Parameterized Bounded-Depth Frege Is not Optimal
نویسندگان
چکیده
منابع مشابه
A Parameterized Bounded-Depth Frege is Not Optimal
A general framework for parameterized proof complexity was introduced by Dantchev, Martin, and Szeider [2007]. There the authors show important results on tree-like Parameterized Resolution—a parameterized version of classical Resolution—and their gap complexity theorem implies lower bounds for that system. The main result of the present paper significantly improves upon this by showing optimal...
متن کاملBounded Arithmetic and Constant Depth Frege Proofs
We discuss the Paris-Wilkie translation from bounded arithmetic proofs to bounded depth propositional proofs in both relativized and non-relativized forms. We describe normal forms for proofs in bounded arithmetic, and a definition of Σ -depth for PK-proofs that makes the translation from bounded arithmetic to propositional logic particularly transparent. Using this, we give new proofs of the w...
متن کاملBounded-Depth Frege Lower Bounds for Weaker Pigeonhole Principles
We prove a quasi-polynomial lower bound on the size of bounded-depth Frege proofs of the pigeonhole principle PHPm n where m 1 1 polylog n n. This lower bound qualitatively matches the known quasi-polynomial-size bounded-depth Frege proofs for these principles. Our technique, which uses a switching lemma argument like other lower bounds for boundeddepth Frege proofs, is novel in that the tautol...
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 کاملLower Bounds for Bounded Depth Frege Proofs via Buss-Pudlák Games
We present a simple proof of the bounded-depth Frege lower bounds of Pitassi et. al. and Krajı́ček et. al. for the pigeonhole principle. Our method uses the interpretation of proofs as two player games given by Pudlák and Buss. Our lower bound is conceptually simpler than previous ones, and relies on tools and intuition that are well-known in the context of computational complexity. This makes t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ACM Transactions on Computation Theory
سال: 2012
ISSN: 1942-3454,1942-3462
DOI: 10.1145/2355580.2355582