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Automatizability and Simple Stochastic Games

  • Lei Huang
  • Toniann Pitassi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)

Abstract

The complexity of simple stochastic games (SSGs) has been open since they were defined by Condon in 1992. Despite intensive effort, the complexity of this problem is still unresolved. In this paper, building on the results of [4], we establish a connection between the complexity of SSGs and the complexity of an important problem in proof complexity–the proof search problem for low depth Frege systems. We prove that if depth-3 Frege systems are weakly automatizable, then SSGs are solvable in polynomial-time. Moreover we identify a natural combinatorial principle, which is a version of the well-known Graph Ordering Principle (GOP), that we call the integer-valued GOP (IGOP). We prove that if depth-2 Frege plus IGOP is weakly automatizable, then SSG is in P.

Keywords

Proof System Search Problem Stochastic Game Arithmetic Formula Payoff Game 
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 2011

Authors and Affiliations

  • Lei Huang
    • 1
  • Toniann Pitassi
    • 1
  1. 1.University of TorontoCanada

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