Strategies for combining decision procedures

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Strategies for Combining Decision Procedures

Implementing efficient algorithms for combining decision procedures has been a challenge and their correctness precarious. In this paper we describe an inference system that has the classical Nelson-Oppen procedure at its core and includes several optimizations: variable abstraction with sharing, canonization of terms at the theory level, and Shostak’s streamlined generation of new equalities f...

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We give a detailed survey of the current state-of-the-art methods for combining decision procedures. We review the Nelson-Oppen combination method, Shostak method, and some very recent results on the combination of theories over non-disjoint signatures.

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We present resolution-based decision procedures for the guarded, two-variable and monadic fragments without equality in a uniform way and show how they can be combined. In this way, new decidable fragments are obtained. We make use of a novel technique for describing resolution decision procedures by means of clause schemes. The scheme notation provides a convenient way of specifying decision p...

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We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider methods of establishing such assertions using only restricted forms of distributivity. At the same time, we explore ways in which “local” decision or heuristic procedures for fragments of the theory of the reals can be amal...

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The Nelson-Oppen combination method combines decision procedures for theories satisfying certain conditions into a decision procedure for their union. While the method is known to be correct in the setting of unsorted first-order logic, some current implementations of it appear in tools that use a sorted input language. So far, however, there have been no theoretical results on the correctness ...

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ژورنال

عنوان ژورنال: Theoretical Computer Science

سال: 2006

ISSN: 0304-3975

DOI: 10.1016/j.tcs.2005.11.025