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Undecidability and Hierarchy Results for Parallel Communicating Finite Automata

  • Henning Bordihn
  • Martin Kutrib
  • Andreas Malcher
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6224)

Abstract

Parallel communicating finite automata (PCFAs) are systems of several finite state automata which process a common input string in a parallel way and are able to communicate by sending their states upon request. We consider deterministic and nondeterministic variants and distinguish four working modes. It is known that these systems in the most general mode are as powerful as one-way multi-head finite automata. It is additionally known that the number of heads corresponds to the number of automata in PCFAs in a constructive way. Thus, undecidability results as well as results on the hierarchies induced by the number of heads carry over from multi-head finite automata to PCFAs in the most general mode. Here, we complement these undecidability and hierarchy results also for the remaining working modes. In particular, we show that classical decidability questions are not semi-decidable for any type of PCFAs under consideration. Moreover, it is proven that the number of automata in the system induces infinite hierarchies for deterministic and nondeterministic PCFAs in three working modes.

Keywords

Turing Machine Finite Automaton Input String Input Symbol State Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Henning Bordihn
    • 1
  • Martin Kutrib
    • 2
  • Andreas Malcher
    • 2
  1. 1.Institut für InformatikUniversität PotsdamPotsdamGermany
  2. 2.Institut für InformatikUniversität GiessenGiessenGermany

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