SMT-based robust model checking for signal temporal logic

Abstract

Signal temporal logic (STL) is a temporal logic used to specify properties of continuous signals. STL has been widely applied in specifying, monitoring, and testing properties of hybrid systems that exhibit both discrete and continuous behavior. However, model checking techniques for hybrid systems have primarily been limited to invariant and reachability properties. This paper introduces bounded model checking algorithms and a tool for general STL properties of hybrid systems. Central to our technique is a novel logical foundation for STL, which includes: (i) syntactic separation, decomposing an STL formula into components, with each component depending exclusively on separate segments of a signal; (ii) signal discretization, ensuring a complete abstraction of a signal through a set of discrete elements; and (iii) ϵ-strengthening, reducing robust STL model checking to Boolean STL model checking. With this new foundation, the robust STL model checking problem can be reduced to the satisfiability of a first-order logic formula. This allows us to develop the first model checking algorithm for STL that can guarantee the correctness of STL up to given bound parameters and robustness threshold, along with a pioneering bounded model checker for hybrid systems, called STLmc. We demonstrate the effectiveness of STLmc on a number of hybrid system case studies.