Complexity of Strong Satisfiability Problems for Reactive System Specifications

Abstract

Many fatal accidents involving safety-critical reactive systems have occurred in unexpected situations, which were not considered during the design and test phases of system development. To prevent such accidents, reactive systems should be designed to respond appropriately to any request from an environment at any time. Verifying this property during the specification phase reduces the development costs of safety-critical reactive systems. This property of a specification is commonly known as realizability. The complexity of the realizability problem is 2EXPTIME-complete. We have introduced the concept of strong satisfiability, which is a necessary condition for realizability. Many practical unrealizable specifications are also strongly unsatisfiable. In this paper, we show that the complexity of the strong satisfiability problem is EXPSPACE-complete. This means that strong satisfiability offers the advantage of lower complexity for analysis, compared to realizability. Moreover, we show that the strong satisfiability problem remains EXPSPACE-complete even when only formulae with a temporal depth of at most 2 are allowed.