Verification of scope-dependent hierarchical state machines

A hierarchical state machine (Hsm) 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 (Shsm). We show that Shsms can be exponentially more succinct than Shsms 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 Ltl and Ctl specifications. We also discuss some natural and interesting restrictions of the considered problems for which we can prove that Shsms can be verified as much efficiently as Hsms, still preserving an exponential gap of succinctness.