CIRC is a tool for automated inductive and coinductive theorem proving. It includes an engine based on circular coinduction, which makes CIRC particularly well-suited for proving behavioral properties of infinite data-structures. This paper presents the current status of the coinductive features of the CIRC prover, focusing on new features added over the last two years. The presentation is by examples, showing how CIRC can automatically prove behavioral properties.

In this paper, we introduce an extension of the GSOS rule format with predicates such as termination, convergence and divergence. For this format we generalize the technique proposed by Aceto, Bloom and Vaandrager for the automatic generation of ground-complete axiomatizations of bisimilarity over GSOS systems. Our procedure is implemented in a tool that receives SOS specifications as input and derives the corresponding axiomatizations automatically. This paves the way to checking strong bisimilarity over process terms by means of theorem-proving techniques.

PREG Axiomatizer is a tool used for proving strong bisimilarity between ground terms consisting of operations in the GSOS format extended with predicates. It automatically derives sound and groundcomplete axiomatizations using a technique proposed by the authors of this paper. These axiomatizations are provided as input to the Maude system, which, in turn, is used as a reduction engine for provided ground terms. These terms are bisimilar if and only if their normal forms obtained in this fashion are equal. The motivation of this tool is the optimized handling of equivalence checking between complex ground terms within automated provers and checkers.

Abstract. A notion of generalized regular expressions for a large class of systems modeled as coalgebras, and an analogue of Kleene's theorem and Kleene algebra, were recently proposed by a subset of the authors of this paper. Examples of the systems covered include infinite streams, deterministic automata and Mealy machines. In this paper, we present a tool where the aforementioned expressions can be derived automatically and a novel algorithm to decide whether two expressions are bisimilar or not. The procedure is implemented in the automatic theorem prover CIRC, by reducing coinduction to an entailment relation between an algebraic specification and an appropriate set of equations.