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MFF-condition
In formal language theory, in particular in algorithmic learning theory, a class ''C'' of languages has finite thickness if every string is contained in at most finitely many languages in ''C''. This condition was introduced by Dana Angluin as a sufficient condition In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If then ", is necessary for , because the truth of ... for ''C'' being identifiable in the limit. The related notion of M-finite thickness Given a language ''L'' and an indexed class ''C'' = of languages, a member language ''L''''j'' ∈ ''C'' is called a minimal concept of ''L'' within ''C'' if ''L'' ⊆ ''L''''j'', but not ''L'' ⊊ ''L''''i'' ⊆ ''L''''j'' for any ''L''''i'' ∈ ''C''. The class ''C'' is said to satisfy the MEF-condition if every finite subset ''D'' of a member language ''L''''i'' ∈ ''C'' has a minim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Language Identification In The Limit
Language identification in the limit is a formal model for inductive inference of formal languages, mainly by computers (see machine learning and induction of regular languages). It was introduced by E. Mark Gold in a technical report and a journal article with the same title. In this model, a ''teacher'' provides to a ''learner'' some ''presentation'' (i.e. a sequence of strings) of some formal language. The learning is seen as an infinite process. Each time the learner reads an element of the presentation, it should provide a ''representation'' (e.g. a formal grammar) for the language. Gold defines that a learner can ''identify in the limit'' a class of languages if, given any presentation of any language in the class, the learner will produce only a finite number of wrong representations, and then stick with the correct representation. However, the learner need not be able to announce its correctness; and the teacher might present a counterexample to any representation arbitrari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Language Theory
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings of the language. Each string concatenated from symbols of this alphabet is called a word, and the words that belong to a particular formal language are sometimes called ''well-formed words'' or ''well-formed formulas''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, which consists of its formation rules. In computer science, formal languages are used among others as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages in which the words of the language represent concepts that are associated with particular meanings or semantics. In computational complexity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithmic Learning Theory
Algorithmic learning theory is a mathematical framework for analyzing machine learning problems and algorithms. Synonyms include formal learning theory and algorithmic inductive inference. Algorithmic learning theory is different from statistical learning theory in that it does not make use of statistical assumptions and analysis. Both algorithmic and statistical learning theory are concerned with machine learning and can thus be viewed as branches of computational learning theory. Distinguishing characteristics Unlike statistical learning theory and most statistical theory in general, algorithmic learning theory does not assume that data are random samples, that is, that data points are independent of each other. This makes the theory suitable for domains where observations are (relatively) noise-free but not random, such as language learning and automated scientific discovery. The fundamental concept of algorithmic learning theory is learning in the limit: as the number of d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Language
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings of the language. Each string concatenated from symbols of this alphabet is called a word, and the words that belong to a particular formal language are sometimes called ''well-formed words'' or ''well-formed formulas''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, which consists of its formation rules. In computer science, formal languages are used among others as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages in which the words of the language represent concepts that are associated with particular meanings or semantics. In computational complexity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dana Angluin
Dana Angluin is a professor emeritus of computer science at Yale University. She is known for foundational work in computational learning theory and distributed computing. Education Angluin received her B.A. (1969) and Ph.D. (1976) at University of California, Berkeley. Her thesis, entitled "An application of the theory of computational complexity to the study of inductive inference" was one of the first works to apply complexity theory to the field of inductive inference. Angluin joined the faculty at Yale in 1979. Research Angluin has written highly cited papers on computational learning theory, where she studied learning from noisy examples and learning regular sets from queries and counterexamples (the L* algorithm). In distributed computing, she co-invented the population protocol model and studied the problem of consensus. In probabilistic algorithms, she has studied randomized algorithms for Hamiltonian circuits and matchings.D Angluin (1976). "An Application of the The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sufficient Condition
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If then ", is necessary for , because the truth of is guaranteed by the truth of (equivalently, it is impossible to have without ). Similarly, is sufficient for , because being true always implies that is true, but not being true does not always imply that is not true. In general, a necessary condition is one that must be present in order for another condition to occur, while a sufficient condition is one that produces the said condition. The assertion that a statement is a "necessary ''and'' sufficient" condition of another means that the former statement is true if and only if the latter is true. That is, the two statements must be either simultaneously true, or simultaneously false. In ordinary English (also natural language) "necessary" and "sufficient" indicate relations betw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
