More on the relative strength of counting principles
نویسندگان
چکیده
We give exponential size lower bounds for bounded-depth Frege proofs of variants of the bijective (‘onto’) version of the pigeonhole principle, even given additional axiom schemas for modular counting principles. As a consequence we show that for bounded-depth Frege systems the general injective version of the pigeonhole principle is exponentially more powerful than its bijective version. Furthermore this yields a slightly simpler proof of exponential separations between modular counting principles in boundeddepth Frege systems.
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