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  2. Ogden's lemma - Wikipedia

    en.wikipedia.org/wiki/Ogden's_lemma

    Ogden's lemma is often stated in the following form, which can be obtained by "forgetting about" the grammar, and concentrating on the language itself: If a language L is context-free, then there exists some number (where p may or may not be a pumping length) such that for any string s of length at least p in L and every way of "marking" p or more of the positions in s, s can be written as

  3. Automata theory - Wikipedia

    en.wikipedia.org/wiki/Automata_theory

    Automata theory is closely related to formal language theory. In this context, automata are used as finite representations of formal languages that may be infinite. Automata are often classified by the class of formal languages they can recognize, as in the Chomsky hierarchy, which describes a nesting relationship between major classes of automata.

  4. Chomsky hierarchy - Wikipedia

    en.wikipedia.org/wiki/Chomsky_hierarchy

    The Chomsky hierarchy in the fields of formal language theory, computer science, and linguistics, is a containment hierarchy of classes of formal grammars. A formal grammar describes how to form strings from a language's vocabulary (or alphabet) that are valid according to the language's syntax.

  5. Induction of regular languages - Wikipedia

    en.wikipedia.org/wiki/Induction_of_regular_languages

    Mapping [note 2] each equivalence E to the corresponding quotient automaton language L(A a,b,c,d / E) obtains the partially ordered set shown in the picture. Each node's language is denoted by a regular expression. The language may be recognized by quotient automata w.r.t. different equivalence relations, all of which are shown below the node.

  6. Formalism (linguistics) - Wikipedia

    en.wikipedia.org/wiki/Formalism_(linguistics)

    Rudolph Carnap defined the meaning of the adjective formal in 1934 as follows: "A theory, a rule, a definition, or the like is to be called formal when no reference is made in it either to the meaning of the symbols (for example, the words) or to the sense of the expressions (e.g. the sentences), but simply and solely to the kinds and order of the symbols from which the expressions are ...

  7. Formal linguistics - Wikipedia

    en.wikipedia.org/wiki/Formal_linguistics

    [2] [3] In this view, language is regarded as arising from a mathematical relationship between meaning and form. The formal description of language was further developed by linguists including J. R. Firth and Simon Dik, giving rise to modern grammatical frameworks such as systemic functional linguistics and functional discourse grammar.

  8. Emptiness problem - Wikipedia

    en.wikipedia.org/wiki/Emptiness_problem

    The emptiness problem is the question of determining whether a language is empty given some representation of it, such as a finite-state automaton. [1] For an automaton having n {\displaystyle n} states, this is a decision problem that can be solved in O ( n 2 ) {\displaystyle O(n^{2})} time , [ 2 ] or in time O ( n + m ) {\displaystyle O(n+m ...

  9. Unambiguous finite automaton - Wikipedia

    en.wikipedia.org/wiki/Unambiguous_finite_automaton

    In automata theory, an unambiguous finite automaton (UFA) is a nondeterministic finite automaton (NFA) such that each word has at most one accepting path. Each deterministic finite automaton (DFA) is an UFA, but not vice versa. DFA, UFA, and NFA recognize exactly the same class of formal languages. On the one hand, an NFA can be exponentially ...