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Article Dans Une Revue Theoretical Computer Science Année : 2006

Operations preserving recognizable languages


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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Dates et versions

hal-00112842 , version 1 (09-11-2006)


  • HAL Id : hal-00112842 , version 1


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