Deciding Entailments in Inductive Separation Logic with Tree Automata

Radu Iosif (1) , Adam Rogalewicz (2) , Tomáš Vojnar (2)

1 VERIMAG - IMAG - VERIMAG
2 FIT / BUT - Faculty of Information Technology [Brno]

Separation Logic (SL) with inductive definitions is a natural formalism for specifying complex recursive data structures, used in compositional verification of programs manipulating such structures. The key ingredient of any automated verification procedure based on SL is the decidability of the entailment problem. In this work, we reduce the entailment problem for a non-trivial subset of SL describing trees (and beyond) to the language inclusion of tree automata (TA). Our reduction provides tight complexity bounds for the problem and shows that entailment in our fragment is EXPTIME-complete. For practical purposes, we leverage from recent advances in automata theory, such as inclusion checking for non-deterministic TA avoiding explicit determinization. We implemented our method and present promising preliminary experimental results.

Domaines: Logique en informatique [cs.LO]

Radu Iosif, Adam Rogalewicz, Tomáš Vojnar. Deciding Entailments in Inductive Separation Logic with Tree Automata. 12th International Symposium on Automated Technology for Verification and Analysis (ATVA 2014), Nov 2014, Sydney, Australia. pp.201-218, ⟨10.1007/978-3-319-11936-6_15⟩. ⟨hal-01418889⟩