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EXPSPACE-Complete Variant of Countdown Games, and Simulation on Succinct One-Counter Nets

  • Petr JančarEmail author
  • Petr Osička
  • Zdeněk Sawa
Conference paper
  • 196 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11123)

Abstract

We answer an open complexity question for simulation preorder of succinct one-counter nets (i.e., one-counter automata with no zero tests where counter increments and decrements are integers written in binary), by showing that all relations between bisimulation equivalence and simulation preorder are EXPSPACE-hard for these nets. We describe a reduction from reachability games whose EXPSPACE-completeness in the case of succinct one-counter nets was shown by Hunter [RP 2015], by using other results. We also provide a direct self-contained EXPSPACE-completeness proof for a special case of such reachability games, namely for a modification of countdown games that were shown EXPTIME-complete by Jurdzinski, Sproston, Laroussinie (LMCS 2008); in our modification the initial counter value is not given but is freely chosen by the first player.

Keywords

Succinct one-counter net Simulation Countdown game Complexity 

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Copyright information

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Authors and Affiliations

  1. 1.Department of Computer Science, Faculty of SciencePalacký University OlomoucOlomoucCzechia
  2. 2.Department of Computer ScienceFEI, Technical University of OstravaOstravaCzechia

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