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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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Abstract: We consider the problem of existential quantifier elimination for Boolean formulas in Conjunctive Normal Form (CNF). We present a new method for solving this problem called Derivation of Dependency-Sequents (DDS). A Dependency-sequent (D-sequent) is used to record that a set of quantified variables is redundant under a partial assignment. We introduce a resolution-like operation called join that produces a new D-sequent from two existing D-sequents. We also show that DDS is compositional, i.e. if our input formula is a conjunction of independent formulas, DDS automatically recognizes and exploits this information. We introduce an algorithm based on DDS and present experimental results demonstrating its potential.
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Citations
Playing with Quantified Satisfaction
Nikolaj Bjorner,Mikoláš Janota +1 more
- 18 Dec 2015
TL;DR: The algorithm is based on recent progress in solving Quantified Boolean Formulas, but it generalizes beyond propositional logic to theories, such aslinear arithmetic over integers, linear arithmetic over reals, algebraic data-types and arrays.
Theory and Applications of Satisfiability Testing - SAT 2015: 18th International Conference Austin, TX, USA, September 24-27, 2015 Proceedings
Marienus Heule,Sean A. Weaver +1 more
- 01 Jan 2015
TL;DR: A stochastic local search (SLS) solver for SAT named CCAnr is presented, which is based on the configuration checking strategy and has good performance on non-random SAT instances and can be further improved by using a preprocessor CP3.
27
Solving QBF with Free Variables
William Klieber,Mikoláš Janota,Joao Marques-Silva,Edmund M. Clarke +3 more
- 16 Sep 2013
TL;DR: This article shows how clause/cube learning for DPLL-based closed-QBF solvers can be extended to solve QBFs with free variables by introducing sequents that generalize clauses and cubes and allow learning facts of the form "under a certain class of assignments, the input formula is logically equivalent to a certain quantifier-free formula".
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Removal of Quantifiers by Elimination of Boundary Points
TL;DR: This paper considers the problem of elimination of existential quantifiers from a Boolean CNF formula by adding resolvent clauses of F eliminating boundary points and develops a method of quantifier elimination similar to that described in [9].
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•Posted Content
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.
4
References
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Martin Davis,George Logemann,Donald W. Loveland +2 more
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Matthew W. Moskewicz,Conor F. Madigan,Ying Zhao,Lintao Zhang,Sharad Malik +4 more
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Symbolic Model Checking
Edmund M. Clarke,Kenneth L. McMillan,Sérgio Campos,Vassili Hartonas-Garmhausen +3 more
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TL;DR: Using symbolic model checking techniques it is possible to verify industrial-size finite state systems and models with more than 10120 states have been verified using special techniques.
A Computing Procedure for Quantification Theory
Martin Davis,Hilary Putnam +1 more
TL;DR: In the present paper, a uniform proof procedure for quantification theory is given which is feasible for use with some rather complicated formulas and which does not ordinarily lead to exponentiation.
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