A Dendroidal Process Calculus

The Dendroidal Process Calculus (DPC) is designed as a new theory for modeling concurrent and distributed computations and systems, equipped with a non-sequential and compositional semantics. In this theory, a parallel composition is parameterized by a graph at the vertices of which subprocesses are located. Communication is allowed only between subprocesses related by an edge in this graph. Moreover, an observational equivalence based on barbs as well as a weak bisimilarity equivalence are defined and an adequacy theorem relating these two notions is proved. DPC is shown to be a conservative extension of both top-down tree automata and of the process algebra CCS, and to endow CCS with a non-sequential semantics. The expressiveness of this theory looks promising to describe and analyze some phenomena arising in weak memory models and in network security. As an illustration of potential applications, an associated notion of tree shuffle is introduced and analyzed.