Rational series and their languages
Rational series and their languages
Regular expressions into finite automata
Theoretical Computer Science
Partial derivatives of regular expressions and finite automaton constructions
Theoretical Computer Science
Digital images and formal languages
Handbook of formal languages, vol. 3
Characterization of Glushkov automata
Theoretical Computer Science
Automata, Languages, and Machines
Automata, Languages, and Machines
On the Determinization of Weighted Finite Automata
SIAM Journal on Computing
Finite-state transducers in language and speech processing
Computational Linguistics
Derivatives of rational expressions with multiplicity
Theoretical Computer Science
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We take an active interest in the problem of conversion of a Weighted Finite Automaton (WFA) into a \mathbb{K}-expression. The known algorithms give an exponential size expression in the number of states of the given automaton. We study the McNaughton-Yamada algorithm in the case of multiplicities and then we show that the resulting \mathbb{K}-expression is in the Star Normal Form (SNF) defined by Brüggemann-Klein [3]. The Glushkov algorithm computes an (n + 1)-state automaton from an expression having n occurrences of letters even in the multiplicity case [5]. We reverse this procedure and get a linear size \mathbb{K}-expression from a Glushkov WFA. A characterization of Glushkov WFAs which are not in SNF is given. This characterization allows us to emphasize a normal form for \mathbb{K}-expressions. As for SNF in the boolean case, we show that every \mathbb{K}-expression has an equivalent one in normal form having the same Glushkov WFA. We end with an algorithm giving a small normal form \mathbb{K}-expression from a Glushkov WFA.