The classical satisfiability problem (SAT) is used as a natural and general tool to express and solve combinatorial problems that are in NP. We postulate that provability for implicational intuitionistic propositional logic (IIPC) can serve as a similar natural tool to express problems in Pspace. This approach can be particularly convenient for two reasons. One is that provability in full IPC (with all connectives) can be reduced to provability of implicational formulas of order three. Another advantage is a convenient interpretation in terms of simple alternating automata. Additionally, we distinguish some natural subclasses of IIPC corresponding to the complexity classes NP and co-NP. Our experimental results show that a simple decision procedure requires a significant amount of time only in a small fraction of cases.

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