Proofs from temporal hypotheses by symbolic simulation

Abstract

DMOD is a system for modeling and simulating real-time, discrete-event systems. It formalizes the popular discrete-event simulation technique but retains its powerful intuitions such as events, state, causality, event preemption, and variable advance of simulation time. DMOD has been successfully applied to analysis of real systems in telecommunications. This paper describes a method of using DMOD to prove an important class of temporal properties of the form property p holds infinitely often. The method is illustrated by verifying a robotic arm controller, a hybrid system with both discrete and continuous state. An important aspect of this method is that considerable control can be exercised over how efficiently theorems are proved. System models, temporal properties, and theorem provers are all programs in the logic programming language CLP(R). Algorithmic knowledge about how to efficiently compute abstractions needed for proof, and how to control the shape and size of search spaces can be encoded in these programs. Proofs are constructed by executing these programs. As an example of the resulting efficiency, the robotic arm controller is verified in just a few seconds.