Complexity of Strong Satisfiability Problems for Reactive System Specifications

Abstract

SUMMARYMany 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.

Combining Unification and Rewriting in Proofs for Modal Logics with First-order Undefinable Frames

“…We have proposed a practical application of a proof method for LTL, which is considered an extension of modal logic, in security analyses [24,25], bioinformatics [26][27][28], system verification [29][30][31][32][33], and system synthesis [34,35]. We will adapt modal unification and rewriting to these applications.…”

Bounded Strong Satisfiability Checking of Reactive System Specifications

“…To represent condition 4, however, we do require meta-level universal quantification. The representation of the conditions is based on that of the reduction from another tiling problem (which is EXPSPACE-complete) to the (unbounded) strong satisfiability problem in [6].…”

“…Strong satisfiability is the property that for any input sequence there is a response that satisfies a given specification. Strong satisfiability can be checked with less complexity than realizability [6]. Although this property is a necessary condition, many practical unrealizable specifications are also strongly unsatisfiable [7].…”

“…Because the complexity of the realizability problem is 2EXPTIME-complete [8], and that of the strong satisfiability problem is EXPSPACE-complete [6], bounded strong satisfiability offers the advantage of less complex analysis compared with realizability and strong satisfiability. We implemented our method, and found that it can handle larger specifications than existing techniques based on other properties, and can detect deficiencies efficiently.…”

Efficiency of the strong satisfiability checking procedure for reactive system specifications

“…Previously, we studied the theoretical complexity of the strong satisfiability problem and found that strong satisfiability offers the advantage of lower theoretical complexity compared to reliability [15]. However, the practical complexity of strong satisfiability has not been demonstrated.…”