Verimag

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206
10 janvier 2017 - 14h00
Reasoning in the Bernays-Schonfinkel-Ramsey Fragment of Separation Logic
par Cristina Serban de VERIMAG



Abstract: Separation Logic (SL) is a well-known assertion language used in Hoare-style modular proof systems for programs with dynamically allocated data structures. In this paper we investigate the fragment of first-order SL restrictedto the Bernays-Schonfinkel-Ramsey quantifier prefix ∃∗∀∗, where the quantified variables range over the set of memory locations. When this set is uninterpreted (has no associated theory) the fragment is PSPACE-complete, which matches the complexity of the quantifier-free fragment. However, SL becomes undecidable when the quantifier prefix belongs to ∃∗∀∗∃∗ instead, or when the memory locations are interpreted as integers with linear arithmetic constraints, thus setting a sharp boundary for decidability within SL. We have implemented a decision procedure for the decidable fragment of ∃∗∀∗ SL as a specialized solver inside a DPLL(T) architecture, within the CVC4 SMT solver. The evaluation of our implementation was carried out using two sets of verification conditions, produced by (i) an inductive SL prover, and (ii) a weakest precondition-based verification condition generator. Experimental data shows that automated quantifier instantiation has little overhead, compared to manual model-based instantiation.




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