Validity of CTL Queries Revisited

Abstract

We systematically investigate temporal logic queries in model checking, adding to the seminal paper by William Chan at CAV 2000. Chan’s temporal logic queries are CTL specifications where one unspecified subformula is to be filled in by the model checker in such a way that the specification becomes true. Chan defined a fragment of CTL queries called $\mbox{CTL}^{v}$ which guarantees the existence of a unique strongest solution. The starting point of our paper is a counterexample to this claim. We then show how the research agenda of Chan can be realized by modifying his fragment appropriately. To this aim, we investigate the criteria required by Chan, and define two new fragments $\mbox{CTL}^{v}_{new}$ and $\mbox{CTL}^{d}$ where the first is the one originally intended; the latter fragment also provides unique strongest solutions where possible but admits also cases where the set of solutions is empty.

This work was supported by the European Community Research Training Network “Games and Automata for Synthesis and Validation” (GAMES) and by the Austrian Science Fund Project Z29-N04.