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Communication Dans Un Congrès Année : 2003

Operations preserving recognizable languages

Résumé

Given a subset S of N, filtering a word a_0a_1 ... a_n by S consists in deleting the letters a_i such that i is not in S. By a natural generalization, denote by L[S], where L is a language, the set of all words of L filtered by S. The filtering problem is to characterize the filters S such that, for every recognizable language L, L[S] is recognizable. In this paper, the filtering problem is solved, and a unified approach is provided to solve similar questions, including the removal problem considered by Seiferas and McNaughton. There are two main ingredients on our approach: the first one is the notion of residually ultimately periodic sequences, and the second one is the notion of representable transductions.
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Dates et versions

hal-00112814 , version 1 (09-11-2006)

Identifiants

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Jean Berstel, Luc Boasson, Olivier Carton, Bruno Petazzoni, Jean-Eric Pin. Operations preserving recognizable languages. FCT'03, 2003, Malmo, Sweden. pp.343-354, ⟨10.1007/978-3-540-45077-1_32⟩. ⟨hal-00112814⟩
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