Operations Preserving Recognizable Languages

Abstract. Given a subset S of N, filtering a word a0a1 · · · an by S consists in deleting the letters ai 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.

• Type: Conference
• Year: 2003
• Where: FCT
• Authors: Jean Berstel, Luc Boasson, Olivier Carton, Bruno Petazzoni, Jean-Eric Pin
• Keywords: FCT 2003, Natural Generalization, Recognizable Language L, Unified Approach