The complexity of stochastic games
Information and Computation
A subexponential randomized algorithm for the simple stochastic game problem
Information and Computation
Using the Groebner basis algorithm to find proofs of unsatisfiability
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On Interpolation and Automatization for Frege Systems
SIAM Journal on Computing
Some Consequences of Cryptographical Conjectures for S_2^1 and EF
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
Optimality of size-width tradeoffs for resolution
Computational Complexity
Resolution is Not Automatizable Unless W[P] is Tractable
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
On the automatizability of resolution and related propositional proof systems
Information and Computation
Relativized NP Search Problems and Propositional Proof Systems
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Combinatorial structure and randomized subexponential algorithms for infinite games
Theoretical Computer Science
Settling the complexity of computing two-player Nash equilibria
Journal of the ACM (JACM)
The Complexity of Computing a Nash Equilibrium
SIAM Journal on Computing
The Complexity of Solving Stochastic Games on Graphs
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
New Algorithms for Solving Simple Stochastic Games
Electronic Notes in Theoretical Computer Science (ENTCS)
Simple stochastic games with few random vertices are easy to solve
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Optimality of size-degree tradeoffs for polynomial calculus
ACM Transactions on Computational Logic (TOCL)
Mean-payoff games and propositional proofs
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Automatizability and simple stochastic games
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Automatizability and simple stochastic games
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
The proof-search problem between bounded-width resolution and bounded-degree semi-algebraic proofs
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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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.