A Unified Display Proof Theory for Bunched Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
Automated cyclic entailment proofs in separation logic
CADE'11 Proceedings of the 23rd international conference on Automated deduction
The complexity of abduction for separated heap abstractions
SAS'11 Proceedings of the 18th international conference on Static analysis
Information and Computation
Automated verification of recursive programs with pointers
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Nondeterministic Phase Semantics and the Undecidability of Boolean BI
ACM Transactions on Computational Logic (TOCL)
Studia Logica
A theorem prover for Boolean BI
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The tree width of separation logic with recursive definitions
CADE'13 Proceedings of the 24th international conference on Automated Deduction
Proof search for propositional abstract separation logics via labelled sequents
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
A proof system for separation logic with magic wand
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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Separation logic has proven an effective formalism for the analysis of memory-manipulating programs. We show that the purely propositional fragment of separation logic is undecidable. In fact, for *any* choice of concrete heap-like model of separation logic, validity in that model remains undecidable. Besides its intrinsic technical interest, this result also provides new insights into the nature of decidable fragments of separation logic. In addition, we show that a number of propositional systems which approximate separation logic are undecidable as well. In particular, these include both Boolean BI and Classical BI. All of our undecidability results are obtained by means of a single direct encoding of Minsky machines.