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Combining Satisfiability Procedures for Unions of Theories with a Shared Counting Operator

Nicolini E., Ringeissen C., Rusinowitch M.

Fundamenta Informaticae

2011

Vol. 105, nr 1/2

163-187

We present some decidability results for the universal fragment of theories modeling data structures and endowed with arithmetic constraints. More precisely, all the theories taken into account extend a theory that constrains the function symbol for the successor. A general decision procedure is obtained, by devising an appropriate calculus based on superposition. Moreover, we derive a decidability result for the combination of the considered theories for data structures and some fragments of arithmetic by applying a general combination schema for theories sharing a common subtheory. The effectiveness of the resulting algorithm is ensured by using the proposed calculus and a careful adaptation of standard methods for reasoning about arithmetic, such as Gauss elimination, Fourier-Motzkin elimination and Groebner bases computation.