Reasoning about sequences of memory states

Rémi Brochenin (1) , Stephane Demri (1, 2) , Etienne Lozes (1, 3)

1 LSV - Laboratoire Spécification et Vérification [Cachan]
2 CNRS - Centre National de la Recherche Scientifique
3 ENS Cachan - École normale supérieure - Cachan

Motivated by the verification of programs with pointer variables, we introduce a temporal logic LTL mem whose underlying assertion language is the quantifier-free fragment of separation logic and the temporal logic on the top of it is the standard linear-time temporal logic LTL. We analyze the complexity of various model-checking and satisfiability problems for LTL mem , considering various fragments of separation logic (including pointer arithmetic), various classes of models (with or without constant heap), and the influence of fixing the initial memory state. We provide a complete picture based on these criteria. Our main decidability result is pspace-completeness of the satisfiability problems on the record fragment and on a classical fragment allowing pointer arithmetic. Σ 0 1-completeness or Σ 1 1-completeness results are established for various problems by reducing standard problems for Minsky machines, and underline the tightness of our decidability results.

Mots clés: separation logic; temporal logic; Büchi automaton; complexity; linear-time temporal logic LTL; Minsky machine; test formula; pointer arithmetic; model-checking; PSPACE

Domaines: Informatique [cs]; Logique en informatique [cs.LO]; Théorie et langage formel [cs.FL]

Rémi Brochenin, Stephane Demri, Etienne Lozes. Reasoning about sequences of memory states. Annals of Pure and Applied Logic, 2009, ⟨10.1016/j.apal.2009.07.004⟩. ⟨hal-01905172⟩