Decidability of model checking with the temporal logic EF

The branching-time temporal logic EF is a simple, but natural fragment of computation tree logic (CTL) and the modal-calculus. We study the decidability of the model checking problem for EF and innnite-state systems. We use process rewrite systems (PRS) to describe innnite-state systems and deene a hierarchy of subclasses of PRS that includes Petri nets, pushdown processes, Basic Parallel Processes (BPP), context-free processes and PA-Processes. Then we establish the exact limits of the decidability of model checking with EF in this hierarchy. Model checking with EF is undecidable for Petri nets and even for parallel push-down automata (the pushdown extension of Basic Parallel Processes). On the other hand, model checking with EF is decidable for PAD, a process model that subsumes both PA-processes and pushdown processes.