Polynomial size proofs of the propositional pigeonhole principle
نویسندگان
چکیده
منابع مشابه
Polynomial Size Proofs of the Propositional Pigeonhole Principle
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...
متن کاملQuasipolynomial 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...
متن کاملAn Exponenetioal Lower Bound to the Size of Bounded Depth Frege Proofs of the Pigeonhole Principle
We prove lower bounds of the form exp (n " d) ; " d > 0; on the length of proofs of an explicit sequence of tautologies, based on the Pigeonhole Principle, in proof systems using formulas of depth d; for any constant d: This is the largest lower bound for the strongest proof system, for which any superpolynomial lower bounds are known.
متن کاملThe Pigeonhole Principle
Theorem 1.1. If n + 1 objects are put into n boxes, then at least one box contains two or more objects. Proof. Trivial. Example 1.1. Among 13 people there are two who have their birthdays in the same month. Example 1.2. There are n married couples. How many of the 2n people must be selected in order to guarantee that one has selected a married couple? Other principles related to the pigeonhole ...
متن کاملIAS/PCMI Summer Session 2000 Clay Mathematics Undergraduate Program Advanced Course on Computational Complexity Lecture 13: Polynomial-Size Frege Proofs of the Pigeonhole Principle
The pigeonhole principle states that there is no one-to-one function from a set of size n to a set of size n − 1. In other words, if n pigeons are put into n − 1 holes, then at least one hole will be occupied by more than one pigeon. This simple fact has an astonishing variety of applications in mathematics. It also corresponds to a tautology that has been used extensively in the study of the c...
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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 1987
ISSN: 0022-4812,1943-5886
DOI: 10.2307/2273826