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Combination Methods for Satisfiability and Model-Checking of Infinite-State Systems

Silvio Ghilardi 1 Enrica Nicolini 2 Silvio Ranise 2 Daniele Zucchelli 1, 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
Abstract : Manna and Pnueli have extensively shown how a mixture of first-order logic (FOL) and discrete Linear time Temporal Logic (LTL) is sufficient to precisely state verification problems for the class of reactive systems. Theories in FOL model the (possibly infinite) data structures used by a reactive system while LTL specifies its (dynamic) behavior. In this paper, we derive undecidability and decidability results for both the satisfiability of (quantifier-free) formulae and the model-checking of safety properties by lifting combination methods for (non-disjoint) theories in FOL. The proofs of our decidability results suggest how decision procedures for the constraint satisfiability problem of theories in FOL and algorithms for checking the satisfiability of propositional LTL formulae can be integrated. This paves the way to employ efficient Satisfiability Modulo Theories solvers in the model-checking of infinite state systems. We illustrate our techniques on two examples.
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Submitted on : Monday, March 14, 2011 - 5:32:54 PM
Last modification on : Tuesday, November 22, 2022 - 5:32:24 PM

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Silvio Ghilardi, Enrica Nicolini, Silvio Ranise, Daniele Zucchelli. Combination Methods for Satisfiability and Model-Checking of Infinite-State Systems. Automated Deduction - CADE-21, Jul 2007, Bremen, Germany. pp.362-378, ⟨10.1007/978-3-540-73595-3_25⟩. ⟨inria-00576597⟩



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