This paper develops a framework for solving temporal-logic query-checking problems for a class of infinite-state system models that compute with integer-valued variables (so-called Presburger systems, in which Presburger formulas are used to define system behavior). The temporal-logic query checking problem may be formulated as follows: given a model and a temporal logic formula with placeholders, compute a set of assignments of formulas to placeholders such that the resulting temporal formula is satisfied by the given model. Temporal-logic query checking has proved useful as a means for requirements and design understanding; existing work, however, has focused only on propositional temporal logic and finite-state systems.Our method is based on a symbolic model-checking technique that relies on proof search. The paper first introduces this model-checking approach and then shows how it can be adapted to solving the temporal queries in which formulas may contain integer variables. We also present experimental results showing the computational efficacy of our approach.

This paper presents a local algorithm for solving the universal parametric real-time model-checking problem. The problem may be phrased as follows: given a real-time system and temporal formula, both of which may contain parameters, and a constraint over the parameters, does every allowed parameter assignment ensure that the real-time system satisfies the formula? Our approach relies on translating these model-checking problems into predicate equation systems, and then using an efficient proof-search algorithm to solve these systems. Experimental data shows that our method substantially outperforms existing approaches for systems that contain errors, while exhibiting comparable behavior for systems that are correct. This fast error-detection capability of our technique makes it especially interesting for design approaches in which model checkers are used "early and often" to detect design errors in an ongoing manner.