Abstract. We describe the design and implementation of an automated theorem prover realising a fully general notion of cyclic proof. Our tool, called Cyclist, is able to construct proofs obeying a very general cycle scheme in which leaves may be linked to any other matching node in the proof, and to verify the general, global infinitary condition on such proof objects ensuring their soundness. Cyclist is based on a new, generic theory of cyclic proofs that can be instantiated to a wide variety of logics. We have developed three such concrete instantiations, based on: (a) first-order logic with inductive definitions; (b) entailments of pure separation logic; and (c) Hoare-style termination proofs for pointer programs. Experiments run on these instantiations indicate that Cyclist offers significant potential as a future platform for inductive theorem proving.

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We show that the satisfiability problem for the "symbolic heap" fragment of separation logic with general inductively defined predicates -which includes most fragments employed in program verification -is decidable. Our decision procedure is based on the computation of a certain fixed point from the definition of an inductive predicate, called its "base", that exactly characterises its satisfiability.A complexity analysis of our decision procedure shows that it runs, in the worst case, in exponential time. In fact, we show that the satisfiability problem for our inductive predicates is EXPTIMEcomplete, and becomes NP-complete when the maximum arity over all predicates is bounded by a constant.Finally, we provide an implementation of our decision procedure, and analyse its performance both on a synthetically generated set of test formulas, and on a second test set harvested from the separation logic literature. For the large majority of these test cases, our tool reports times in the low milliseconds.

We establish foundational results on the computational complexity of deciding entailment in Separation Logic with general inductive predicates whose underlying base language allows for pure formulas, pointers and existentially quantified variables. We show that entailment is in general undecidable, and ExpTime-hard in a fragment recently shown to be decidable by Iosif et al. Moreover, entailment in the base language is Π P 2 -complete, the upper bound even holds in the presence of list predicates. We additionally show that entailment in essentially any fragment of Separation Logic allowing for general inductive predicates is intractable even when strong syntactic restrictions are imposed. * Supported by the French ANR, ReacHard (grant ANR-11-BS02-001).

We introduce a framework for the symbolic verification of epistemic properties of programs expressed in a class of general-purpose programming languages. To this end, we reduce the verification problem to that of satisfiability of first-order formulae in appropriate theories. We prove the correctness of our reduction and we validate our proposal by applying it to two examples: the dining cryptographers problem and the ThreeBallot voting protocol. We put forward an implementation using existing solvers, and report experimental results showing that the approach can perform better than state-of-the-art symbolic model checkers for temporal-epistemic logic.