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

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


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.


Membership Problem Reachability Problem Counter Machine Binary Word Pushdown Automaton 
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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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