Finite n-tape automata over possibly infinite alphabets: Extending a theorem of Eilenberg et al.

被引：2

作者：

Choffrut, Christian ^{[1
]}

Grigorieff, Serge

机构：

[1] Univ Paris 07, LIAFA, F-75251 Paris 05, France

来源：

THEORETICAL COMPUTER SCIENCE | 2009年 / 410卷 / 01期

关键词：

Finite automata; First order logic; Synchronous relations; Infinite alphabets; DEFINABLE RELATIONS;

D O I：

10.1016/j.tcs.2008.07.018

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Eilenberg, Elgot and Shepherdson showed in 1969. [S. Eilenberg, C.C. Elgot, J.C. Shepherdson, Sets recognized by n-tape automata, journal of Algebra 13 (1969) 447-464], that a relation on finite words over a finite, non-unary alphabet with p letters is definable in first order logic with p + 2 predicates for the relations equal length, prefix and last letter is a (for each letter a is an element of Sigma 7) if and only if it can be recognized by a finite multitape synchronous automaton, i.e., one whose read heads move simultaneously. They left open the characterization in the case of infinite alphabets, and proposed some conjectures concerning them. We solve all problems and sharpen the main theorem of [S. Eilenberg, C.C. Elgot, J.C. Shepherdson, Sets recognized by n-tape automata, journal of Algebra 13 (1969)447-464]. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：16 / 34

页数：19