On the essence of parallel independence for the double-pushout and sesqui-pushout approaches

Parallel independence between transformation steps is a basic notion in the algebraic approaches to graph transformation, which is at the core of some static analysis techniques like Critical Pair Analysis. We propose a new categorical condition of parallel independence and show its equivalence with two other conditions proposed in the literature, for both left-linear and non-left-linear rules. Next we present some preliminary experimental results aimed at comparing the three conditions with respect to computational efficiency. To this aim, we implemented the three conditions, for left-linear rules only, in the Verigraph system, and used them to check parallel independence of pairs of overlapping redexes generated from some sample graph transformation systems over categories of typed graphs

Interactions between Causal Structures in Graph Rewriting Systems

Graph rewrite formalisms are a powerful approach to modeling complex molecular systems. They capture the intrinsic concurrency of molecular interactions, thereby enabling a formal notion of mechanism (a partially ordered set of events) that explains how a system achieves a particular outcome given a set of rewrite rules. It is then useful to verify whether the mechanisms that emerge from a given model comply with empirical observations about their mutual interference. In this work, our objective is to determine whether a specific event in the mechanism for achieving X prevents or promotes the occurrence of a specific event in the mechanism for achieving Y. Such checks might also be used to hypothesize rules that would bring model mechanisms in compliance with observations. We define a rigorous framework for defining the concept of interference (positive or negative) between mechanisms induced by a system of graph-rewrite rules and for establishing whether an asserted influence can be realized given two mechanisms as an input.Comment: In Proceedings CREST 2018, arXiv:1901.0007

Parallelism in AGREE transformations

The AGREE approach to graph transformation allows to specify rules that clone items of the host graph, controlling in a finegrained way how to deal with the edges that are incident, but not matched, to the rewritten part of the graph. Here, we investigate in which ways cloning (with controlled embedding) may affect the dependencies between two rules applied to the same graph. We extend to AGREE the classical notion of parallel independence between the matches of two rules to the same graph, identifying sufficient conditions that guarantee that two rules can be applied in any order leading to the same result

M-adhesive transformation systems with nested application conditions. Part 1: parallelism, concurrency and amalgamation

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Nested application conditions generalise the well-known negative application conditions and are important for several application domains. In this paper, we present Local Church–Rosser, Parallelism, Concurrency and Amalgamation Theorems for rules with nested application conditions in the framework of M-adhesive categories, where M-adhesive categories are slightly more general than weak adhesive high-level replacement categories. Most of the proofs are based on the corresponding statements for rules without application conditions and two shift lemmas stating that nested application conditions can be shifted over morphisms and rules

String Diagram Rewrite Theory III: Confluence with and without Frobenius

In this paper we address the problem of proving confluence for string diagram rewriting, which was previously shown to be characterised combinatorically as double-pushout rewriting with interfaces (DPOI) on (labelled) hypergraphs. For standard DPO rewriting without interfaces, confluence for terminating rewrite systems is, in general, undecidable. Nevertheless, we show here that confluence for DPOI, and hence string diagram rewriting, is decidable. We apply this result to give effective procedures for deciding local confluence of symmetric monoidal theories with and without Frobenius structure by critical pair analysis. For the latter, we introduce the new notion of path joinability for critical pairs, which enables finitely many joins of a critical pair to be lifted to an arbitrary context in spite of the strong non-local constraints placed on rewriting in a generic symmetric monoidal theory

Adequacy Issues in Reactive Systems: Barbed Semantics for Mobile Ambients

Reactive systems represent a meta-framework aimed at deriving behavioral congruences for those specification formalisms whose operational semantics is provided by rewriting rules. The aim of this thesis is to address one of the main issues of the framework, concerning the adequacy of the standard observational semantics (the IPO and the saturated one) in modelling the concrete semantics of actual formalisms. The problem is that IPO-bisimilarity (obtained considering only minimal labels) is often too discriminating, while the saturated one (via all labels) may be too coarse, and intermediate proposals should then be put forward. We then introduce a more expressive semantics for reactive systems which, thanks to its flexibility, allows for recasting a wide variety of observational, bisimulation-based equivalences. In particular, we propose suitable notions of barbed and weak barbed semantics for reactive systems, and an efficient characterization of them through the IPO-transition systems. We also propose a novel, more general behavioural equivalence: L-bisimilarity, which is able to recast both its IPO and saturated counterparts, as well as the barbed one. The equivalence is parametric with respect to a set L of reactive systems labels, and it is shown that under mild conditions on L it is a congruence. In order to provide a suitable test-bed, we instantiate our proposal over the asynchronous CCS and, most importantly, over the mobile ambients calculus, whose semantics is still in a flux

Integrated Structure and Semantics for Reo Connectors and Petri Nets

In this paper, we present an integrated structural and behavioral model of Reo connectors and Petri nets, allowing a direct comparison of the two concurrency models. For this purpose, we introduce a notion of connectors which consist of a number of interconnected, user-defined primitives with fixed behavior. While the structure of connectors resembles hypergraphs, their semantics is given in terms of so-called port automata. We define both models in a categorical setting where composition operations can be elegantly defined and integrated. Specifically, we formalize structural gluings of connectors as pushouts, and joins of port automata as pullbacks. We then define a semantical functor from the connector to the port automata category which preserves this composition. We further show how to encode Reo connectors and Petri nets into this model and indicate applications to dynamic reconfigurations modeled using double pushout graph transformation