Extracting Counterexamples from Transitive-Closure-Based Model Checking

We address the problem of how to extract counterexamples for the transitive-closure-based model checking (TCMC) technique. TCMC is a representation of the CTLFC (CTL with fairness constraints) model checking problem in first-order logic with transitive closure (FOLTC) and has been implemented in the Alloy Analyzer. It is a declarative, symbolic model checking method. As a CTL model checking method, TCMC is defined over transition systems and states (rather than paths) and therefore, returns a transition system with a bug as a counterexample. Our contribution is to isolate a counterexample path/subgraph in a declarative manner by adding constraints that do not depend on the property. Our method does not require extensions to Alloy.