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

It Is Easy to Be Wise After the Event: Communicating Finite-State Machines Capture First-Order Logic with "Happened Before"