RAIRO - Theoretical Informatics and Applications

Research Article

Returning and non-returning parallel communicating finite automata are equivalent

Ashish Choudharya1, Kamala Krithivasana2 and Victor Mitranaa3a4

a1 Dept of Computer Science and Engineering, Indian Institute of Technology, Madras, Chennai, 600036 India; ashishc@cse.iitm.ernet.in

a2 Dept of Computer Science and Engineering, Indian Institute of Technology, Madras, Chennai, 600036 India; kamala@iitm.ernet.in

a3 Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei 14, 010014, Bucharest, Romania.

a4 Research Group in Mathematical Linguistics, Rovira i Virgili University, Pl. Imperial Tarraco 1, 43005, Tarragona, Spain; vmi@urv.net

Abstract

A parallel communicating automata system consists of several automata working independently in parallel and communicating with each other by request with the aim of recognizing a word. Rather surprisingly, returning parallel communicating finite automata systems are equivalent to the non-returning variants. We show this result by proving the equivalence of both with multihead finite automata. Some open problems are finally formulated.

(Received May 24 2005)

(Accepted March 30 2006)

(Online publication July 18 2007)

Key Words:

  • Formal languages;
  • parallel communicating finite automata system;
  • multihead finite automaton;
  • computational power

Mathematics Subject Classification:

  • 68Q45;
  • 68Q68
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