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Radu Grigore

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3 papers
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3

LPAR Conference 2013 Conference Paper

On QBF Proofs and Preprocessing

  • Mikolás Janota
  • Radu Grigore
  • João Marques-Silva 0001

Abstract QBFs (quantified boolean formulas), which are a superset of propositional formulas, provide a canonical representation for PSPACE problems. To overcome the inherent complexity of QBF, significant effort has been invested in developing QBF solvers as well as the underlying proof systems. At the same time, formula preprocessing is crucial for the application of QBF solvers. This paper focuses on a missing link in currently-available technology: How to obtain a certificate (e. g. proof) for a formula that had been preprocessed before it was given to a solver? The paper targets a suite of commonly-used preprocessing techniques and shows how to reconstruct certificates for them. On the negative side, the paper discusses certain limitations of the currently-used proof systems in the light of preprocessing. The presented techniques were implemented and evaluated in the state-of-the-art QBF preprocessor bloqqer.

JELIA Conference 2010 Conference Paper

Counterexample Guided Abstraction Refinement Algorithm for Propositional Circumscription

  • Mikolás Janota
  • Radu Grigore
  • João Marques-Silva 0001

Abstract Circumscription is a representative example of a nonmonotonic reasoning inference technique. Circumscription has often been studied for first order theories, but its propositional version has also been the subject of extensive research, having been shown equivalent to extended closed world assumption (ECWA). Moreover, entailment in propositional circumscription is a well-known example of a decision problem in the second level of the polynomial hierarchy. This paper proposes a new Boolean Satisfiability (SAT)-based algorithm for entailment in propositional circumscription that explores the relationship of propositional circumscription to minimal models. The new algorithm is inspired by ideas commonly used in SAT-based model checking, namely counterexample guided abstraction refinement. In addition, the new algorithm is refined to compute the theory closure for generalized close world assumption (GCWA). Experimental results show that the new algorithm can solve problem instances that other solutions are unable to solve.

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