Model checking systems and specifications with parameterized atomic propositions

In classical LTL model checking, both the system and the specification are over a finite set of atomic propositions. We present a natural extension of this model, in which the atomic propositions are parameterized by variables ranging over some (possibly infinite) domain. For example, by parameterizing the atomic propositions send and receive by a variable x ranging over possible messages, the specification specifies that not only each send signal is followed by a receive signal, but also that the content of the received message agrees with the content of the one sent. Our extended setting consists of Variable LTL (VLTL) - a specification formalism that extends LTL with atomic propositions parameterized by variables, and abstract systems - systems in which atomic propositions may be parameterized by variables. We study the model-checking problem in this setting. We show that while the general setting is undecidable, some useful special cases are decidable. In particular, for fragments of VLTL that restrict the quantification over the variables, the model checking is PSPACE-complete, and thus is not harder than the LTL model checking problem. The latter result conveys the strength and advantage of our setting.