Communicating finite-state machines, first-order logic, and star-free propositional dynamic logic

Message sequence charts (MSCs) naturally arise as executions of communicating finite-state machines (CFMs), in which processes exchange messages through unbounded FIFO channels. We study the first-order logic MSCs, featuring Lamport's happened-before relation. To this end, we introduce a star-free version propositional dynamic (PDL) with loop and converse. Our main results state that (i) every sentence can be transformed into an equivalent PDL (and conversely), (ii) translated CFM. This answers open question settles exact relation between CFMs fragments monadic second-order logic. As byproduct, show over MSCs has three-variable property.