Verification of scope-dependent hierarchical state machines

Abstract

A hierarchical state machine (H sm) is a finite state machine where a vertex can either expand to another hierarchical state machine ( box) or be a basic vertex ( node). Each node is labeled with atomic propositions. We study an extension of such model which allows atomic propositions to label also boxes (S hsm). We show that S hsms can be exponentially more succinct than S hsms and verification is in general harder by an exponential factor. We carefully establish the computational complexity of reachability, cycle detection, and model checking against general L tl and C tl specifications. We also discuss some natural and interesting restrictions of the considered problems for which we can prove that S hsms can be verified as much efficiently as H sms, still preserving an exponential gap of succinctness.