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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 27 (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 (3 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
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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Cited by 5 (1 self)
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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
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 3 (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).
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.
Verified AIG Algorithms in ACL2
"... AndInverter Graphs (AIGs) are a popular way to represent Boolean functions (like circuits). AIG simplification algorithms can dramatically reduce an AIG, and play an important role in modern hardware verification tools like equivalence checkers. In practice, these tricky algorithms are implemented ..."
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AndInverter Graphs (AIGs) are a popular way to represent Boolean functions (like circuits). AIG simplification algorithms can dramatically reduce an AIG, and play an important role in modern hardware verification tools like equivalence checkers. In practice, these tricky algorithms are implemented with optimized C or C++ routines with no guarantee of correctness. Meanwhile, many interactive theorem provers can now employ SAT or SMT solvers to automatically solve finite goals, but no theorem prover makes use of these advanced, AIGbased approaches. We have developed two ways to represent AIGs within the ACL2 theorem prover. One representation, HonsAIGs, is especially convenient to use and reason about. The other, Aignet, is the opposite; it is styled after modern AIG packages and allows for efficient algorithms. We have implemented functions for converting between these representations, random vector simulation, conversion to CNF, etc., and developed reasoning strategies for verifying these algorithms. Aside from these contributions towards verifying AIG algorithms, this work has an immediate, practical benefit for ACL2 users who are using GL to bitblast finite ACL2 theorems: they can now optionally trust an offtheshelf SAT solver to carry out the proof, instead of using the builtin BDD package. Looking to the future, it is a first step toward implementing verified AIG simplification algorithms that might further improve GL performance. 1