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2010
Abstract One of the main shortcomings of the traditional methods for combining theories is the complexity of guessing the arrangement of the variables shared by the individual theories. This paper presents a reformulation of the Nelson-Oppen method that takes into account explicit equality propagation and can ignore pairs of shared variables that the theories do not care about. We show the correctness of the new approach and present care functions for the theories of uninterpreted functions and the theory of arrays.
2011 •
Abstract. One of the main shortcomings of the traditional methods for combining theories is the complexity of guessing the arrangement of the variables shared by the individual theories. This paper presents a reformulation of the Nelson-Oppen method that takes into account explicit equality propagation and can ignore pairs of shared variables that the theories do not care about. We show the correctness of the new approach and present care functions for the theory of uninterpreted functions and the theory of arrays.
1996 •
Decision procedures are increasingly being employed for deciding or simplifying propositional combinations of ground equalities involving uninterpreted function symbols, linear arithmetic, arrays, and other theories. Two approaches for constructing decision procedures for combinations of ground theories were pioneered in the late seventies. In the approach of Nelson and Oppen, decision procedures for two disjoint theories are combined by introducing variables to name subterms and iteratively propagating any deduced equalities between variables from one theory to another. Shostak employs a different approach that works far more efficiently in practice. He uses an optimized implementation of the congruence closure procedure for ground equality over uninterpreted function symbols to combine theories that are canonizable and algebraically solvable. Many useful theories have these properties. Shostak's algorithm is subtle and complex and his description of this procedure is lacking in rigor. We present, for the first time, a careful development and clarification of Shostak's procedure that corrects several mistakes in Shostak's original presentation. Our analysis serves as a useful basis for the implementation, extension, and further optimization of Shostak's decision procedure.
… Margherita Ligure, Italy, April 8-10 …
A generalization of Shostak's method for combining decision procedures2002 •
Annals of Mathematics …
Delayed Theory Combination Vs. Nelson-Oppen for Satisfiability Modulo Theories: A Comparative Analysis2009 •
1977 •
We restrict attention to the validity problem for unquantied dis- junctions of literals (possibly negated atomic formulae) over the do- main of integers, or what is just as good, the satisability problem for unquantied conjunctions. When = is the only predicate symbol and all function symbols are left uninterpreted, or when is the only pred- icate symbol (taking its standard
2006 •
Electronic Notes in Theoretical Computer Science
A Local Graph-rewriting System for Deciding Equality in Sum-product Theories2007 •
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