Symbolic Model Checking for Rectangular Hybrid Systems

Abstract

An important case of hybrid systems are the rectangular automata. First, rectangular dynamics can naturally and arbitrarily closely approximate more general, nonlinear dynamics. Second, rectangular automata are the most general type of hybrid systems for which model checking -in particular, LTL model checking- is decidable. However, on one hand, the original proofs of decidability did not suggest practical algorithms and, on the other hand, practical symbolic model-checking procedures -such as those implemented in HyTECH- were not known to terminate on rectangular automata. We remedy this unsatisfactory situation: we present a symbolic method for LTL model checking which can be performed by HYTECH and is guaranteed to terminate on all rectangular automata. We do so by proving that our method for symbolic LTL model checking terminates on an infinite-state transition system if the trace-equivalence relation of the system has finite index, which is the case for all rectangular automata.