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Quantifier Elimination With Structural Learning.
TL;DR: A new definition of D-sequents is introduced that enables their re-usability and a theory showing under what conditions a D-sequent can be safely re-used is developed.
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Abstract: We consider the Quantifier Elimination (QE) problem for propositional CNF formulas with existential quantifiers. QE plays a key role in formal verification. Earlier, we presented an approach based on the following observation. To perform QE, one just needs to add a set of clauses depending on free variables that makes the quantified clauses (i.e. clauses with quantified variables) redundant. To implement this approach, we introduced a branching algorithm making quantified clauses redundant in subspaces and merging the results of branches. To implement this algorithm we developed the machinery of D-sequents. A D-sequent is a record stating that a quantified clause is redundant in a specified subspace. Redundancy of a clause is a structural property (i.e. it holds only for a subset of logically equivalent formulas as opposed to a semantic property). So, re-using D-sequents is not as easy as re-using conflict clauses in SAT-solving. In this paper, we address this problem. We introduce a new definition of D-sequents that enables their re-usability. We develop a theory showing under what conditions a D-sequent can be safely re-used.
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Citations
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Partial Quantifier Elimination By Certificate Clauses.
TL;DR: This work studies a modification of the Quantifier Elimination (QE) problem called Partial QE) for propositional CNF formulas and implements a PQE algorithm that bears some similarity to a SAT-solver with conflict driven learning.
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Partial Quantifier Elimination With Learning.
TL;DR: The new PQE algorithm is different from its predecessor in two aspects: first, the new algorithm can learn and reuse D-sequents and thus backtracks as soon as the current target clause is proved redundant in the current subspace.
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Partial Quantifier Elimination And Property Generation
TL;DR: In this paper , partial quantifier elimination (PQE) is used for property generation for propositional CNF formulas with existential quantifiers, where one can limit the set of clauses taken out of the scope of quantifiers to a small subset of clauses.
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On Efficient Algorithms For Partial Quantifier Elimination
Eugene Goldberg
- 03 Jun 2024
TL;DR: This paper introduces two theoretical results enabling the reuse of learned information in Partial Quantifier Elimination (PQE) solvers, improving efficiency by leveraging semantic properties, similar to conflict clause learning in SAT solving.
References
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Matthew W. Moskewicz,Conor F. Madigan,Ying Zhao,Lintao Zhang,Sharad Malik +4 more
- 22 Jun 2001
TL;DR: The development of a new complete solver, Chaff, is described which achieves significant performance gains through careful engineering of all aspects of the search-especially a particularly efficient implementation of Boolean constraint propagation (BCP) and a novel low overhead decision strategy.
GRASP—a new search algorithm for satisfiability
João P. Marques Silva,Karem A. Sakallah +1 more
- 10 Nov 1996
TL;DR: Experimental results obtained from a large number of benchmarks, including many from the field of test pattern generation, indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely effective for aLarge number of representative classes of SAT instances.
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Quantifier elimination by Dependency Sequents
Eugene Goldberg,Panagiotis Manolios +1 more
- 01 Oct 2012
TL;DR: In this article, a Dependency-sequent (D-sequent) is used to record that a set of quantified variables is redundant under a partial assignment, and the join operation that produces new D-sequents from existing ones.
Quantifier elimination via clause redundancy
Eugene Goldberg,Panagiotis Manolios +1 more
- 11 Dec 2013
TL;DR: A quantifier elimination algorithm based on a new type of D- sequents called clause D-sequents that express redundancy of clauses rather than variables is introduced that significantly extend the ability to introduce and algorithmically exploit redundancy.
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Quantifier Elimination by Dependency Sequents
TL;DR: This work introduces an algorithm based on DDS, a new method for solving the problem of existential quantifier elimination for Boolean CNF formulas, and shows that DDS is compositional, i.e., if the authors' input formula is a conjunction of independent formulas, DDS automatically recognizes and exploits this information.
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