Towards Proved Formal Specification and Verification of STL Operators as Synchronous Observers

Signal Temporal Logic (STL) is a convenient formalism to express bounded horizon properties of autonomous critical systems. STL extends LTL to real-valued signals and associates a non-singleton bound interval to each temporal operators. In this work we provide a rigorous encoding of non-nested discrete-time STL formulas into Lustre synchronous observers. Our encoding provides a three-valued online semantics for the observers and therefore enables both the verification of the property and the search of counter-examples. A key contribution of this work is an instrumented proof of the validity of the implementation. Each node is proved correct with respect to the original STL semantics. All the experiments are automated with the Kind2 model-checker and the Z3 SMT solver.