LTL Generalized Model Checking Revisited

Given a 3-valued abstraction of a program (possibly generated using static program analysis and predicate abstraction) and a temporal logic formula, generalized model checking (GMC) checks whether there exists a concretization of that abstraction that satisfies the formula. In this paper, we revisit generalized model checking for linear time (LTL) properties. First, we show that LTL GMC is 2EXPTIME-complete in the size of the formula and polynomial in the model, where the degree of the polynomial depends on the formula, instead of EXPTIME-complete and quadratic as previously believed. The definition of GMC depends on a definition of concretization and completeness preorder. The usual definition of concretization is tailored for branching-time model checking. We then study a simpler linear completeness preorder for relating program abstractions. We show that LTL GMC with this preorder is only EXPSPACE-complete in the size of the formula, and can be solved in linear time and logarithmic space in the size of the model. Finally, we identify classes of formulas for which the model complexity of GMC is reduced.


PDF