Choreographic languages describe possible sequences of interactions among a set of agents. Typical models are based on languages or automata over sending and receiving actions. Pomsets provide a more compact alternative by using a partial order over these actions and by not making explicit the possible interleaving of concurrent actions. However, pomsets offer no compact representation of choices. For example, if an agent Alice can send one of two possible messages to Bob three times, one would need a set of 2 × 2 × 2 distinct pomsets to represent all possible branches of Alice's behaviour. This paper proposes an extension of pomsets, named branching pomsets, with a branching structure that can represent Alice's behaviour using 2 + 2 + 2 ordered actions. We encode choreographies as branching pomsets and show that the pomset semantics of the encoded choreographies are bisimilar to their operational semantics.

Parenn is the typical generalisation of the Dyck language to multiple types of parentheses. We generalise its notion of balancedness to allow parentheses of different types to freely commute. We show that balanced regular and ω-regular languages can be characterised by syntactic constraints on regular and ω-regular expressions and, using the shuffle on trajectories operator, we define grammars for balanced-by-construction expressions with which one can express every balanced regular and ωregular language.

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A communication protocol is realisable if it can be faithfully implemented in a distributed fashion by communicating agents. Pomsets offer a way to compactly represent concurrency in communication protocols and have been recently used for the purpose of realisability analysis.In this paper we focus on the recently introduced branching pomsets, which also compactly represent choices. We define well-formedness conditions on branching pomsets, inspired by multiparty session types, and we prove that the well-formedness of a branching pomset is a sufficient condition for the realisability of the represented communication protocol.