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

This is joint work with Benedikt Bollig and Paul Gastin, presented at CONCUR’18.

A pattern in a permutation is a subsequence with a specific relative order. What can we say about a typical large random permutation that avoids a particular pattern? We use a variety of approaches. For certain classes we give a geometric description that relates these classes to other types of well-studied concepts like random walks or random trees. Using the right geometric description we can find the the distribution of certain statistics like the number and location of fixed points.

We propose a type-based analysis to infer the session protocols of channels in an ML-like concurrent functional language. Combining and extending well-known techniques, we develop a type-checking system that separates the underlying ML type system from the typing of sessions. Without using linearity, our system guarantees communication safety and partial lock freedom. It also supports provably complete session inference with no programmer annotations. We exhibit the usefulness of our system with interesting examples, including one which is not typable in substructural type systems.

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