A compositional view of derivations as interactive processes with applications to regulated and distributed rewriting

The derivation process in rewriting systems, especially in Chomskyan grammars, can be seen as consisting of four stages: (1) selection of the production to apply from a supply of productions available at that step, (2) check of applicability of the production, possibly on different matches, (3) selection of the match at which to apply the production, (4) actual application. In this paper, we explore the different ways in which models of regulated and distributed rewriting have extended these four basic mechanisms and we propose a unifying perspective on them in terms of interaction between two agents, expressed through a particular form of conditional rewriting systems. This introduces a compositional view of derivation processes, where different components, playing specific roles and exhibiting specific behaviours, can be made to communicate and combined into different models of derivation. Existing models of regulated and distributed rewriting can thus be reformulated in this new framework, and new ones can be obtained.