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"... Lower bounds for myopic DPLL algorithms with a cut heuristic∗ Dmitry Itsykson†and Dmitry Sokolov† ..."
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Lower bounds for myopic DPLL algorithms with a cut heuristic∗ Dmitry Itsykson†and Dmitry Sokolov†
The complexity of inversion of explicit Goldreich’s function by DPLL algorithms
, 2010
"... The Goldreich’s function has n binary inputs and n binary outputs. Every output depends on d inputs and is computed from them by the fixed predicate of arity d. Every Goldreich’s function is defined by it’s dependency graph G and predicate P. In 2000 O. Goldreich formulated a conjecture that if G is ..."
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is an expander and P is a random predicate of arity d then the corresponding function is one way. In 2005 M. Alekhnovich, E. Hirsch and D. Itsykson proved the exponential lower bound on the complexity of inversion of Goldreich’s function based on linear predicate and random graph by myopic DPLL agorithms
Exponential lower bounds for the running time of DPLL algorithms on satisfiable formulas
, 2004
"... DPLL (for Davis, Putnam, Logemann, and Loveland) algorithms form the largest family of contemporary algorithms for SAT (the propositional satis ability problem) and are widely used in applications. The recursion trees of DPLL algorithm executions on unsatis able formulas are equivalent to tree ..."
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DPLL (for Davis, Putnam, Logemann, and Loveland) algorithms form the largest family of contemporary algorithms for SAT (the propositional satis ability problem) and are widely used in applications. The recursion trees of DPLL algorithm executions on unsatis able formulas are equivalent to treelike resolution proofs. Therefore, lower bounds for treelike resolution (which are known since 1960s) apply to them.
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"... This report documents the programme and the outcomes of the Dagstuhl Seminar 14421 “Optimal algorithms and proofs”. The seminar brought together researchers working in computational and proof complexity, logic, and the theory of approximations. Each of these areas has its own, but connected notion o ..."
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This report documents the programme and the outcomes of the Dagstuhl Seminar 14421 “Optimal algorithms and proofs”. The seminar brought together researchers working in computational and proof complexity, logic, and the theory of approximations. Each of these areas has its own, but connected notion of optimality; and the main aim of the seminar was to bring together researchers from these different areas, for an exchange of ideas, techniques, and open questions, thereby triggering new research collaborations across established research boundaries.
On optimal heuristic randomized semidecision procedures, with applications to proof complexity and cryptography
, 2010
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www.stacsconf.org ON OPTIMAL HEURISTIC RANDOMIZED SEMIDECISION PROCEDURES, WITH APPLICATION TO PROOF COMPLEXITY
"... Abstract. The existence of a (p)optimal propositional proof system is a major open question in (proof) complexity; many people conjecture that such systems do not exist. Krajíček and Pudlák [KP89] show that this question is equivalent to the existence of an algorithm that is optimal 1 on all propos ..."
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Abstract. The existence of a (p)optimal propositional proof system is a major open question in (proof) complexity; many people conjecture that such systems do not exist. Krajíček and Pudlák [KP89] show that this question is equivalent to the existence of an algorithm that is optimal 1 on all propositional tautologies. Monroe [Mon09] recently gave a conjecture implying that such algorithm does not exist. We show that in the presence of errors such optimal algorithms do exist. The concept is motivated by the notion of heuristic algorithms. Namely, we allow the algorithm to claim a small number of false “theorems ” (according to any polynomialtime samplable distribution on nontautologies) and err with bounded probability on other inputs. Our result can also be viewed as the existence of an optimal proof system in a class of proof systems obtained by generalizing automatizable proof systems. 1.
Optimal acceptors and optimal proof systems
"... Abstract. Unless we resolve the P vs NP question, we are unable to say whether there is an algorithm (acceptor) that accepts Boolean tautologies in polynomial time and does not accept nontautologies (with no time restriction). Unless we resolve the coNP vs NP question, we are unable to say whether ..."
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Abstract. Unless we resolve the P vs NP question, we are unable to say whether there is an algorithm (acceptor) that accepts Boolean tautologies in polynomial time and does not accept nontautologies (with no time restriction). Unless we resolve the coNP vs NP question, we are unable to say whether there is a proof system that has a polynomialsize proof for every tautology. In such a situation, it is typical for complexity theorists to search for “universal ” objects; here, it could be the “fastest ” acceptor (called optimal acceptor) and a proof system that has the “shortest ” proof (called optimal proof system) for every tautology. Neither of these objects is known to the date. In this survey we review the connections between these questions and generalizations of acceptors and proof systems that lead or may lead to universal objects. 1 Introduction and basic definitions
Lower bounds of static LovászSchrijver calculus proofs for Tseitin tautologies
 Zapiski Nauchnyh Seminarov POMI
"... We prove an exponential lower bound on the size of static LovászSchrijver proofs of Tseitin tautologies. We use several techniques, namely, translating static LS+ proof into Positivstellensatz proof of Grigoriev et al., extracting a “good ” expander out of a given graph by removing edges and vertic ..."
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We prove an exponential lower bound on the size of static LovászSchrijver proofs of Tseitin tautologies. We use several techniques, namely, translating static LS+ proof into Positivstellensatz proof of Grigoriev et al., extracting a “good ” expander out of a given graph by removing edges and vertices of Alekhnovich et al., and proving linear lower bound on the degree of Positivstellensatz proofs for Tseitin tautologies. 1
Distributional Word Problem for Tseitin
"... Abstract. The main criticism of known algebraic distributional NP (DistNP) complete problems is based on the fact that they contain too many specific relations to simulate a Turing machine. In this paper we present a construction of the semigroup with very few relations and word problem that is Dist ..."
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Abstract. The main criticism of known algebraic distributional NP (DistNP) complete problems is based on the fact that they contain too many specific relations to simulate a Turing machine. In this paper we present a construction of the semigroup with very few relations and word problem that is DistNP complete. Our construction follows Tseitin ideas [Tse56]. We modify original construction to work with words in standard binary presentation and arbitrary semigroups without any special conditions on its relations. The study of average case complexity (i.e. complexity of algorithms for problems with probability distribution on instances) is hard and interesting from many points of view. For example, in industry, it is interesting to understand the behavior of programs on most common inputs, or in cryptography, hardness of a cipher in the worst case is not too interesting. In [Lev86] Levin defined a notion of distributional NPcomplete problem (DistNPcomplete) where decision problem component belongs to NP and every
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