Operations preserving recognizable languages

Abstract : Given a strictly increasing sequence s of non-negative integers, filtering a word a_0a_1 ... a_n by s consists in deleting the letters ai such that i is not in the set {s_0, s_1, ...}. 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 regular language L, L[s] is regular. 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. Our approach relies on a detailed study of various residual notions, notably residually ultimately periodic sequences and residually rational transductions.
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Contributeur : Jean-Eric Pin <>
Soumis le : jeudi 9 novembre 2006 - 19:16:34
Dernière modification le : vendredi 12 avril 2019 - 10:18:03
Document(s) archivé(s) le : mardi 6 avril 2010 - 18:54:58


  • HAL Id : hal-00112842, version 1


Jean Berstel, Luc Boasson, Olivier Carton, Bruno Petazzoni, Jean-Eric Pin. Operations preserving recognizable languages. Theoretical Computer Science, Elsevier, 2006, 354, pp.405-420. ⟨hal-00112842⟩



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