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Modular Termination and Combinability for Superposition Modulo Counter Arithmetic

Christophe Ringeissen 1 Valerio Senni 1 
1 CASSIS - Combination of approaches to the security of infinite states systems
FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174), Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : Modularity is a highly desirable property in the development of satisfiability procedures. In this paper we are interested in using a dedicated superposition calculus to develop satisfiability procedures for (unions of) theories sharing counter arithmetic. In the first place, we are concerned with the termination of this calculus for theories representing data structures and their extensions. To this purpose, we prove a modularity result for termination which allows us to use our superposition calculus as a satisfiability procedure for combinations of data structures. In addition, we present a general combinability result that permits us to use our satisfiability procedures into a non-disjoint combination method a la Nelson-Oppen without loss of completeness. This latter result is useful whenever data structures are combined with theories for which superposition is not applicable, like theories of arithmetic.
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Submitted on : Thursday, October 27, 2011 - 5:26:06 PM
Last modification on : Friday, January 21, 2022 - 3:08:58 AM

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Christophe Ringeissen, Valerio Senni. Modular Termination and Combinability for Superposition Modulo Counter Arithmetic. Frontiers of Combining Systems, 8th International Symposium, FroCoS'2011, Oct 2011, Saarbruecken, Germany. pp.211-226, ⟨10.1007/978-3-642-24364-6_15⟩. ⟨inria-00636589⟩



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