Reachability in Register Machines with Polynomial Updates

  • Alain Finkel
  • Stefan Göller
  • Christoph Haase
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8087)


This paper introduces a class of register machines whose registers can be updated by polynomial functions when a transition is taken, and the domain of the registers can be constrained by linear constraints. This model strictly generalises a variety of known formalisms such as various classes of Vector Addition Systems with States. Our main result is that reachability in our class is PSPACE-complete when restricted to one register. We moreover give a classification of the complexity of reachability according to the type of polynomials allowed and the geometry induced by the range-constraining formula.


Residue Class Chinese Remainder Theorem Reachability Problem Prime Number Theorem Register Machine 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Alain Finkel
    • 1
  • Stefan Göller
    • 2
  • Christoph Haase
    • 1
  1. 1.LSV - CNRS & ENS CachanFrance
  2. 2.Institut für InformatikUniversität BremenGermany

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