Completing codes in a sofic shift
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- 作者：Marie-Pierre Bé ; al ; Dominique Perrin
- 关键词：Automata and formal languages ; Codes ; Complete codes ; Sofic shifts ; Symbolic dynamics ; Variable length codes
- 刊名：Theoretical Computer Science
- 出版年：2009
- 出版时间：6 October 2009
- 年：2009
- 卷：410
- 期：43
- 页码：4423-4431
- 全文大小：605 K
文摘
We define a code in a sofic shift as a set of blocks of symbols of the shift such that any block of the shift has at most one decomposition into code words. It is maximal if it is not strictly included in another one. Such a code is complete in the sofic shift if any block of the shift occurs within some concatenation of code words. We prove that a maximal code in an irreducible sofic shift is complete in this shift. We give an explicit construction of a regular completion of a regular code in a sofic shift. This extends the well known result of Ehrenfeucht and Rozenberg to the case of codes in sofic systems. We also give a combinatorial proof of a result concerning the polynomial of a code in a sofic shift.