligence Research in Switzerland. He is also director of the Artificial Intelligence Initiative and professor of the Computer Science program in the Computer, Electrical, and Mathematical Sciences and Engineering (CEMSE) division at the King Abdullah University of Science and Technology (KAUST) in Saudi Arabia. He is best known for his work on long short-term memory (LSTM), a type of neural network architecture which was the dominant technique for various natural language processing tasks in research and commercial applications in the 2010s. He also introduced principles of dynamic neural networks, meta-learning, generative adversarial networks and linear transformers, all of which are widespread in modern AI. == Career == Schmidhuber completed his undergraduate (1987) and PhD (1991) studies at the Technical University of Munich in Munich, Germany. His PhD advisors were Wilfried Brauer and Klaus Schulten. He taught there from 2004 until 2009. From 2009 to 2021, he was a professor of artificial intelligence at the Università della Svizzera Italiana in Lugano, Switzerland. He has served as the director of Dalle Molle Institute for Artificial Intelligence Research (IDSIA), a Swiss AI lab, since 1995. Since 2021, he has also been the director of the AI Initiative at the King Abdullah University of Science and Technology (KAUST). In 2014, Schmidhuber formed a company, NNAISENSE, to work on commercial applications of artificial intelligence in fields such as finance, heavy industry and self-driving cars. Sepp Hochreiter, Jaan Tallinn, and Marcus Hutter are advisers to the company. Sales were under US$11 million in 2016; however, Schmidhuber states that the current emphasis is on research and not revenue. NNAISENSE raised its first round of capital funding in January 2017. Schmidhuber's overall goal is to create an all-purpose AI by training a single AI in sequence on a variety of narrow tasks, but as of 2026 he has said that the focus of NNAISENSE has shifted from artificial general intelligence to asset management. == Research == In the 1980s, backpropagation did not work well for deep learning with long credit assignment paths in artificial neural networks. To overcome this problem, Schmidhuber (1991) proposed a hierarchy of recurrent neural networks (RNNs) pre-trained one level at a time by self-supervised learning. It uses predictive coding to learn internal representations at multiple self-organizing time scales, facilitating downstream deep learning. The RNN hierarchy can be collapsed into a single RNN, by distilling a higher level chunker network into a lower level automatizer network. In 1993, a chunker solved a deep learning task whose depth exceeded 1000. In 1991, Schmidhuber published adversarial neural networks that contest with each other in the form of a zero-sum game, where one network's gain is the other network's loss. The first network is a generative model that models a probability distribution over output patterns. The second network learns by gradient descent to predict the reactions of the environment to these patterns. This was called "artificial curiosity". In 2014, this principle was used in the creation of the generative adversarial network, which Schmidhuber describes as a special case of artificial curiosity where the environmental reaction is 1 or 0 depending on whether the first network's output is in a given set. Schmidhuber supervised the 1991 diploma thesis of his student Sepp Hochreiter which he considered "one of the most important documents in the history of machine learning". It studied the neural history compressor and analyzed and overcame the vanishing gradient problem. This led to the creation of long short-term memory (LSTM), a type of recurrent neural network. The name LSTM was introduced in a tech report in 1995, leading to the most cited LSTM publication, published in 1997 and co-authored by Hochreiter and Schmidhuber. The standard LSTM architecture was introduced in 2000 by Felix Gers, Schmidhuber, and Fred Cummins. Today's "vanilla LSTM" using backpropagation through time was published with his student Alex Graves in 2005, and its connectionist temporal classification (CTC) training algorithm in 2006. CTC was applied to end-to-end speech recognition with LSTM. In 2014, the state of the art was training “very deep neural network” with 20 to 30 layers. Stacking too many layers led to a steep reduction in training accuracy, known as the "degradation" problem. In May 2015, Rupesh Kumar Srivastava, Klaus Greff, and Schmidhuber used LSTM principles to create the highway network, a feedforward neural network with hundreds of layers, much deeper than previous networks. In Dec 2015, the residual neural network (ResNet) was published, which is a variant of the highway network. In 1992, Schmidhuber published fast weights programmer, an alternative to recurrent neural networks. It has a slow feedforward neural network that learns by gradient descent to control the fast weights of another neural network through outer products of self-generated activation patterns, and the fast weights network itself operates over inputs. This was later shown to be equivalent to the unnormalized linear transformer. In 2011, Schmidhuber's team at IDSIA with his postdoc Dan Ciresan also achieved dramatic speedups of convolutional neural networks (CNNs) using graphics processing units (GPUs), based on CNN designs introduced much earlier by Kunihiko Fukushima. An earlier CNN on GPU by Chellapilla et al. (2006) was 4 times faster than an equivalent implementation on CPU. The deep CNN of Dan Ciresan et al. (2011) at IDSIA was 60 times faster and achieved the first superhuman performance in a computer vision contest in August 2011. Between 15 May 2011 and 10 September 2012, these CNNs won four more image competitions and improved the state of the art on multiple image benchmarks. The approach has become central to the field of computer vision. == Credit disputes == Schmidhuber has controversially argued that he and other researchers have been denied adequate recognition for their contribution to the field of deep learning, in favour of Geoffrey Hinton, Yoshua Bengio and Yann LeCun, who shared the 2018 Turing Award for their work in deep learning. He wrote a "scathing" 2015 article arguing that Hinton, Bengio and LeCun "heavily cite each other" but "fail to credit the pioneers of the field". In a statement to the New York Times, Yann LeCun wrote that "Jürgen is manically obsessed with recognition and keeps claiming credit he doesn't deserve for many, many things... It causes him to systematically stand up at the end of every talk and claim credit for what was just presented, generally not in a justified manner." Schmidhuber replied that LeCun did this "without any justification, without providing a single example", and published details of numerous priority disputes with Hinton, Bengio and LeCun. The term "schmidhubered" has been jokingly used in the AI community to describe Schmidhuber's habit of publicly challenging the originality of other researchers' work, a practice seen by some in the AI community as a "rite of passage" for young researchers. Some suggest that Schmidhuber's significant accomplishments have been underappreciated due to his confrontational personality. == Recognition == Schmidhuber received the Helmholtz Award of the International Neural Network Society in 2013, and the Neural Networks Pioneer Award of the IEEE Computational Intelligence Society in 2016 for "pioneering contributions to deep learning and neural networks." He is a member of the European Academy of Sciences and Arts. He has been referred to as the "father of modern AI", the "father of generative AI", and the "father of deep learning". Schmidhuber himself, however, has called Alexey Grigorevich Ivakhnenko the "father of deep learning", and gives credit to many even earlier AI pioneers. The New York Times ran a profile under the headline "When A.I. Matures, It May Call Jürgen Schmidhuber 'Dad'", highlighting his early work on deep learning and his long‑term vision for self‑improving AI. == Views == Schmidhuber is a proponent of open source AI, and believes that they will become competitive against commercial closed-source AI. Since the 1970s, Schmidhuber wanted to create "intelligent machines that could learn and improve on their own and become smarter than him within his lifetime." He differentiates between two types of AIs: tool AI, such as those for improving healthcare, and autonomous AIs that set their own goals, perform their own research, and explore the universe. He has worked on both types for de

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  How to Choose an AI Art Generator

  Looking for the best AI art generator? An AI art 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 art generator slots into your workflow and pays for itself fast. Read on for hands-on impressions, pricing tiers, and the standout features that matter.

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  Karsten Borgwardt

  Karsten Borgwardt (born 1980) is a German computer scientist and biologist specializing in machine learning and computational biology. Since February 2023, he has been a director at the Max Planck Institute of Biochemistry in Martinsried, Germany, where he leads the Department of Machine Learning and Systems Biology. == Education and career == Borgwardt was born in Kaiserslautern. He obtained a Diplom (equivalent to a master’s degree) in computer science from LMU Munich in 2004 and a Master of Science in biology from the University of Oxford in 2003. In 2007, he obtained his PhD from LMU Munich in computer science. Following a postdoctoral position at the University of Cambridge, he became a research group leader for machine learning and computational biology at the Max Planck Institute for Biological Cybernetics and the former Max Planck Institute for Developmental Biology in Tübingen in 2008. In 2011, Borgwardt was appointed professor of data mining in the life sciences at the University of Tübingen. In 2014, he joined ETH Zurich as an associate professor in the Department of Biosystems Science and Engineering (D-BSSE) and was promoted to full professor in 2017. During his tenure at ETH Zurich, he coordinated significant research programs, including two Marie Curie Innovative Training Networks and the Personalized Swiss Sepsis Study, focusing on the prediction of sepsis using machine learning. In 2023, he was appointed as Scientific Member of the Max Planck Society and as Director at the Max Planck Institute of Biochemistry in Martinsried. == Research contributions == Borgwardt’s research integrates big data analysis with biomedical research. He develops novel machine learning algorithms to detect patterns and statistical dependencies in large biological and medical datasets. His work aims to enable the automatic generation of new knowledge from big data and to understand the relationship between the function of biological systems and their molecular properties, which is fundamental for personalized medicine. == Awards and honors == During his studies, he was a scholar of the Stiftung Maximilianeum, and the Bavarian Foundation for the Promotion of the Gifted. Borgwardt received scholarships from the Studienstiftung des deutschen Volkes in 2002 and 2007. His PhD dissertation received the Heinz Schwärtzel Dissertation Award for Foundations of Computer Science in 2007. As a professor in Tübingen, he was awarded the Alfried-Krupp-Förderpreis for Young Professors in 2013. In 2015, he received an SNSF Starting Grant. In 2014, 2015 and 2016, he was listed in “Top 40 under 40” in Germany rankings selected by Capital magazine. In 2018, Borgwardt was named among “25 individuals who have the potential to shape the next 25 years” by Focus magazine. In 2023, Borgwardt received an honorary professorship from LMU Munich by the Faculty of Chemistry and Pharmacy. Publications from Borgwardt's group have received the Outstanding Student Paper Award in NIPS in 2009, the SIB Graduate Paper Award in 2020 and SIB Remarkable Output Awards in 2020 and 2021 from the Swiss Institute of Bioinformatics (SIB). == Selected publications == Weisfeiler-Lehman Graph Kernels (’‘Journal of Machine Learning Research’’, 2011): Introduced an efficient graph kernel based on the Weisfeiler-Lehman algorithm. “Direct antimicrobial resistance prediction from clinical MALDI-TOF mass spectra using machine learning” (’‘Nature Medicine’’, 2022): showcased the feasibility of predicting antimicrobial resistance from readily collected mass spectrometry data in the hospital. The new method is able to identify antibiotic resistance 24 hours earlier than previous methods.

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  NHS COVID-19

  NHS COVID-19 was a voluntary contact tracing app for monitoring the spread of the COVID-19 pandemic in England and Wales, in use from 24 September 2020 until 27 April 2023. It was available for Android and iOS smartphones, and could be used by anyone aged 16 or over. Two versions of the app were created. The first was commissioned by NHSX and developed by the Pivotal division of American software company VMware. A pilot deployment began in May 2020, but on 18 June development of the app was abandoned in favour of a second design using the Apple/Google Exposure Notification system. Scotland and Northern Ireland had separate contact tracing apps. A 2023 study estimated that in its first year of use, the app's contact tracing function prevented an estimated 1 million cases, and 9,600 deaths. == Description == The app allowed users to: See the alert level of their local authority area (in Wales) or information about restrictions (in England); to enable this, the user must enter the first half of their postcode "Check in" at places displaying an NHS QR code poster (no longer required by legislation after 26 January 2022, removed from the app the next month) Be notified when they have been in close contact with someone who has tested positive for the virus Be notified when local health protection teams determine that people with the virus had attended a business or other venue around the same time as the user Check their symptoms, and book a coronavirus test if necessary If asked to self-isolate, receive information and a daily "countdown". At first, "close contact" was defined as being within 2 metres for 15 minutes, or within 4 metres for a longer time. These time durations were reduced from 29 October 2020, to as little as three minutes when the other person is at their most infectious, i.e. soon after they begin showing symptoms. === Implementation === The Android app was coded in Kotlin, and the iOS app in Swift. The backend used Java and is deployed to Amazon Web Services using Terraform. The code of the app and back-end is open-source and available on GitHub. == Context == The app was part of the UK's test and trace programme which was chaired by Dido Harding; from 12 May 2020 Tom Riordan, chief executive of Leeds City Council, led the tracing effort. == First phase and cancellation == === Description === In March 2020, NHSX commissioned a contact tracing app to monitor the spread in the United Kingdom of the coronavirus disease 2019 (COVID-19) in the 2020 pandemic, developed by the Pivotal division of American software company VMware. The app used a centralised approach, in contrast to the Google / Apple contact tracing project. NHSX consulted ethicists and GCHQ's National Cyber Security Centre (NCSC) about the privacy aspects. The app recorded the make and model of the phone and asked the user for their postcode area. It generated a unique installation identification number and also a daily identification number. It then used Bluetooth Low Energy (BLE) to record the daily identification number of other users nearby. If a user was unwell, they could tell the app about symptoms which are characteristic of COVID-19, such as a fever and cough. These details were then passed to a central NHS server. This would assess the information and notify other users that have been in contact, giving them appropriate advice such as physical distancing. The NHS would also arrange for a swab test of the unwell user and the outcome would determine further notifications to contacts: if the test confirmed infection with COVID-19, the contacts would be asked to isolate. By June 2020, £11.8 million had been spent on the app; in 2020–21, £35 million was spent on the app. === Deployment === The first public trial of the app began on the Isle of Wight on 5 May 2020 and by 11 May it had been downloaded 55,000 times. When the first national contact tracing schemes were launched – Test, Trace, Protect in Wales on 13 May, then on 28 May NHS Test and Trace in England, and Test and Protect in Scotland – the app was not ready to be included. Replying to a question at the government's daily briefing on 8 June, Hancock was unable to give a date for rollout of the app in England, saying it would be brought in "when it's right to do so". On 17 June, Lord Bethell, junior minister for Innovation at the Department of Health and Social Care, said "we're seeking to get something going before the winter ... it isn't a priority for us at the moment". On 18 June, Health Secretary Matt Hancock announced development would switch to the Apple/Google system after admitting that Apple's restrictions on usage of Bluetooth prevented the app from working effectively. At the same press briefing Dido Harding, leader of the UK's test and trace programme, said "What we've done in really rigorously testing both our own Covid-19 app and the Google-Apple version is demonstrate that none of them are working sufficiently well enough to be actually reliable to determine whether any of us should self-isolate for two weeks [and] that's true across the world". === Concerns === The first, ultimately rejected, version of the app was subject to privacy concerns, the government backtracking on initial statements that the data collected from the app would not be shared outside the NHS. Matthew Gould, CEO of NHSX, the government department responsible for the app, said the data would be accessible to other organisations, but did not disclose which. Data collected would not necessarily be anonymised and would be held in a centralised repository. Over 150 of the UK's security and privacy experts warned the app's data could be used by 'a bad actor (state, private sector, or hacker)' to spy on citizens. Fears were discussed by the House of Commons' Human Rights Select Committee about plans for the app to record user location data. Parliament's Joint Committee on Human Rights said this version of the app should not be released without proper privacy protections. The second version of the app, released nationwide, addressed these concerns by employing a decentralised framework, the Apple/Google Exposure Notification system. Under this system, users remain pseudonymous: a person diagnosed with COVID-19 does not know which people are informed about an encounter, and contacted persons do not receive any information about the person diagnosed with COVID-19. The functionality of the app was also questioned in late April and early May 2020, as the software's use of Bluetooth required the app to be constantly running, meaning users could not use other apps or lock their device if the app was to function properly. The developers of the app were said to have found a way of working around this restriction. === Related contracts === Faculty – a company linked to Cambridge Analytica – provided research and modelling to NHSX in support of the response to the pandemic. Palantir, also linked to Cambridge Analytica, provided their data management platform. These contracts began in February and March respectively. == Second phase == As outlined on cancellation of the first app on 18 June 2020, the Department of Health and Social Care published on 30 July a brief description of the "next phase" app. Users would be able to scan a QR code at venues they visit, and later be notified if they had visited a place which was the source of a number of infections; the app would also assist with identifying symptoms and ordering a test. By using the Exposure Notification system from Apple and Google, personal data would be decentralised. Zuhlke Engineering Ltd, the UK branch of Swiss-based Zühlke Group, used 70 staff to complete the development of the app in 12 weeks. Zuhlke Engineering was awarded "Development Team of the Year" title at UK IT Industry awards in November 2021 for development of NHS COVID-19 application. === Timeline === Testing of the app by NHS volunteer responders, and selected residents of the Isle of Wight and the London Borough of Newham, began around 13 August. The app was made available to the public (aged 16 or over) in England and Wales on 24 September. An updated app released on 29 October, in part from collaboration with the Alan Turing Institute, improved the accuracy of measurements of the distance between the user's phone and other phones. At the same time, the duration threshold for determining exposure was reduced; this was expected to lead to an increase in the number of users told to self-isolate. An update to the app in April 2021, timed to coincide with easing of restrictions on hospitality businesses, was blocked by Apple and Google. It was intended that users who tested positive would be asked to share their history of visited venues, to assist in warning others, but this would have contravened assurances by Apple and Google that location data from devices would not be shared. === Statistics and effectiveness === The app was downloaded six million times on the first day it was generally availa

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  StarDict

  StarDict, developed by Hu Zheng (胡正), is a free GUI released under the GPL-3.0-or-later license for accessing StarDict dictionary files (a dictionary shell). It is the successor of StarDic, developed by Ma Su'an (馬蘇安), continuing its version numbers. According to StarDict's earlier homepage on SourceForge, the project has been removed from SourceForge due to copyright infringement reports. It moved to Google Code and then back to SourceForge, while development is now seemingly continued on GitHub. == Supported platforms == StarDict runs under Linux, Windows, FreeBSD, Maemo and Solaris. Dictionaries of the user's choice are installed separately. Dictionary files can be created by converting dict files. Several programs compatible with the StarDict dictionary format are available for different platforms. For the iPhone, iPod Touch and iPad, applications available in the App Store include GuruDic, TouchDict, weDict, Dictionary Universal, Alpus and others, as well as the free iStarDict, which is available for the Cydia Store. == Dictionaries available == One can find here the partial list of FreeDict dictionaries which can be converted to the StarDict format. These include, in particular, some older versions of Webster's dictionary and many dictionaries for various languages. == Features == While StarDict is in scan mode, results are displayed in a tooltip, allowing easy dictionary lookup. When combined with Freedict, StarDict will quickly provide rough translations of foreign language websites. On September 25, 2006, an online version of Stardict began operation. This online version includes access to all the major dictionaries of StarDict, as well as Wikipedia in Chinese. Previous versions of StarDict were very similar to the PowerWord dictionary program, which is developed by a Chinese company, KingSoft. Since version 2.4.2, however, StarDict has diverged from the design of PowerWord by increasing its search capabilities and adding lexicons in a variety of languages. This was assisted by the collaboration of many developers with the author. == sdcv == Evgeniy A. Dushistov produced a command line version of StarDict called sdcv. It employed all the dictionary files that belong to StarDict. It is written in C++ and licensed under the terms of the GNU General Public License. sdcv runs under Linux, FreeBSD, and Solaris. As in StarDict, dictionaries of the user's choice have to be installed separately. At the end of 2006, software developer Hu Zheng cited personal financial problems as an excuse to charge users for downloading dictionary files from his website, which temporarily aroused strong doubts and dissatisfaction in the Linux community. In the end, under the pressure of public opinion, the charging plan was forced to be canceled and ended hastily.

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  Sepp Hochreiter

  Josef "Sepp" Hochreiter (born 14 February 1967) is a German computer scientist. Since 2018 he has led the Institute for Machine Learning at the Johannes Kepler University of Linz after having led the Institute of Bioinformatics from 2006 to 2018. In 2017 he became the head of the Linz Institute of Technology (LIT) AI Lab. Hochreiter is also a founding director of the Institute of Advanced Research in Artificial Intelligence (IARAI). Previously, he was at Technische Universität Berlin, at University of Colorado Boulder, and at the Technical University of Munich. He is a chair of the Critical Assessment of Massive Data Analysis (CAMDA) conference. Hochreiter has made contributions in the fields of machine learning, deep learning and bioinformatics, most notably the development of the long short-term memory (LSTM) neural network architecture, but also in meta-learning, reinforcement learning and biclustering with application to bioinformatics data. == Scientific career == === Long short-term memory (LSTM) === Hochreiter developed the long short-term memory (LSTM) neural network architecture in his diploma thesis in 1991 leading to the main publication in 1997. LSTM overcomes the problem of numerical instability in training recurrent neural networks (RNNs) that prevents them from learning from long sequences (vanishing or exploding gradient). In 2007, Hochreiter and others successfully applied LSTM with an optimized architecture to very fast protein homology detection without requiring a sequence alignment. LSTM networks have also been used in Google Voice for transcription and search, and in the Google Allo chat app for generating response suggestion with low latency. === Other machine learning contributions === Beyond LSTM, Hochreiter has developed "Flat Minimum Search" to increase the generalization of neural networks and introduced rectified factor networks (RFNs) for sparse coding which have been applied in bioinformatics and genetics. Hochreiter introduced modern Hopfield networks with continuous states and applied them to the task of immune repertoire classification. Hochreiter worked with Jürgen Schmidhuber in the field of reinforcement learning on actor-critic systems that learn by "backpropagation through a model". Hochreiter has been involved in the development of factor analysis methods with application to bioinformatics, including FABIA for biclustering, HapFABIA for detecting short segments of identity by descent and FARMS for preprocessing and summarizing high-density oligonucleotide DNA microarrays to analyze RNA gene expression. In 2006, Hochreiter and others proposed an extension of the support vector machine (SVM), the "Potential Support Vector Machine" (PSVM), which can be applied to non-square kernel matrices and can be used with kernels that are not positive definite. Hochreiter and his collaborators have applied PSVM to feature selection, including gene selection for microarray data. == Awards == Hochreiter was awarded the IEEE CIS Neural Networks Pioneer Prize in 2021 for his work on LSTM.

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