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From Post Systems to the Reachability Problems for Matrix Semigroups and Multicounter Automata

  • Igor Potapov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3340)

Abstract

The main result of this paper is the reduction of PCP(n) to the vector reachability problem for a matrix semigroup generated by n 4 × 4 integral matrices. It follows that the vector reachability problem is undecidable for a semigroup generated by 7 integral matrices of dimension 4. The question whether the vector reachability problem is decidable for n = 2 and n = 3 remains open. Also we show that proposed technique can be applied to Post’s tag-systems. As a result we define new classes of counter automata that lie on the border between decidability and undecidability.

Keywords

Membership Problem Reachability Problem Counter Machine Binary Word Pushdown 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 2004

Authors and Affiliations

  • Igor Potapov
    • 1
  1. 1.Department of Computer ScienceUniversity of LiverpoolLiverpoolU.K.

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