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14
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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Cited by 28 (3 self)
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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.
The SAT2002 Competition
, 2002
"... SAT Competition 2002 held in MarchMay 2002 in conjunction with SAT 2002 (the Fifth International Symposium on the Theory and Applications of Satisfiability Testing). About 30 solvers and 2300 benchmarks took part in the competition, which required more than 2 CPU years to complete the evaluation ..."
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Cited by 22 (2 self)
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SAT Competition 2002 held in MarchMay 2002 in conjunction with SAT 2002 (the Fifth International Symposium on the Theory and Applications of Satisfiability Testing). About 30 solvers and 2300 benchmarks took part in the competition, which required more than 2 CPU years to complete the evaluation. In this report
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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Cited by 6 (0 self)
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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
Several notes on the power of GomoryChvátal cuts
, 2003
"... We prove that the Cutting Plane proof system based on GomoryChvátal cuts polynomially simulates the liftandproject system with integer coecients written in unary. The restriction on coefficients can be omitted when using Krajícek's cutfree Gentzenstyle extension of both systems. We also ..."
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Cited by 4 (0 self)
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We prove that the Cutting Plane proof system based on GomoryChvátal cuts polynomially simulates the liftandproject system with integer coecients written in unary. The restriction on coefficients can be omitted when using Krajícek's cutfree Gentzenstyle extension of both systems. We also prove that Tseitin tautologies have short proofs in this extension (of any of these systems and with any coefficients).
Conflict Directed Lazy Decomposition
"... Abstract. Two competing approaches to handling complex constraints in satisfaction and optimization problems using SAT and LCG/SMT technology are: decompose the complex constraint into a set of clauses; or (theory) propagate the complex constraint using a standalone algorithm and explain the propaga ..."
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Abstract. Two competing approaches to handling complex constraints in satisfaction and optimization problems using SAT and LCG/SMT technology are: decompose the complex constraint into a set of clauses; or (theory) propagate the complex constraint using a standalone algorithm and explain the propagation. Each approach has its benefits. The decomposition approach is prone to an explosion in size to represent the problem, while the propagation approach may require exponentially more search since it does not have access to intermediate literals for explanation. In this paper we show how we can obtain the best of both worlds by lazily decomposing a complex constraint propagator using conflicts to direct it. If intermediate literals are not helpful for conflicts then it will act like the propagation approach, but if they are helpful it will act like the decomposition approach. Experimental results show that it is never much worse than the better of the decomposition and propagation approaches, and sometimes better than both. 1
A Fast Untestability Proof for SATbased ATPG
"... (ATPG) based on Boolean satisfiability (SAT) has been shown to be a beneficial complement to traditional ATPG techniques. Boolean solvers work on instances given in Conjunctive Normal Form (CNF). The required transformation of the ATPG problem into CNF is one main part of SATbased ATPG and needs a ..."
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(ATPG) based on Boolean satisfiability (SAT) has been shown to be a beneficial complement to traditional ATPG techniques. Boolean solvers work on instances given in Conjunctive Normal Form (CNF). The required transformation of the ATPG problem into CNF is one main part of SATbased ATPG and needs a significant portion of the overall run time. Solving the SAT instance is the other main part. Here, the time needed is often negligible – especially for untestable faults This paper presents a preprocessing technique that accelerates the classification of untestable faults. Those occur more frequently with increasing design sizes in industrial practice. In order to avoid overhead on testable faults, an untestability prediction is motivated. This increases the robustness of the entire ATPG process. The efficiency of the proposed method is shown during the experiments. I.
CHOCKLER, KROENING, PURANDARE: COMPUTING MUTATION COVERAGE IN INTERPOLATIONBASED MODEL CHECKING 1 Computing Mutation Coverage in Interpolationbased Model Checking
"... Abstract—Coverage is a means to quantify the quality of a system specification, and is frequently applied to assess progress in system validation. Coverage is a standard measure in testing, but is very difficult to compute in the context of formal verification. We present efficient algorithms for i ..."
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Abstract—Coverage is a means to quantify the quality of a system specification, and is frequently applied to assess progress in system validation. Coverage is a standard measure in testing, but is very difficult to compute in the context of formal verification. We present efficient algorithms for identifying those parts of the system that are covered by a given property. Our algorithm is integrated into stateoftheart SATbased Model Checking using Craig interpolation. The key insight of our algorithm is the reuse of previously computed inductive invariants and counterexamples. This reuse permits a a rapid completion of the vast majority of tests, and enables the computation of a coverage measure with 96 % accuracy with only 5x the runtime of the Model Checker. Index Terms—Model Checking, Coverage, Interpolation