![]() One is to define replacement in a very general way, ex-plicitly allowing replacement to be constrained by input and output contexts, as in two-level rules (Koskenniemi 1983), but without the re-striction of only single-symbol replacements. We consider here the replacement operation in the context of finite-state grammars. Linguistic descriptions in phonology, morphol-ogy, and syntax typically make use of an op-eration that replaces some symbol or sequence of symbols by another sequence or symbol. The Replace Operator Lauri Karttunen Rank Xerox Research Centreį-38240 Meylan, France paper introduces to the calculus of Replace expressions denote regular relations, defined in terms of othe Is the set of all strings over symbols in V,Ĭan also be described as the set of finite-length strings that can be generated byĬoncatenating arbitrary elements of V allowing the use of the same element multiple times.This paper introduces to the calculus of regular expressions a replace operator and defines a set of replacement expressions that concisely encode alternate variations of the operation. If V is a set of symbols or characters then V* Is defined as the smallest superset of V that contains theĮmpty string ε and is closed under the string concatenation operation.Ģ. It is widely used for regular expressions, which is theĬontext in which it was introduced by Stephen Kleene to characterise certain automata, where it Mathematics it is more commonly known as the free monoid construction. In mathematical logic and computer science, the Kleene star (or Kleene operator or KleeneĬlosure) is a unary operation, either on sets of strings or on sets of symbols or characters. For differentĭefinitions of automata, the recognizable languages are different. The above definition of automata the recognizable languages are regular languages. The recognizable languages are the set of languages that are recognized by some automaton. The language L ⊆ Σ* recognized by anĪutomaton is the set of all the words that are accepted by the automaton. F⊆Q) called accept states.Īn automaton can recognize a formal language. q0 is the start state, that is, the state of the automaton before any input has been. ![]()
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