AI Headshot Generator For Linkedin

AI Headshot Generator For Linkedin — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Lesk algorithm

  The Lesk algorithm is a classical algorithm for word sense disambiguation introduced by Michael E. Lesk in 1986. It operates on the premise that words within a given context are likely to share a common meaning. This algorithm compares the dictionary definitions of an ambiguous word with the words in its surrounding context to determine the most appropriate sense. Variations, such as the Simplified Lesk algorithm, have demonstrated improved precision and efficiency. However, the Lesk algorithm has faced criticism for its sensitivity to definition wording and its reliance on brief glosses. Researchers have sought to enhance its accuracy by incorporating additional resources like thesauruses and syntactic models. == Overview == The Lesk algorithm is based on the assumption that words in a given "neighborhood" (section of text) will tend to share a common topic. A simplified version of the Lesk algorithm is to compare the dictionary definition of an ambiguous word with the terms contained in its neighborhood. Versions have been adapted to use WordNet. An implementation might look like this: for every sense of the word being disambiguated one should count the number of words that are in both the neighborhood of that word and in the dictionary definition of that sense the sense that is to be chosen is the sense that has the largest number of this count. A frequently used example illustrating this algorithm is for the context "pine cone". The following dictionary definitions are used: PINE 1. kinds of evergreen tree with needle-shaped leaves 2. waste away through sorrow or illness CONE 1. solid body which narrows to a point 2. something of this shape whether solid or hollow 3. fruit of certain evergreen trees As can be seen, the best intersection is Pine #1 ⋂ Cone #3 = 2. == Simplified Lesk algorithm == In Simplified Lesk algorithm, the correct meaning of each word in a given context is determined individually by locating the sense that overlaps the most between its dictionary definition and the given context. Rather than simultaneously determining the meanings of all words in a given context, this approach tackles each word individually, independent of the meaning of the other words occurring in the same context. "A comparative evaluation performed by Vasilescu et al. (2004) has shown that the simplified Lesk algorithm can significantly outperform the original definition of the algorithm, both in terms of precision and efficiency. By evaluating the disambiguation algorithms on the Senseval-2 English all words data, they measure a 58% precision using the simplified Lesk algorithm compared to the only 42% under the original algorithm. Note: Vasilescu et al. implementation considers a back-off strategy for words not covered by the algorithm, consisting of the most frequent sense defined in WordNet. This means that words for which all their possible meanings lead to zero overlap with current context or with other word definitions are by default assigned sense number one in WordNet." Simplified LESK Algorithm with smart default word sense (Vasilescu et al., 2004) The COMPUTEOVERLAP function returns the number of words in common between two sets, ignoring function words or other words on a stop list. The original Lesk algorithm defines the context in a more complex way. == Criticisms == Unfortunately, Lesk’s approach is very sensitive to the exact wording of definitions, so the absence of a certain word can radically change the results. Further, the algorithm determines overlaps only among the glosses of the senses being considered. This is a significant limitation in that dictionary glosses tend to be fairly short and do not provide sufficient vocabulary to relate fine-grained sense distinctions. A lot of work has appeared offering different modifications of this algorithm. These works use other resources for analysis (thesauruses, synonyms dictionaries or morphological and syntactic models): for instance, it may use such information as synonyms, different derivatives, or words from definitions of words from definitions. == Lesk variants == Original Lesk (Lesk, 1986) Adapted/Extended Lesk (Banerjee and Pederson, 2002/2003): In the adaptive lesk algorithm, a word vector is created corresponds to every content word in the wordnet gloss. Concatenating glosses of related concepts in WordNet can be used to augment this vector. The vector contains the co-occurrence counts of words co-occurring with w in a large corpus. Adding all the word vectors for all the content words in its gloss creates the Gloss vector g for a concept. Relatedness is determined by comparing the gloss vector using the Cosine similarity measure. There are a lot of studies concerning Lesk and its extensions: Wilks and Stevenson, 1998, 1999; Mahesh et al., 1997; Cowie et al., 1992; Yarowsky, 1992; Pook and Catlett, 1988; Kilgarriff and Rosensweig, 2000; Kwong, 2001; Nastase and Szpakowicz, 2001; Gelbukh and Sidorov, 2004.

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  Internettolken

  Internettolken (or InternetPreter) is a web-based machine translating tool. As the first Swedish online translating service, it was started in 2002 and included the English and Swedish languages. Today, there are 14 languages with more than 120 possible combinations. The service is free up to 150 words per day, and as a 2,000-word free testing account. It is available both on its website, and as a gadget on iGoogle. The interface is either English or Swedish. Being a dictionary-based tool, with its own translation software, it can sometimes offer a more accurate translation than Google Translate and others, although the grammar will be incorrect. == Languages currently available ==

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  AI Voice Assistants Reviews: What Actually Works in 2026

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

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  AI Humanizers Reviews: What Actually Works in 2026

  Curious about the best AI humanizer? An AI humanizer 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 humanizer 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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  Texture artist

  A texture artist is an individual who develops textures for digital media, usually for video games, movies, web sites and television shows or things like 3D posters. These textures can be in the form of 2D or (rarely) 3D art that may be overlaid onto a polygon mesh to create a realistic 3D model. Texture artists often take advantage of web sites for the purposes of marketing their art and self-promotion of their skills with the goal of gaining employment from a professional game studio or to join a team working on a "mod" (modification) of an existing game in hopes of establishing industry or trade credentials.

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  Wolfgang Ketter

  Wolfgang Ketter (born Traben-Trarbach, Germany, 1972) is Chaired Professor of Information Systems for a Sustainable Society at the University of Cologne. and a prominent scientist in the application of artificial intelligence, machine learning and intelligent agents in the design of smart markets, including demand response mechanisms and in particular automated auctions. He is a co-founder of the open energy system platform Power TAC, an automated retail electricity trading platform that simulates the performance of retail markets in an increasingly prosumer- and renewable-energy-influenced electricity landscape. == Career == === Advisory roles === Ketter is an advisor on the energy transition to the German government, in particular, the energy-intensive German state of North Rhine-Westphalia. He is also a fellow of the World Economic Forum and member of the WEF Global Council on Future Mobility and the Global New Mobility Coalition, contributing on the use of AI and machine learning to address issues arising from growth in electrification of energy such as the use of batteries as virtual power plants, the management of electric vehicle charging to prevent grid congestion, or the potential for peer-to-peer electricity trading. Ketter has also been an advisor for over a decade to the Port of Rotterdam on the design of energy cooperatives and energy trading platforms as well as one of the largest auction companies in the world, Royal FloraHolland, where his initial research led to a redesign of auction mechanisms and decision support systems. The cumulative research project team received the Association for Information Systems Impact Award in 2020 === Research === Ketter’s research is multidisciplinary, addressing the overlap of AI and ML in the economics of retail energy and mobility markets. The industry and policy applications of his research interconnect in large-scale projects such as the EU Smart city development project Ruggedised, for which the Erasmus University-based team's publication on the optimization of the City of Rotterdam's electric transit bus network was recognized with the Institute for Operations Research and the Management Sciences Daniel H. Wagner runner-up award. His research focuses on the use of competitive benchmarking and intelligent agents in virtual world simulations of retail energy markets as part of a smart grid. A small-scale version of the Power TAC project led to a publication on demand side management, 'A simulation of household behavior under variable prices' that has several hundred citations in publications representing a variety of scientific disciplines. Two of his publications in the Management Information Systems Quarterly journal and one in Energy Economics form the foundation for the current Power TAC platform. In 2016 and 2019 he was Chair of the Workshop on Information Technologies and Systems. Ketter is Coordinator of the Key Research Initiative Sustainable Smart Energy & Mobility at the University of Cologne, where he is a chaired Professor of Information Systems for a Sustainable Society. At the Rotterdam School of Management, Erasmus University, he is Professor of Next Generation Information Systems as well as Director of the Erasmus Centre for Future Energy Business and Academic Director of Smart Cities and Smart Energy at the Erasmus Centre of Data Analytics. He has been a visiting professor at the Haas School of Business and Berkeley Institute of Data Science, University of California at Berkeley in 2016 to 2017.

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  Mealy machine

  In the theory of computation, a Mealy machine is a finite-state machine whose output values are determined both by its current state and the current inputs. This is in contrast to a Moore machine, whose output values are determined solely by its current state. A Mealy machine is a deterministic finite-state transducer: for each state and input, at most one transition is possible. == History == The Mealy machine is named after George H. Mealy, who presented the concept in a 1955 paper, "A Method for Synthesizing Sequential Circuits". == Formal definition == A Mealy machine is a 6-tuple ( S , S 0 , Σ , Λ , T , G ) {\displaystyle (S,S_{0},\Sigma ,\Lambda ,T,G)} consisting of the following: a finite set of states S {\displaystyle S} a start state (also called initial state) S 0 {\displaystyle S_{0}} which is an element of S {\displaystyle S} a finite set called the input alphabet Σ {\displaystyle \Sigma } a finite set called the output alphabet Λ {\displaystyle \Lambda } a transition function T : S × Σ → S {\displaystyle T:S\times \Sigma \rightarrow S} mapping pairs of a state and an input symbol to the corresponding next state. an output function G : S × Σ → Λ {\displaystyle G:S\times \Sigma \rightarrow \Lambda } mapping pairs of a state and an input symbol to the corresponding output symbol. In some formulations, the transition and output functions are coalesced into a single function T : S × Σ → S × Λ {\displaystyle T:S\times \Sigma \rightarrow S\times \Lambda } . "Evolution across time" is realized in this abstraction by having the state machine consult the time-changing input symbol at discrete "timer ticks" t 0 , t 1 , t 2 , . . . {\displaystyle t_{0},t_{1},t_{2},...} and react according to its internal configuration at those idealized instants, or else having the state machine wait for a next input symbol (as on a FIFO) and react whenever it arrives. == Comparison of Mealy machines and Moore machines == Mealy machines tend to have fewer states: Different outputs on arcs (n2) rather than states (n). When implemented as electronic circuits (rather than as mathematical abstractions or code): Moore machines are safer to use than Mealy machines: Outputs change at the clock edge (always one cycle later). In Mealy machines, input change can cause output change as soon as logic is done — a big problem when two machines are interconnected – asynchronous feedback may occur if one isn't careful. Mealy machines react faster to inputs: React in the same cycle—they don't need to wait for the clock. In Moore machines, more logic may be necessary to decode state into outputs—more gate delays after clock edge. == Diagram == The state diagram for a Mealy machine associates an output value with each transition edge, in contrast to the state diagram for a Moore machine, which associates an output value with each state. When the input and output alphabet are both Σ, one can also associate to a Mealy automata a Helix directed graph (S × Σ, (x, i) → (T(x, i), G(x, i))). This graph has as vertices the couples of state and letters, each node is of out-degree one, and the successor of (x, i) is the next state of the automata and the letter that the automata output when it is instate x and it reads letter i. This graph is a union of disjoint cycles if the automaton is bireversible. == Examples == === Simple === A simple Mealy machine has one input and one output. Each transition edge is labeled with the value of the input (shown in red) and the value of the output (shown in blue). The machine starts in state Si. (In this example, the output is the exclusive-or of the two most-recent input values; thus, the machine implements an edge detector, outputting a 1 every time the input flips and a 0 otherwise.) === Complex === More complex Mealy machines can have multiple inputs as well as multiple outputs. == Applications == Mealy machines provide a rudimentary mathematical model for cipher machines. Considering the input and output alphabet the Latin alphabet, for example, then a Mealy machine can be designed that given a string of letters (a sequence of inputs) can process it into a ciphered string (a sequence of outputs). However, although a Mealy model could be used to describe the Enigma, the state diagram would be too complex to provide feasible means of designing complex ciphering machines. Moore/Mealy machines are DFAs that have also output at any tick of the clock. Modern CPUs, computers, cell phones, digital clocks and basic electronic devices/machines have some kind of finite state machine to control it. Simple software systems, particularly ones that can be represented using regular expressions, can be modeled as finite state machines. There are many such simple systems, such as vending machines or basic electronics. By finding the intersection of two finite state machines, one can design in a very simple manner concurrent systems that exchange messages for instance. For example, a traffic light is a system that consists of multiple subsystems, such as the different traffic lights, that work concurrently.

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  Best AI Paraphrasing Tools in 2026

  Curious about the best AI paraphrasing tool? An AI paraphrasing tool 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 paraphrasing tool 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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  Just This Once

  Just This Once is a 1993 romance novel written in the style of Jacqueline Susann by a Macintosh IIcx computer named "Hal" in collaboration with its programmer, Scott French. French reportedly spent $40,000 and 8 years developing an artificial intelligence program to analyze Susann's works and attempt to create a novel that Susann might have written. A legal dispute between the estate of Jacqueline Susann and the publisher resulted in a settlement to split the profits, and the book was referenced in several legal journal articles about copyright laws. The book had two small print runs totaling 35,000 copies, receiving mixed reviews. == Creation == The novel's creation spanned the fields of artificial intelligence, expert systems, and natural language processing. Scott French first scanned and analyzed portions of two books by Jacqueline Susann, Valley of the Dolls and Once Is Not Enough, to determine constituents of Susann's writing style, which French stated was the most difficult task. This analysis extracted several hundred components including frequency and type of sexual acts and sentence structure. "Once you're there, the writer's style emerges, part of her actual personality comes out, and the computer can be programmed to make a story." French also created several thousand rules to govern tone, plotting, scenes, and characters. The text generated by Hal, the computer, was intended to mimic what Susann might have written, although the output required significant editing. French credits Hal's work with "almost 100% of the plot, 100% of the theme and style." French estimates that he wrote 10% of the prose, the computer Hal wrote about 25% of the prose, and the remaining two-thirds was more of a collaboration between the two. A typical scenario to write a scene would involve Hal asking questions that French would answer (for example, Hal might ask about the "cattiness factor" involved in a meeting between two key female characters, and French would reply with a range of 1 to 10), and the computer would then generate a few sentences to which French would make minor edits. The process would repeat for the next few sentences until the scene was written. == Legal issues == Jacqueline Susann's publisher was skeptical of the legality of Just This Once, although French doubted that an author's thought processes could be copyrighted. Susann's estate reportedly threatened to sue Scott French but the parties settled out of court; the settlement involved splitting profits between the parties but the terms of the settlement were not disclosed. The publication of Just This Once raised questions in the legal profession concerning how copyright law applies to computer-generated works derived from an analysis of other copyrighted works, and whether the generation of such works infringes on copyright. The publications on this topic suggested that the copyright laws of the time were ill-equipped to deal with computer-generated creative works. == Reception == The book's publisher Steven Shragis of Carol Group said of the novel, "I'm not going to say this is a great literary work, but it's every bit as good as anything out in this field, and better than an awful lot." The novel received some positive early reviews. In USA Today, novelist Thomas Gifford compared Just This Once to another novel in the same genre, American Star by Jackie Collins. Gifford concluded: "If you do like this stuff, you'd be much, much better off with the one written by the computer." The Dead Jackie Susann Quarterly declared that Susann "would be proud. Lots of money, sleaze, disease, death, oral sex, tragedy and the good girl gone bad." Other reviews were mixed. Publishers Weekly wrote, "If the books of Jacqueline Susann and Harold Robbins seem formulaic, this debut novel of sin and success in Las Vegas outdoes them all. And that, in a way, is the point.... All novelty rests in the conceit of computer authorship, not in the story itself." Library Journal stated "French invested eight years and $50,000 in a scheme to use artificial intelligence to fulfill his authentic, if dubious, desire to generate a trashy novel a la Jacqueline Susann. Shallow, beautiful-people characters are flatly conceived and randomly accessed in a formulaic plot ... a sexy, boring morality tale. Of possible interest to computer buffs for its use of Expert Systems and the virtual promise of more worthy possibilities; others should read Susann." Kirkus Reviews wrote: "The deal here is that author French is not the author, he's just the midwife, having allegedly programmed his computer to write about our times just the way Susann would... almost perfectly capturing glamorous Jackie's turgid but E-Z reading prose style and ultrareliable mix of sex, glitz, dope 'n' despair.... One wonders, though, if French's tale spinning PC will do as well on the talkshows as Jackie did. The computer weenies have been trying to tell us for years, garbage in-garbage out."

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  Corpus manager

  A corpus manager (corpus browser or corpus query system) is a tool for multilingual corpus analysis, which allows effective searching in corpora. A corpus manager usually represents a complex tool that allows one to perform searches for language forms or sequences. It may provide information about the context or allow the user to search by positional attributes, such as lemma, tag, etc. These are called concordances. Other features include the ability to search for collocations, frequency statistics as well as metadata information about the processed text. The narrower meaning of corpus manager refers only to the server side or the corpus query engine, whereas the client side is simply called the user interface. A corpus manager can be software installed on a personal computer or it might be provided as a web service. == List of corpus managers == BNCweb – a web-based interface for the British National Corpus CQPweb - a web-based interface for the study of a large variety of corpora including the Spoken BNC2014 BYU-BNC – a website that allows searches of the British National Corpora and others created at Brigham Young University Coma – a tool extension of the system EXMARaLDA for working with oral corpora on a computer NoSketch Engine – a free open-source corpus management system combining Manatee (back-end) and Bonito (web interface) KonText – an extended and modified web interface to NoSketch Engine (a Bonito replacement) Sketch Engine – text corpus management and analysis software with more than 500 corpora in 90+ languages Spoco WordSmith Tools – a software package primarily for linguists

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  Top 10 AI Text-to-video Tools Compared (2026)

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

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  AI Blog Writers: Free vs Paid (2026)

  Shopping for the best AI blog writer? An AI blog writer 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 blog writer slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

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  Confusion network

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

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  Finite-state transducer

  A finite-state transducer (FST) is a finite-state machine with two memory tapes, following the terminology for Turing machines: an input tape and an output tape. This contrasts with an ordinary finite-state automaton, which has a single tape. An FST is a type of finite-state automaton (FSA) that maps between two sets of symbols. An FST is more general than an FSA. An FSA defines a formal language by defining a set of accepted strings, while an FST defines a relation between sets of strings. An FST will read a set of strings on the input tape and generate a set of relations on the output tape. An FST can be thought of as a translator or relater between strings in a set. In morphological parsing, an example would be inputting a string of letters into the FST, the FST would then output a string of morphemes. == Overview == An automaton can be said to recognize a string if we view the content of its tape as input. In other words, the automaton computes a function that maps strings into the set {0,1}. Alternatively, we can say that an automaton generates strings, which means viewing its tape as an output tape. On this view, the automaton generates a formal language, which is a set of strings. The two views of automata are equivalent: the function that the automaton computes is precisely the indicator function of the set of strings it generates. The class of languages generated by finite automata is known as the class of regular languages. The two tapes of a transducer are typically viewed as an input tape and an output tape. On this view, a transducer is said to transduce (i.e., translate) the contents of its input tape to its output tape, by accepting a string on its input tape and generating another string on its output tape. It may do so nondeterministically and it may produce more than one output for each input string. A transducer may also produce no output for a given input string, in which case it is said to reject the input. In general, a transducer computes a relation between two formal languages. Each string-to-string finite-state transducer relates the input alphabet Σ to the output alphabet Γ. Relations R on Σ×Γ that can be implemented as finite-state transducers are called rational relations. Rational relations that are partial functions, i.e. that relate every input string from Σ to at most one Γ, are called rational functions. Finite-state transducers are often used for phonological and morphological analysis in natural language processing research and applications. Pioneers in this field include Ronald Kaplan, Lauri Karttunen, Martin Kay and Kimmo Koskenniemi. A common way of using transducers is in a so-called "cascade", where transducers for various operations are combined into a single transducer by repeated application of the composition operator (defined below). == Formal construction == Formally, a finite transducer T is a 6-tuple (Q, Σ, Γ, I, F, δ) such that: Q is a finite set, the set of states; Σ is a finite set, called the input alphabet; Γ is a finite set, called the output alphabet; I is a subset of Q, the set of initial states; F is a subset of Q, the set of final states; and δ ⊆ Q × ( Σ ∪ { ϵ } ) × ( Γ ∪ { ϵ } ) × Q {\displaystyle \delta \subseteq Q\times (\Sigma \cup \{\epsilon \})\times (\Gamma \cup \{\epsilon \})\times Q} (where ε is the empty string) is the transition relation. We can view (Q, δ) as a labeled directed graph, known as the transition graph of T: the set of vertices is Q, and ( q , a , b , r ) ∈ δ {\displaystyle (q,a,b,r)\in \delta } means that there is a labeled edge going from vertex q to vertex r. We also say that a is the input label and b the output label of that edge. NOTE: This definition of finite transducer is also called letter transducer (Roche and Schabes 1997); alternative definitions are possible, but can all be converted into transducers following this one. Define the extended transition relation δ ∗ {\displaystyle \delta ^{}} as the smallest set such that: δ ⊆ δ ∗ {\displaystyle \delta \subseteq \delta ^{}} ; ( q , ϵ , ϵ , q ) ∈ δ ∗ {\displaystyle (q,\epsilon ,\epsilon ,q)\in \delta ^{}} for all q ∈ Q {\displaystyle q\in Q} ; and whenever ( q , x , y , r ) ∈ δ ∗ {\displaystyle (q,x,y,r)\in \delta ^{}} and ( r , a , b , s ) ∈ δ {\displaystyle (r,a,b,s)\in \delta } then ( q , x a , y b , s ) ∈ δ ∗ {\displaystyle (q,xa,yb,s)\in \delta ^{}} . The extended transition relation is essentially the reflexive transitive closure of the transition graph that has been augmented to take edge labels into account. The elements of δ ∗ {\displaystyle \delta ^{}} are known as paths. The edge labels of a path are obtained by concatenating the edge labels of its constituent transitions in order. The behavior of the transducer T is the rational relation [T] defined as follows: x [ T ] y {\displaystyle x[T]y} if and only if there exists i ∈ I {\displaystyle i\in I} and f ∈ F {\displaystyle f\in F} such that ( i , x , y , f ) ∈ δ ∗ {\displaystyle (i,x,y,f)\in \delta ^{}} . This is to say that T transduces a string x ∈ Σ ∗ {\displaystyle x\in \Sigma ^{}} into a string y ∈ Γ ∗ {\displaystyle y\in \Gamma ^{}} if there exists a path from an initial state to a final state whose input label is x and whose output label is y. === Weighted automata === Finite State Transducers can be weighted, where each transition is labelled with a weight in addition to the input and output labels. A Weighted Finite State Transducer (WFST) over a set K of weights can be defined similarly to an unweighted one as an 8-tuple T=(Q, Σ, Γ, I, F, E, λ, ρ), where: Q, Σ, Γ, I, F are defined as above; E ⊆ Q × ( Σ ∪ { ϵ } ) × ( Γ ∪ { ϵ } ) × Q × K {\displaystyle E\subseteq Q\times (\Sigma \cup \{\epsilon \})\times (\Gamma \cup \{\epsilon \})\times Q\times K} (where ε is the empty string) is the finite set of transitions; λ : I → K {\displaystyle \lambda :I\rightarrow K} maps initial states to weights; ρ : F → K {\displaystyle \rho :F\rightarrow K} maps final states to weights. In order to make certain operations on WFSTs well-defined, it is convenient to require the set of weights to form a semiring. Two typical semirings used in practice are the log semiring and tropical semiring: nondeterministic automata may be regarded as having weights in the Boolean semiring. Two weighted FST can be composed. == Operations on finite-state transducers == The following operations defined on finite automata also apply to finite transducers: Union. Given transducers T and S, there exists a transducer T ∪ S {\displaystyle T\cup S} such that x [ T ∪ S ] y {\displaystyle x[T\cup S]y} if and only if x [ T ] y {\displaystyle x[T]y} or x [ S ] y {\displaystyle x[S]y} . Concatenation. Given transducers T and S, there exists a transducer T ⋅ S {\displaystyle T\cdot S} such that x [ T ⋅ S ] y {\displaystyle x[T\cdot S]y} if and only if there exist x 1 , x 2 , y 1 , y 2 {\displaystyle x_{1},x_{2},y_{1},y_{2}} with x = x 1 x 2 , y = y 1 y 2 , x 1 [ T ] y 1 {\displaystyle x=x_{1}x_{2},y=y_{1}y_{2},x_{1}[T]y_{1}} and x 2 [ S ] y 2 . {\displaystyle x_{2}[S]y_{2}.} Kleene closure. Given a transducer T, there might exist a transducer T ∗ {\displaystyle T^{}} with the following properties: and x [ T ∗ ] y {\displaystyle x[T^{}]y} does not hold unless mandated by (k1) or (k2). Composition. Given a transducer T on alphabets Σ and Γ and a transducer S on alphabets Γ and Δ, there exists a transducer T ∘ S {\displaystyle T\circ S} on Σ and Δ such that x [ T ∘ S ] z {\displaystyle x[T\circ S]z} if and only if there exists a string y ∈ Γ ∗ {\displaystyle y\in \Gamma ^{}} such that x [ T ] y {\displaystyle x[T]y} and y [ S ] z {\displaystyle y[S]z} . This operation extends to the weighted case. This definition uses the same notation used in mathematics for relation composition. However, the conventional reading for relation composition is the other way around: given two relations T and S, ( x , z ) ∈ T ∘ S {\displaystyle (x,z)\in T\circ S} when there exist some y such that ( x , y ) ∈ S {\displaystyle (x,y)\in S} and ( y , z ) ∈ T . {\displaystyle (y,z)\in T.} Projection to an automaton. There are two projection functions: π 1 {\displaystyle \pi _{1}} preserves the input tape, and π 2 {\displaystyle \pi _{2}} preserves the output tape. The first projection, π 1 {\displaystyle \pi _{1}} is defined as follows: Given a transducer T, there exists a finite automaton π 1 T {\displaystyle \pi _{1}T} such that π 1 T {\displaystyle \pi _{1}T} accepts x if and only if there exists a string y for which x [ T ] y . {\displaystyle x[T]y.} :The second projection, π 2 {\displaystyle \pi _{2}} is defined similarly. Determinization. Given a transducer T, we want to build an equivalent transducer that has a unique initial state and such that no two transitions leaving any state share the same input label. The powerset construction can be extended to transducers, or even weighted transducers, but sometimes fails to halt; indeed, some non-deterministic transducers do not admit equivalent

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  Katia Sycara

  Ekaterini Panagiotou Sycara (Greek: Κάτια Συκαρά) is a Greek computer scientist. She is an Edward Fredkin Research Professor of Robotics in the Robotics Institute, School of Computer Science at Carnegie Mellon University internationally known for her research in artificial intelligence, particularly in the fields of negotiation, autonomous agents and multi-agent systems. She directs the Advanced Agent-Robotics Technology Lab at Robotics Institute, Carnegie Mellon University. She also serves as academic advisor for PhD students at both Robotics Institute and Tepper School of Business. == Education and early life == Born in Greece, she went to the United States to pursue advanced education through various scholarships, including a Fulbright (1965-1969). She received a B.S. in applied mathematics from Brown University, M.S. in electrical engineering from the University of Wisconsin–Milwaukee, and PhD in computer science from Georgia Institute of Technology. == Research and career == Sycara is a pioneer in the field of semantic web, case-based reasoning, autonomous agents and multi-agent systems. She has authored or co-authored more than 700 technical papers dealing with multi-agent systems, software agents, web services, semantic web, human–computer interaction, human-robot interaction, negotiation, case-based reasoning and the application of these techniques to crisis action planning, scheduling, manufacturing, healthcare management, financial planning and e-commerce.[1] She has led multimillion-dollar research effort funded by DARPA, NASA, AFOSR, ONR, AFRL, NSF and industry. Through an ONR MURI program and though the COABS DARPA program, Prof. Sycara's group has developed the RETSINA multiagent infrastructure, a toolkit that enables the development of heterogeneous software agents that can dynamically coordinate in open information environments (e.g. the Internet). RETSINA has been used in multiple applications including supporting human joint mission teams for crisis response; creating autonomous agents for situation awareness and information fusion; financial portfolio management, negotiations and coalition formation for e-commerce, and coordinating robots for Urban Search and Rescue. Sycara is one of the contributors to the development of OWL-S, the Darpa-sponsored language for Semantic Web services, as well as matchmaking and brokering software for agent discovery, service integration and semantic interoperation. === Academic service === Sycara is the founding Editor-in-Chief of the journal Autonomous Agents and Multi-Agent Systems; Editor-in-Chief, of the Springer Series on Agents; and Area Editor of AI and Management Science, the journal "Group Decision and Negotiation." She is a member of the Editorial Board, the Kluwer book series on "Multiagent Systems, Artificial Societies and Simulated Organizations"; member of the editorial board, the journals "Agent Oriented Software Engineering", "Web Intelligence and Agent Technologies", "Journal of Infonomics", "Fundamenda Informaticae", and "Concurrent Engineering: Research and Applications"; and member of the editorial board of the "ETAI journal on the Semantic Web" (1998–2001). She was on the Editorial Board of "IEEE Intelligent Systems and their Applications" (1992–1996), and "AI in Engineering" (1990–1996). She is a member of the Scientific Advisory Board of France Telecom, 2003-2009; member of the Scientific Advisory Board of the Institute of Informatics and Telecommunications of the Greek National Research Center Demokritos, 2004-2012; member of the AAAI Executive Council (1996–99); member of the OASIS Technical committee on the development of UDDI (Universal Description and Discovery for Interoperability) software which is an industry standard; and an invited expert for W3C (the World Wide Web Consortium) Working Group on Web Services Architecture. She was a founding member of the Board of Directors of the International Foundation of Multiagent Systems (IFMAS), and founding member of the Semantic Web Science Association. Sycara served as the program chair of the Second International Semantic Web Conference (ISWC 2003); general chair, of the Second International Conference on Autonomous Agents (Agents 98); chair of the Steering Committee of the Agents Conference (1999–2001); scholarship chair of AAAI (1993–1999); and the US co-chair for the US-Europe Semantic Web Services Initiative. === Awards and honors === Sycara is a Fellow of Institute of Electrical and Electronics Engineers (IEEE), and a Fellow of American Association for Artificial Intelligence (AAAI). Sycara is the recipient of the 2002 ACM/SIGART Agents Research Award. She is also the recipient of the 2015 Group Decision and Negotiation (GDN) Award of the Institute for Operations Research and the Management Sciences (INFORMS) GDN Section for her outstanding contributions to the field of group decision and negotiation. According to the citation of the award: Katia Sycara is widely acknowledged as one of the leading researchers in the field of autonomous software agents and in particular on problems related to joint decision making and negotiations of such agents. Her work is characterized by a unique combination of methods from Artificial Intelligence and research on human negotiations, and thus has contributed to significant advances in both fields. Sycara's robot teams have won multiple international awards. In the 2005 Robocup Urban Search and Rescue (US Open) held in Atlanta, her team won the First-in-Class Award for Autonomy, and the First-in-Class Award for Mobility. Two years later, again in Atlanta, she led another team that became a world champions in the 2007 International Robocup Search and Rescue Simulation League Competition. In 2008, her robotic team placed third in the Worldwide Robocup Championship Competition in the Urban Search and Rescue Virtual robots League held in Beijing, China. In 2005, she received the Outstanding Alumnus Award from the University of Wisconsin–Milwaukee. She was awarded an Honorary Doctorate from the University of the Aegean in 2004.

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