Proof Complexity of Pigeonhole
نویسنده
چکیده
منابع مشابه
$P \ne NP$, propositional proof complexity, and resolution lower bounds for the weak pigeonhole principle
Recent results established exponential lower bounds for the length of any Resolution proof for the weak pigeonhole principle. More formally, it was proved that any Resolution proof for the weak pigeonhole principle, with n holes and any number of pigeons, is of length Ω(2n ǫ ), (for a constant ǫ = 1/3). One corollary is that certain propositional formulations of the statement P 6= NP do not hav...
متن کاملP != NP, propositional proof complexity, and resolution lower bounds for the weak pigeonhole principle
Recent results established exponential lower bounds for the length of any Resolution proof for the weak pigeonhole principle. More formally, it was proved that any Resolution proof for the weak pigeonhole principle, with n holes and any number of pigeons, is of length fl(2 ), (for a constant e = 1/3). One corollary is that certain propositional formulations of the statement P / NP do not have s...
متن کاملProof Complexity of Pigeonhole Principles
The pigeonhole principle asserts that there is no injective mapping from m pigeons to n holes as long as m > n. It is amazingly simple, expresses one of the most basic primitives in mathematics and Theoretical Computer Science (counting) and, for these reasons, is probably the most extensively studied combinatorial principle. In this survey we try to summarize what is known about its proof comp...
متن کاملPolynomial 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 کاملImproved Resolution Lower Bounds for the Weak Pigeonhole Principle
Recently, Raz Raz01] established exponential lower bounds on the size of resolution proofs of the weak pigeonhole principle. We give another proof of this result which leads to better numerical bounds.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001