Compositional Verification with Stutter-invariant Propositional Projection Temporal Logic

This paper investigates compositional verification with Propositional Projection Temporal Logic (PPTL). To this end, a sublogic Stutter-invariant PPTL (written as PPTLst) is first proposed. As a specification language, PPTLst helps designers get rid of irrelevant detail in compositional verification of a concurrent system since the projection construct of PPTLst allows designers to assert formulas over points of interest through an execution. In this way, modules can be abstracted based on their local properties defined by projection construct, and substitution of modules by the abstracted ones will not affect overall properties of the system. PPTLst is proved to be able to capture all stutter-invariant properties expressive in PPTL. Further, an algorithm translating PPTL formulas to PPTLst ones is also given. And the complexity of the algorithm is accordingly studied. Moreover, an example– automatic gas station, is studied to illustrate compositional verification with PPTLst. Key–Words: Propositional projection temporal logic, Stutter-invariance, Compositional verification, Partial-order model-checking