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Satisfiability Modulo Non-Disjoint Combinations of Theories Connected via Bridging Functions

Paula Chocron 1, 2 Pascal Fontaine 3 Christophe Ringeissen 2
2 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
3 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
LORIA - FM - Department of Formal Methods , Inria Nancy - Grand Est, MPII - Max-Planck-Institut für Informatik
Abstract : The Nelson-Oppen combination method is ubiquitous in all Satisfiability Modulo Theories solvers. However, one of its major drawbacks is to be restricted to disjoint unions of theories. We investigate the problem of extending this combination method to particular non-disjoint unions of theories connected via bridging functions. This problem is of greatest interest for solving verification problems expressed in a combination of data structures and arithmetic. Our work can be viewed as a synthesis of previous contributions by different authors. We investigate here an approach by reduction from non-disjoint to disjoint combination which is particularly well-suited to combine the theory of absolutely free data structures with bridging functions over a target theory. We consider the problem of adapting the combination procedure to get a satisfiability procedure for the standard interpretations of the data structure. We present an enumeration procedure that allows us to revisit the case of lists with length.
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Contributor : Christophe Ringeissen <>
Submitted on : Tuesday, November 25, 2014 - 3:45:35 PM
Last modification on : Monday, November 16, 2020 - 12:00:07 PM


  • HAL Id : hal-01087218, version 1


Paula Chocron, Pascal Fontaine, Christophe Ringeissen. Satisfiability Modulo Non-Disjoint Combinations of Theories Connected via Bridging Functions. Workshop on Automated Deduction: Decidability, Complexity, Tractability, ADDCT 2014. Held as Part of the Vienna Summer of Logic, affiliated with IJCAR 2014 and RTA 2014, Silvio Ghilardi, Ulrike Sattler, Viorica Sofronie-Stokkermans, Jul 2014, Vienna, Austria. ⟨hal-01087218⟩



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