A calculus of concurrent graph-rewriting processes

Abstract

State-of-the-art approaches to controlled graph rewriting focus on the specification of an external control layer over graph-rewriting rule applications and on the input-output semantics of the resulting systems, leading to a decreased relevance of many interesting operational aspects of graph transformation, as studied in the classical theory of algebraic graph rewriting.We propose a novel approach to controlled graph rewriting where we aim at bridging the gap between these two complementary approaches, defining an operational semantics for which classical concepts and results related to independence and parallelism of graph derivations can be recast.The calculus we propose is based on a control layer specified using (a fragment of) Milner's Calculus of Communicating Systems (CCS), where the actions specify the application of graph transformation rules to the current state, according to the Double-Pushout approach (DPO).In particular, we address the following aspects for our controlled graph-rewriting processes: (i) expressiveness of the control language, compared to a minimally complete reference language, Graph Programs, proposed by Habel and Plump; (ii) process equivalence based on labeled transition systems and a structural operational semantics; (iii) a unifying treatment of action independence, considering the corresponding notions from both process algebra and graph-rewriting theory; and (iv) parallelism and concurrency based on the notion of asynchronous (labeled) transition systems, obtained from an asynchronous version of the proposed calculus.