Efficient SMT-Based Model Checking for Signal Temporal Logic

STLmc: Robust STL Model Checking of Hybrid Systems Using SMT

“…The robustness degree of f2 3 is less than in [2,4], since the robustness degree of p 2 is less than in [5,14] = [2,4] + [3,10]. [3,29]. The satisfiability of the SMT encoding can be checked directly using an SMT solver or using the two-step solving algorithm to improve the performance for ODE dynamics.…”

“…Finding a counterexample of ϕ for robust STL model checking can be reduced to finding a counterexample of the -strengthening ϕ + for Boolean STL model checking. The satisfaction of ϕ by the Boolean STL semantics [29,31] is denoted by σ, t |= τ ϕ. We have the following theorem (see our report [42] for details).…”

“…For Boolean STL model checking, there exist refutationally complete bounded model checking algorithms [3,29] with two bound parameters: τ for the time domain, and N for the number of mode changes and variable points. A time point t is a variable point if a truth value of ϕ's subformula changes at t. The algorithms build an SMT encoding Ψ N,τ H,¬ϕ of Boolean STL model checking:…”

“…Recently, several STL model checking techniques have been proposed for hybrid systems [3,29,35]. In particular, the SMT-based bounded model checking algorithms [3,29] are refutation-complete, i.e., they can guarantee correctness up to given bounds. However, these techniques are based on the Boolean semantics of STL instead of quantitative semantics.…”

“…We reduce the robust STL model checking problem to Boolean STL model checking using -strengthening (perturbing the problem by to make it harder to be true), first proposed in [21] for first-order logic and extended to STL. We then apply the refutation-complete bounded model checking algorithm [3,29] to build the SMT encoding of the resulting Boolean STL model checking problem, which can be solved using SMT solvers.…”