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FIFO automata are finite state machines communicating through FIFO queues. They can be used, for instance, to model distributed protocols. Due to the unboundedness of the FIFO queues, several verification problems are undecidable for these systems. In order to model check such systems, one may look for decidable subclasses of FIFO systems. Binary half-duplex systems are systems of two FIFO automata exchanging over a half-duplex channel. They were studied by Cécé and Finkel who established the decidability in polynomial time of several properties. There is no obvious way to generalize the half-duplex property to multiparty systems. Cécé and Finkel proposed some generalizations but concluded that their notions of multiparty half-duplex systems were either too restrictive or too expressive.

Abstract: When working with distant collaborators on the same documents, one often uses a version control system, which is a program tracking the history of files and helping importing modifications brought by others as patches. The implementation of such a system requires to handle lots of situations depending on the operations performed by users on files, and it is thus difficult to ensure that all the corner cases have been correctly addressed. Here, instead of verifying the implementation of such a system, we adopt a complementary approach: we introduce a theoretical model, which is defined abstractly by the universal property that it should satisfy, and work out a concrete description of it. We begin by defining a category of files and patches, where the operation of merging the effect of two coinitial patches is defined by pushout. Since two patches can be incompatible, such a pushout does not necessarily exist in the category, which raises the question of which is the correct category to represent and manipulate files in conflicting state. We provide an answer by investigating the free completion of the category of files under finite colimits, and give an explicit description of this category: its objects are finite sets labeled by lines equipped with a transitive relation and morphisms are partial functions respecting labeling and relations. [Copyright &y& Elsevier]