Reasoning about sequences of memory states

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 1 0 -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.