Open AccessJournal Article
How expressions can code for automata
TLDR
In this article, the authors investigate how it is possible to recover an automaton from a rational expression that has been computed from that automaton using Antimirov's derived term of an expression.Abstract:
In this paper we investigate how it is possible to recover an automaton from a rational expression that has been computed from that automaton. The notion of derived term of an expression, introduced by Antimirov, appears to be instrumental in this problem. The second important ingredient is the co-minimization of an automaton, a dual and generalized Moore algorithm on non-deterministic automata. If an automaton is then sufficiently decorated, the combination of these two algorithms gives the desired result. Reducing the amount of decoration is still the object of ongoing investigation.read more
Citations
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Journal ArticleDOI
Derivatives of rational expressions with multiplicity
TL;DR: This paper formalizes and generalizes the idea of "partial derivatives" introduced in 1995 by Antimirov, in order to obtain a construction of an automaton with multiplicity from a rational expression describing a formal power series with coefficients in a semiring.
Book ChapterDOI
The language, the expression, and the (small) automaton
TL;DR: A survey of the means that allow to go from one representation of the languages to the other and how, and to what extend, one can keep them small is given in this paper, with a focus on the comparison between the expressions that can be computed from a given automaton and on the construction of the derived term automaton of an expression.
Journal ArticleDOI
Series-Parallel Automata and Short Regular Expressions
Nelma Moreira,Rogério Reis +1 more
TL;DR: This work presents a class of acyclic automata for which it is possible to obtain in time O(n$^{2}$ log n) an equivalent regular expression of size O( n) and presents an algorithm for the generation of automata of this class and an enumerative formula for the underlying digraphs with a given number of vertices.
Journal Article
Derivation of rational expressions with multiplicity
TL;DR: In this article, a generalization of the partial derivatives of rational expressions, due to Antimirov, to rational expressions with multiplicity is introduced, which allows to deal with rational power series, and automata and expressions with multiplication as well.
Journal Article
On the number of broken derived terms of a rational expression
TL;DR: Bounds are given on the number of broken derived terms (a variant of Antimirov’s ‘partial derivatives’) of a rational expression E and it is shown that this number is less than or equal to 2`(E) + 1 in the general case.
References
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Journal ArticleDOI
Derivatives of Regular Expressions
TL;DR: In this paper the notion of a derivative of a regular expression is introduced atld the properties of derivatives are discussed and this leads, in a very natural way, to the construction of a state diagram from a regularexpression containing any number of logical operators.
Journal ArticleDOI
Programming Techniques: Regular expression search algorithm
TL;DR: A method for locating specific character strings embedded in character text is described and an implementation of this method in the form of a compiler is discussed.
Journal ArticleDOI
Regular Expressions and State Graphs for Automata
Robert McNaughton,Hisao Yamada +1 more
TL;DR: Algorithms are presented for converting a state graph describing thebehavior of an automaton to a regular expression describing the behavior of the same automaton, and for converting an regular expression into a stategraph.
Book
Theory of computation
TL;DR: This chapter discusses models for Finite Automata Regular Expressions Context-Free Grammars Pushdown Automata Turing Machines Functions, Relations, and Translations, and properties of these models.