A Decision Procedure for Guarded Separation Logic Complete Entailment Checking for Separation Logic with Inductive Definitions

We develop a doubly exponential decision procedure for the satisfiability problem of guarded separation logic —a novel fragment featuring user-supplied inductive predicates, Boolean connectives, and separating including restricted (guarded) versions negation, magic wand, septraction. Moreover, we show that dropping guards any preceding connectives leads to an undecidable fragment. further apply our reason about entailments in popular symbolic heap logic. In particular, obtain between (quantifier-free) heaps with predicate definitions bounded treewidth ( SL btw )—one most expressive decidable fragments Together recently shown 2ExpTime -hardness said fragment, conclude entailment is -complete—thereby closing previously open complexity gap.