Graph grammars for distributed systems

Abstract

In the paper we define grammars on a class of labeled, partially ordered hypergraphs, called distributed systems. A distributed system models both the spatial and the temporal aspects of a real system through the relations of adjacency and causality. Terminal symbols represent the (deterministic, certain) past history of the system while nonterminal symbols model the (possibly nondeterministic, potential) future history of the system. The (context free) productions of a grammar represent the possible stand-alone evolutions of system components. From the productions, we obtain a (possibly infinite) number of rewriting rules, which model the synchronized evolution of adjacent system components. The (terminal) distributed systems derived within a given grammar represent the alternative deterministic, concurrent computations of a single nondeterministic system which is thus completely modeled by the grammar.