Integrating Boolean and Mathematical Solving: Foundations, Basic Algorithms and Requirements

Audemard, Gilles and Bertoli, Piergiorgio and Cimatti, Alessandro and Kornilowicz, Artur and Sebastiani, Roberto (2002) Integrating Boolean and Mathematical Solving: Foundations, Basic Algorithms and Requirements. UNSPECIFIED.

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    In the last years we have witnessed an impressive advance in the efficiency of boolean solving techniques, which has brought large previously intractable problems at the reach of state-of-the-art solvers. Unfortunately, simple boolean expressions are not expressive enough for representing many real-world problems, which require handling also integer or real values and operators. On the other hand, mathematical solvers, like computer-algebra systems or constraint solvers, cannot handle efficiently problems involving heavy boolean search, or do not handle them at all. In this paper we present the foundations and the basic algorithms for a new class of procedures for solving boolean combinations of mathematical propositions, which combine boolean and mathematical solvers, and we highlight the main requirements that boolean and mathematical solvers must fulfill in order to achieve the maximum benefits from their integration. Finally we show how existing systems are captured by our framework.

    Item Type: Departmental Technical Report
    Department or Research center: Information Engineering and Computer Science
    Subjects: Q Science > QA Mathematics > QA075 Electronic computers. Computer science
    Uncontrolled Keywords: boolean reasoning, mathematical reasoning, integration of procedures
    Additional Information: In "Artificial Intelligence, Automated Reasoning, and Symbolic Computation. Proc. of Joint AISC 2002 and Calculemus 2002." Marseille, France, 2002. LNAI series N.2385, Springer Verlag.
    Report Number: DIT-02-042
    Repository staff approval on: 21 Jan 2003

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