The Language, the Expression, and the (Small) Automaton

Abstract

Abstract. This survey paper reviews 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. Some emphasis is put 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.

State Elimination Ordering Strategies: Some Experimental Results

“…This last approach is interesting as linear algebra or optimization techniques can be adapted in order to provide new methods to obtain r.e.'s. Sakarovitch [Sak05,Sak09] studied the relationship between the three methods and in particular showed that given an order in the set of states Q the regular expressions obtained by two different methods can be reduced to each other by the application of a specific subset of algebraic properties.…”

The Complexity of Regular(-Like) Expressions

“…A comparison of the state elimination algorithm [10], algorithms based on Arden's lemma [13], or McNaughton-Yamada's algorithm [51], is given in [59]. There it is pointed out, that all of these approaches are more or less reformulations of the same underlying algorithmic idea, and can be recast as variations of the standard state elimination algorithm.…”

Series-Parallel Automata and Short Regular Expressions

“…Sakarovitch [29,30] analysed the conversion algorithms between equivalent regular expressions and finite automata, and establishes some relationships between the regular expressions obtained from a given automaton by applying different methods of computing a regular expression from an automaton. Lombardy and Sakarovitch [22] consider the problem of retrieving an automaton A from an equivalent regular expression that was obtained from A.…”