The Tree Width of Separation Logic with Recursive Definitions

Radu Iosif (1) , Adam Rogalewicz (2) , Jiri Simacek (1, 2)

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

Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current results report on techniques to decide satisfiability and validity of entail-ments for Separation Logic(s) over lists (possibly with data). In this paper we establish a more general decidability result. We prove that any Separation Logic formula using rather general recursively defined predicates is decidable for satis-fiability, and moreover, entailments between such formulae are decidable for validity. These predicates are general enough to define (doubly-) linked lists, trees, and structures more general than trees, such as trees whose leaves are chained in a list. The decidability proofs are by reduction to decidability of Monadic Second Order Logic on graphs with bounded tree width.

Domaines: Logique en informatique [cs.LO]

Radu Iosif, Adam Rogalewicz, Jiri Simacek. The Tree Width of Separation Logic with Recursive Definitions. 24th International Conference on Automated Deduction (CADE 24), Jun 2013, Lake Placid, NY, United States. pp.21-38, ⟨10.1007/978-3-642-38574-2_2⟩. ⟨hal-01418897⟩