Exponential Lower Bounds on the Size of Clause BasedSemantic
نویسنده
چکیده
We consider the clause{based version of the general model of semantic derivations proposed by Kraj cek. Resolution refutation proof is a special deterministic version of fanin-2 clause{based derivation. We prove the following combinatorial lower bound on the length of such derivations. Let F be a k-partite hypergraph, with at most b points in each part such that no point belongs to more than d edges and any two edges share at most points. If jFj k(d + 1)=2 then no CNF containing such a hypergraph among its clauses, can have a fanin-l semantic derivation of length smaller than exp k 2 b(l+). When applied to the generalized pigeonhole principle PHP m n and to blocking principles for nite geometries, this directly yields exponential lower bounds on the length of their semantic derivations, including the exp ? (n 2 =(lm)) lower bound for the length of fanin-l clause{based semantic derivation of PHP m n .
منابع مشابه
Capacity Bounds and High-SNR Capacity of the Additive Exponential Noise Channel With Additive Exponential Interference
Communication in the presence of a priori known interference at the encoder has gained great interest because of its many practical applications. In this paper, additive exponential noise channel with additive exponential interference (AENC-AEI) known non-causally at the transmitter is introduced as a new variant of such communication scenarios. First, it is shown that the additive Gaussian ch...
متن کاملSimplified and Improved Resolution Lower Bounds
We give simple new lower bounds on the lengths of Resolution proofs for the pigeonhole principle and for randomly generated formulas. For random formulas, our bounds signiicantly extend the range of formula sizes for which non-trivial lower bounds are known. For example, we show that with probability approaching 1, any Resolution refutation of a randomly chosen 3-CNF formula with at most n 6=5?...
متن کاملQualifying Exam Writeup: Lower Bounds for Treelike Resolution Refutations of Random CNFs Using Encoding Techniques
Propositional proof complexity is an area of complexity theory that addresses the question of whether the class NP is closed under complement, and also provides a theoretical framework for studying practical applications such as SAT solving. Some of the most well-studied contradictions are random k-CNF formulas where each clause of the formula is chosen uniformly at random from all possible cla...
متن کاملA Framework for Proving Proof Complexity Lower Bounds on Random CNFs Using Encoding Techniques
Propositional proof complexity is an area of complexity theory that addresses the question of whether the class NP is closed under complement, and also provides a theoretical framework for studying practical applications such as SAT solving. Some of the most well-studied contradictions are random k-CNF formulas where each clause of the formula is chosen uniformly at random from all possible cla...
متن کاملExponential Lower Bounds for DPLL Algorithms on Satisfiable Random 3-CNF Formulas
We consider the performance of a number of DPLL algorithms on random 3-CNF formulas with n variables and m = rn clauses. A long series of papers analyzing so-called “myopic” DPLL algorithms has provided a sequence of lower bounds for their satisfiability threshold. Indeed, for each myopic algorithm A it is known that there exists an algorithm-specific clause-density, rA, such that if r < rA, th...
متن کامل