Quasipolynomial size proofs of the propositional pigeonhole principle
نویسندگان
چکیده
منابع مشابه
Quasipolynomial size proofs of the propositional pigeonhole principle
Cook and Reckhow proved in 1979 that the propositional pigeonhole principle has polynomial size extended Frege proofs. Buss proved in 1987 that it also has polynomial size Frege proofs; these Frege proofs used a completely different proof method based on counting. This paper shows that the original Cook and Reckhow extended Frege proofs can be formulated as quasipolynomial size Frege proofs. Th...
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Cook and Reckhow defined a propositional formulation of the pigeonhole principle. This paper shows that there are Frege proofs of this propositional pigeonhole principle of polynomial size. This together with a result of Haken gives another proof of Urquhart's theorem that Frege systems have an exponential speedup over resolution. We also discuss connections to provability in theories of bounde...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2015
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2015.02.005