AI Email Name Generator

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

• 

  Inferential theory of learning

  Inferential Theory of Learning (ITL) is an area of machine learning which describes inferential processes performed by learning agents. ITL has been continuously developed by Ryszard S. Michalski, starting in the 1980s. The first known publication of ITL was in 1983. In the ITL learning process is viewed as a search (inference) through hypotheses space guided by a specific goal. The results of learning need to be stored. Stored information will later be used by the learner for future inferences. Inferences are split into multiple categories including conclusive, deduction, and induction. In order for an inference to be considered complete it was required that all categories must be taken into account. This is how the ITL varies from other machine learning theories like Computational Learning Theory and Statistical Learning Theory; which both use singular forms of inference. == Usage == The most relevant published usage of ITL was in scientific journal published in 2012 and used ITL as a way to describe how agent-based learning works. According to the journal "The Inferential Theory of Learning (ITL) provides an elegant way of describing learning processes by agents".

  Read more →
• 

  Is an AI Virtual Assistant Worth It in 2026?

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

  Read more →
• 

  Liz Liddy

  Elizabeth DuRoss Liddy (May 12, 1944 – August 21, 2025) was an American computer scientist and academic who was professor of information science and dean of the Syracuse University School of Information Studies. She was a pioneer in the field of natural language processing. == Early life and education == Liddy was born in Dayton, Ohio, on May 14, 1944, and grew up in Utica, New York. She was one of five children, all of whom worked in her father's family business. Liddy attended St. Francis DeSalle High School, where she was awarded a Regent's Scholarship, and eventually attended Daemen College. She was literary editor of her high school year book and edited a literary magazine during her time at college. At Daemen College Liddy studied English language and literature. After graduating Liddy remained in New York, where she volunteered in an elementary school library. She joined the Syracuse University School of Information Studies in 1983, where she started a graduate program in library science. She worked as a faculty librarian at Onondaga Community College whilst earning her degree. Here Liddy worked as a Visiting assistant professor, whilst completing her doctorate part-time in information transfer. Her dissertation research involved natural language processing, a computerized approach to analyzing text. She was hired to the faculty at Syracuse University whilst completing her PhD. == Research and career == In 1994 Liddy was the founding President of TextWise, a semantics-based search engine. The first product she developed was called Document Retrieval Using Linguistic Knowledge (DR-LINK). She left TextWise in 1999, after growing the number of employees to over 50. She started the Syracuse University Center for Natural Language Processing in 1999, and was honored with the university's Outstanding Alumni Award the following year. Liddy was appointed Dean of the School of Information Studies (iSchool) in 2008, and held the position for over ten years. She temporarily left the role in 2015. The school was transformed under her leadership, increasing the enrollment of students by over 70% and launching a graduate certificate in data science. She raised over $20 million to support research and development at Syracuse University. She chaired the iSchool Organization, which connects information science schools all over the world, from 2012 to 2014. Liddy worked to increase the representation of women at the iSchool, through initiatives such as the IT Girls Overnight Retreat – an annual weekend to introduce high school girls to Information Technology. She improved the career development programs of students at Syracuse University, increasing student employment to almost 100% post graduation. Liddy retired as Dean of the iSchool in 2019. === Selected innovations === US 6026388, Liddy, Elizabeth D., "User interface and other enhancements for natural language information retrieval system and method", published August 16, 1995, issued February 15, 2000 US 5963940, Liddy, Elizabeth D., "Natural language information retrieval system and method", published August 16, 1995, issued October 5, 1999 US 6006221, Liddy, Elizabeth D., "Multilingual document retrieval system and method using semantic vector matching", published August 16, 1995, issued December 21, 1999 == Personal life and death == Liddy was married shortly after graduating Daemen College in 1966. She had three children. Liddy died in Charlotte, North Carolina, on August 21, 2025, at the age of 81.

  Read more →
• 

  Transfer-based machine translation

  Transfer-based machine translation is a type of machine translation (MT). It is currently one of the most widely used methods of machine translation. In contrast to the simpler direct model of MT, transfer MT breaks translation into three steps: analysis of the source language text to determine its grammatical structure, transfer of the resulting structure to a structure suitable for generating text in the target language, and finally generation of this text. Transfer-based MT systems are thus capable of using knowledge of the source and target languages. == Design == Both transfer-based and interlingua-based machine translation have the same idea: to make a translation it is necessary to have an intermediate representation that captures the "meaning" of the original sentence in order to generate the correct translation. In interlingua-based MT this intermediate representation must be independent of the languages in question, whereas in transfer-based MT, it has some dependence on the language pair involved. The way in which transfer-based machine translation systems work varies substantially, but in general they follow the same pattern: they apply sets of linguistic rules which are defined as correspondences between the structure of the source language and that of the target language. The first stage involves analysing the input text for morphology and syntax (and sometimes semantics) to create an internal representation. The translation is generated from this representation using both bilingual dictionaries and grammatical rules. It is possible with this translation strategy to obtain fairly high quality translations, with accuracy in the region of 90% (although this is highly dependent on the language pair in question, for example the distance between the two). == Operation == In a rule-based machine translation system the original text is first analysed morphologically and syntactically in order to obtain a syntactic representation. This representation can then be refined to a more abstract level putting emphasis on the parts relevant for translation and ignoring other types of information. The transfer process then converts this final representation (still in the original language) to a representation of the same level of abstraction in the target language. These two representations are referred to as "intermediate" representations. From the target language representation, the stages are then applied in reverse. == Analysis and transformation == Various methods of analysis and transformation can be used before obtaining the final result. Along with these statistical approaches may be augmented generating hybrid systems. The methods which are chosen and the emphasis depends largely on the design of the system, however, most systems include at least the following stages: Morphological analysis. Surface forms of the input text are classified as to part-of-speech (e.g. noun, verb, etc.) and sub-category (number, gender, tense, etc.). All of the possible "analyses" for each surface form are typically made output at this stage, along with the lemma of the word. Lexical categorisation. In any given text some of the words may have more than one meaning, causing ambiguity in analysis. Lexical categorisation looks at the context of a word to try to determine the correct meaning in the context of the input. This can involve part-of-speech tagging and word sense disambiguation. Lexical transfer. This is basically dictionary translation; the source language lemma (perhaps with sense information) is looked up in a bilingual dictionary and the translation is chosen. Structural transfer. While the previous stages deal with words, this stage deals with larger constituents, for example phrases and chunks. Typical features of this stage include concordance of gender and number, and re-ordering of words or phrases. Morphological generation. From the output of the structural transfer stage, the target language surface forms are generated. == Transfer types == One of the main features of transfer-based machine translation systems is a phase that "transfers" an intermediate representation of the text in the original language to an intermediate representation of text in the target language. This can work at one of two levels of linguistic analysis, or somewhere in between. The levels are: Superficial transfer (or syntactic). This level is characterised by transferring "syntactic structures" between the source and target languages. It is suitable for languages in the same family or of the same type, for example in the Romance languages between Spanish, Catalan, French, Italian, etc. Deep transfer (or semantic). This level constructs a semantic representation that is dependent on the source language. This representation can consist of a series of structures which represent the meaning. In these transfer systems predicates are typically produced. The translation also typically requires structural transfer. This level is used to translate between more distantly related languages (e.g. Spanish-English or Spanish-Basque, etc.)

  Read more →
• 

  Jaggies

  Jaggies are visual artifacts in raster images, most frequently from aliasing, which in turn is often caused by non-linear mixing effects producing high-frequency components, or missing or poor anti-aliasing filtering prior to sampling. Jaggies are stair-like lines that appear where there should be "smooth" straight lines or curves. For example, when a nominally straight, un-aliased line steps across one pixel either horizontally or vertically, a "dogleg" occurs halfway through the line, where it crosses the threshold from one pixel to the other. Jaggies should not be confused with most compression artifacts, which are a different phenomenon. == Causes == Jaggies occur due to the "staircase effect". This is because a line represented in raster mode is approximated by a sequence of pixels. Jaggies can occur for a variety of reasons, the most common being that the output device (display monitor or printer) does not have sufficient resolution to portray a smooth line. In addition, jaggies often occur when a bit-mapped image is scaled to a higher resolution. This is one of the advantages that vector graphics have over bitmapped graphics – a vector image can be losslessly scaled to any arbitrary resolution or stretched infinitely in either axis without introducing jaggies. == Solutions == The effect of jaggies can be reduced by a graphics technique known as spatial anti-aliasing. Anti-aliasing smooths out jagged lines by surrounding them with transparent pixels to simulate the appearance of fractionally-filled pixels when viewed at a distance. The downside of anti-aliasing is that it reduces contrast – rather than sharp black/white transitions, there are shades of gray – and the resulting image can appear fuzzy. This is an inescapable trade-off: if the resolution is insufficient to display the desired detail, the output will either be jagged, fuzzy, or some combination thereof. While machine learning-based upscaling techniques such as DLSS can be used to infer this missing information, other types of artifacts may be introduced in the process. In real-time 3D rendering such as in video games, various anti-aliasing techniques are used to remove jaggies created by the edges of polygons and other contrasting lines. Since anti-aliasing can impose a significant performance overhead, games for home computers often allow users to choose the level and type of anti-aliasing in use in order to optimize their experience, whereas on consoles this setting is typically fixed for each title to ensure a consistent experience. While anti-aliasing is generally implemented through graphics APIs like DirectX and Vulkan, some consoles such as the Xbox 360 and PlayStation 3 are also capable of anti-aliasing to little direct performance cost by way of dedicated hardware which performs anti-aliasing on the contents of the framebuffer once it has been rendered by the GPU. Jaggies in bitmaps, such as sprites and surface materials, are most often dealt with by separate texture filtering routines, which are far easier to perform than anti-aliasing filtering. Texture filtering became ubiquitous on PCs after the introduction of 3Dfx's Voodoo GPU. == Notable uses of the term == In the 1985 game Rescue on Fractalus! for the Atari 8-bit computers, the graphics depicting the cockpit of the player's spacecraft contains two window struts, which are not anti-aliased and are therefore very "jagged". The developers made fun of this and named the in-game enemies "Jaggi", and also initially titled the game Behind Jaggi Lines!. The latter idea was scrapped by the marketing department before release.

  Read more →
• 

  Kalman filter

  In statistics and control theory, Kalman filtering (also known as linear quadratic estimation) is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, to produce estimates of unknown variables that tend to be more accurate than those based on a single measurement, by estimating a joint probability distribution over the variables for each time-step. The filter is constructed as a mean squared error minimiser, but an alternative derivation of the filter is also provided showing how the filter relates to maximum likelihood statistics. The filter is named after Rudolf E. Kálmán. Kalman filtering has numerous technological applications. A common application is for guidance, navigation, and control of vehicles, particularly aircraft, spacecraft and ships positioned dynamically. Furthermore, Kalman filtering is much applied in time series analysis tasks such as signal processing and econometrics. Kalman filtering is also important for robotic motion planning and control, and can be used for trajectory optimization. Kalman filtering also works for modeling the central nervous system's control of movement. Due to the time delay between issuing motor commands and receiving sensory feedback, the use of Kalman filters provides a realistic model for making estimates of the current state of a motor system and issuing updated commands. The algorithm works via a two-phase process: a prediction phase and an update phase. In the prediction phase, the Kalman filter produces estimates of the current state variables, including their uncertainties. Once the outcome of the next measurement (necessarily corrupted with some error, including random noise) is observed, these estimates are updated using a weighted average, with more weight given to estimates with greater certainty. The algorithm is recursive. It can operate in real time, using only the present input measurements and the state calculated previously and its uncertainty matrix; no additional past information is required. Optimality of Kalman filtering assumes that errors have a normal (Gaussian) distribution. In the words of Rudolf E. Kálmán, "The following assumptions are made about random processes: Physical random phenomena may be thought of as due to primary random sources exciting dynamic systems. The primary sources are assumed to be independent gaussian random processes with zero mean; the dynamic systems will be linear." Regardless of Gaussianity, however, if the process and measurement covariances are known, then the Kalman filter is the best possible linear estimator in the minimum mean-square-error sense, although there may be better nonlinear estimators. It is a common misconception (perpetuated in the literature) that the Kalman filter cannot be rigorously applied unless all noise processes are assumed to be Gaussian. Extensions and generalizations of the method have also been developed, such as the extended Kalman filter and the unscented Kalman filter which work on nonlinear systems. The basis is a hidden Markov model such that the state space of the latent variables is continuous and all latent and observed variables have Gaussian distributions. Kalman filtering has been used successfully in multi-sensor fusion, and distributed sensor networks to develop distributed or consensus Kalman filtering. == History == The filtering method is named for Hungarian émigré Rudolf E. Kálmán, although Thorvald Nicolai Thiele and Peter Swerling developed a similar algorithm earlier. Richard S. Bucy of the Johns Hopkins Applied Physics Laboratory contributed to the theory, causing it to be known sometimes as Kalman–Bucy filtering. Kalman was inspired to derive the Kalman filter by applying state variables to the Wiener filtering problem. Stanley F. Schmidt is generally credited with developing the first implementation of a Kalman filter. He realized that the filter could be divided into two distinct parts, with one part for time periods between sensor outputs and another part for incorporating measurements. It was during a visit by Kálmán to the NASA Ames Research Center that Schmidt saw the applicability of Kálmán's ideas to the nonlinear problem of trajectory estimation for the Apollo program resulting in its incorporation in the Apollo navigation computer. This digital filter is sometimes termed the Stratonovich–Kalman–Bucy filter because it is a special case of a more general, nonlinear filter developed by the Soviet mathematician Ruslan Stratonovich. In fact, some of the special case linear filter's equations appeared in papers by Stratonovich that were published before the summer of 1961, when Kalman met with Stratonovich during a conference in Moscow. This Kalman filtering was first described and developed partially in technical papers by Swerling (1958), Kalman (1960) and Kalman and Bucy (1961). The Apollo computer used 2k of magnetic core RAM and 36k wire rope [...]. The CPU was built from ICs [...]. Clock speed was under 100 kHz [...]. The fact that the MIT engineers were able to pack such good software (one of the very first applications of the Kalman filter) into such a tiny computer is truly remarkable. Kalman filters have been vital in the implementation of the navigation systems of U.S. Navy nuclear ballistic missile submarines, and in the guidance and navigation systems of cruise missiles such as the U.S. Navy's Tomahawk missile and the U.S. Air Force's Air Launched Cruise Missile. They are also used in the guidance and navigation systems of reusable launch vehicles and the attitude control and navigation systems of spacecraft which dock at the International Space Station. == Overview of the calculation == Kalman filtering uses a system's dynamic model (e.g., physical laws of motion), known control inputs to that system, and multiple sequential measurements (such as from sensors) to form an estimate of the system's varying quantities (its state) that is better than the estimate obtained by using only one measurement alone. As such, it is a common sensor fusion and data fusion algorithm. Noisy sensor data, approximations in the equations that describe the system evolution, and external factors that are not accounted for, all limit how well it is possible to determine the system's state. The Kalman filter deals effectively with the uncertainty due to noisy sensor data and, to some extent, with random external factors. The Kalman filter produces an estimate of the state of the system as an average of the system's predicted state and of the new measurement using a weighted average. The purpose of the weights is that values with better (i.e., smaller) estimated uncertainty are "trusted" more. The weights are calculated from the covariance, a measure of the estimated uncertainty of the prediction of the system's state. The result of the weighted average is a new state estimate that lies between the predicted and measured state, and has a better estimated uncertainty than either alone. This process is repeated at every time step, with the new estimate and its covariance informing the prediction used in the following iteration. This means that Kalman filter works recursively and requires only the last "best guess", rather than the entire history, of a system's state to calculate a new state. The measurements' certainty-grading and current-state estimate are important considerations. It is common to discuss the filter's response in terms of the Kalman filter's gain. The Kalman gain is the weight given to the measurements and current-state estimate, and can be "tuned" to achieve a particular performance. With a high gain, the filter places more weight on the most recent measurements, and thus conforms to them more responsively. With a low gain, the filter conforms to the model predictions more closely. At the extremes, a high gain (close to one) will result in a more jumpy estimated trajectory, while a low gain (close to zero) will smooth out noise but decrease the responsiveness. When performing the actual calculations for the filter (as discussed below), the state estimate and covariances are coded into matrices because of the multiple dimensions involved in a single set of calculations. This allows for a representation of linear relationships between different state variables (such as position, velocity, and acceleration) in any of the transition models or covariances. == Example application == As an example application, consider the problem of determining the precise location of a truck. The truck can be equipped with a GPS unit that provides an estimate of the position within a few meters. The GPS estimate is likely to be noisy; readings 'jump around' rapidly, though remaining within a few meters of the real position. In addition, since the truck is expected to follow the laws of physics, its position can also be estimated by integrating its velocity over time, determined by keeping track of wheel revolutions and the

  Read more →
• 

  AI Resume Builders: Free vs Paid (2026)

  Comparing the best AI resume builder? An AI resume builder is software that uses machine learning to help you get more done — it lowers the barrier so anyone can produce professional output. Privacy matters too: check whether your data trains the model and whether a no-log or enterprise tier is available. Whether you are a beginner or a pro, the right AI resume builder slots into your workflow and pays for itself fast. Below we compare features, pricing, and real output so you can choose with confidence.

  Read more →
• 

  Hideto Tomabechi

  Hideto Tomabechi (苫米地 英人, Tomabechi Hideto; born 1959) is a Japanese cognitive scientist who is an adjunct fellow at Carnegie Mellon University and has had an executive role in several companies. == Early life and education == He grew up in Minato-ku, Tokyo. He graduated from Komaba Toho High School and then joined the University of Massachusetts Amherst. He received his first degree from Sophia University, then joined Mitsubishi Real Estate. Tomabechi was a Fulbright Scholar at Yale University and became member of Yale University Artificial Intelligence Research Center and Yale Cognitive Science Program. Hideto Tomabechi's research topic was: Cognition Models for Language Expressions and Computational Methods (Tomabechi Algorithm). Hideto Tomabechi received his Ph.D. in the field of computational linguistics from Carnegie Mellon University. His 1993 Ph.D. Thesis was entitled "Efficient Unification for Natural Language". == Career timeline == 1992-1998: Director, Justsystem Scientific Institute. 1998: CEO of Cognitive Research Laboratories Inc. 2007: Adjunct Fellow at the Cyber Security & Privacy Research Institute (CyLab) at Carnegie Mellon University. 2020: Visiting professor at Nano & Life Research Center, Waseda University. 2020: Chairman, Resilience Japan, LLC. 2022: Chairman of Japan Society for Foreign Policy. == Brain research == In 1993, Hideto Tomabechi became director of the Development Department. Later, Tomabechi became director of the JustSystems Basic Research Institute Tomabechi researched the basic functions of the human brain and mind. The purpose of brain and consciousness research were to develop the human machine interface. The main areas of research were altered states of consciousness, hypnosis, homeostasis, brain functions, and functions of the human mind in cyberspace. Dr. Tomabechi founded the Bechi Unit, the world's first virtual currency at JustSystems, based on Tomabech Algorithms. == Brainwashing == Tomabechi was the scientist who deprogrammed the leaders of the religious cult responsible for the terrorist attack in the Tokyo subway. The cult (Aum Shinrikyo) brainwashed its people and they carried out the attacks in an influenced state of consciousness.

  Read more →
• 

  Deadbot

  A deadbot, deathbot, or griefbot is a digital avatar, created with artificial intelligence, which resembles a person who is dead. Griefbots employ natural language processing and machine-learning techniques to approximate the style and personality of a deceased person. They may appear as chatbots, voice assistants, or animated avatars, and are often trained on an individual's digital remains. == History == Among the earliest researchers, Muhammad Aurangzeb Ahmad of the University of Washington, developed the Grandpa Bot project, a conversational simulation of his late father designed for his children to interact with. Other efforts include journalist James Vlahos's Dadbot, which evolved into the commercial platform HereAfter AI. Hossein Rahnama's Augmented Eternity research at MIT Media Lab and Toronto Metropolitan University, and game designer Jason Rohrer's "Project December", have enabled users to converse with language-model representations of loved ones. Early commercial projects such as Eternime, founded by Marius Ursache, also popularized the notion of interactive digital immortality. == Cultural and societal impact == Scholars have proposed frameworks and critiques addressing the ethics of these technologies. Tomasz Hollanek and Katarzyna Nowaczyk-Basińska developed a design-ethics taxonomy distinguishing the data donor, data recipient, and interactant. Edina Harbinja and Lilian Edwards formalized the concept of post-mortem privacy, and Carl J. Öhman at the Oxford Internet Institute studied the management of large-scale digital remains. Cultural acceptance varies: while some view them as expressions of remembrance, others regard them as unsettling or ethically problematic. Concerns have been raised about deadbots' potential for creating psychological harm. Griefbots are considered part of the phenomenon of artificial intimacy.

  Read more →
• 

  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.

  Read more →
• 

  AI Pair Programmers: Free vs Paid (2026)

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

  Read more →
• 

  Two-way finite automaton

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

  Read more →
• 

  Video renderer

  A video renderer is software that processes a video file and sends it sequentially to the video display controller card for display on a computer screen. An example of a video renderer, is the VMR-7 that was used by Microsoft's DirectShow. An example of a UNIX video renderer is the one container within GStreamer. Commonly used video renderers are: Enhanced Video Renderer VMR9 Renderless Haali's Video Renderer Madvr Video Renderer JRVR, a part of JRiver Media Center

  Read more →
• 

  NFA minimization

  In automata theory (a branch of theoretical computer science), NFA minimization is the task of transforming a given nondeterministic finite automaton (NFA) into an equivalent NFA that has a minimum number of states, transitions, or both. While efficient algorithms exist for DFA minimization, NFA minimization is PSPACE-complete. No efficient (polynomial time) algorithms are known, and under the standard assumption that P ≠ PSPACE, none exist. The most efficient known algorithm is the Kameda–Weiner algorithm. == Non-uniqueness of minimal NFA == Unlike deterministic finite automata, minimal NFAs may not be unique. There may be multiple NFAs with the same number of states that accept the same regular language, but for which there is no equivalent NFA or DFA with fewer states.

  Read more →
• 

  Pachinko allocation

  In machine learning and natural language processing, the pachinko allocation model (PAM) is a topic model. Topic models are a suite of algorithms to uncover the hidden thematic structure of a collection of documents. The algorithm improves upon earlier topic models such as latent Dirichlet allocation (LDA) by modeling correlations between topics in addition to the word correlations which constitute topics. PAM provides more flexibility and greater expressive power than latent Dirichlet allocation. While first described and implemented in the context of natural language processing, the algorithm may have applications in other fields such as bioinformatics. The model is named for pachinko machines—a game popular in Japan, in which metal balls bounce down around a complex collection of pins until they land in various bins at the bottom. == History == Pachinko allocation was first described by Wei Li and Andrew McCallum in 2006. The idea was extended with hierarchical Pachinko allocation by Li, McCallum, and David Mimno in 2007. In 2007, McCallum and his colleagues proposed a nonparametric Bayesian prior for PAM based on a variant of the hierarchical Dirichlet process (HDP). The algorithm has been implemented in the MALLET software package published by McCallum's group at the University of Massachusetts Amherst. == Model == PAM connects words in V and topics in T with an arbitrary directed acyclic graph (DAG), where topic nodes occupy the interior levels and the leaves are words. The probability of generating a whole corpus is the product of the probabilities for every document: P ( D | α ) = ∏ d P ( d | α ) {\displaystyle P(\mathbf {D} |\alpha )=\prod _{d}P(d|\alpha )}

  Read more →