A Graphical Fusion Calculus

Abstract

We analyze the relationship between Fusion Calculus and graph transformations defined in the Synchronized Hyperedge Replacement (SHR) style. In particular we show that the underlying algebraic structure is the same when the synchronization used in SHR is Milner synchronization. The main difference we see is that Fusion Calculus has an interleaving behaviour while SHR is inherently concurrent. In the paper we introduce the interleaving semantics for SHR with Milner synchronization and show that there is a complete correspondence between the operational semantics of Fusion Calculus and of SHR systems.

Mapping Fusion and Synchronized Hyperedge Replacement into logic programming

“…Hoare synchronization was necessary since our aim was to eventually map Fusion Calculus to logic programming. If the aim is just to compare Fusion Calculus and SHR it is possible to use SHR with Milner synchronization, achieving a much simpler and complete mapping, which considers the LTS of Fusion Calculus instead of reductions (see Lanese and Montanari 2004a).…”

“…This translation was already presented in the MSc thesis of the first author (Lanese 2002) and in Lanese and Montanari (2002). Fusion Calculus was mapped into SHR with Milner synchronization (a simpler task) in Lanese and Montanari (2004a) where Fusion LTS was considered instead of Fusion reduction semantics. The paper Lanese and Montanari (2002) also contains a mapping of Ambient calculus into HSHR.…”

Network Applications of Graph Bisimulation

“…Synchronised graph rewriting has been proposed as a unifying semantic framework for process calculi [12,10,15,3]; to fulfill this project, graphs must be endowed with an abstract notion of behaviour. In this paper we do so by introducing a notion of bisimulation equivalence for a system of context-free synchronising graphs and by proving it a congruence with respect to parallel composition and node restriction.…”