A basic tool for the modeling of Marked-Controlled Reconfigurable Petri Nets

In previous studies, we have introduced marked-controlled net rewriting systems and a subclass of these called marked-controlled reconfigurable Petri nets. In a marked-controlled net rewriting system, a system configuration is described as a Petri net, and a change in configuration is described as a graph rewriting rule. A marked-controlled reconfigurable Petri net is a marked-controlled net rewriting system where a change in configuration amounts to a modification in the flow relations of the places in the domain of the involved rule in accordance with this rule, independently of the context in which this rewriting applies. In both models, the enabling of a rule not only depends on the net topology, but also depends on the net marking according to control places. Even though the expressiveness of Petri nets and marked-controlled reconfigurable Petri nets is the same, with marked-controlled reconfigurable Petri nets, we can easily and directly model concurrent and distributed systems that change their structure dynamically. In this article, we present MCReNet, a tool for the modeling and verification of marked-controlled reconfigurable Petri nets

Towards a Petri net Model for Graph Transformation Systems

Graph transformation systems (GTS) have been successfully proposed as a general, theoretically sound model for concurrency. Petri nets (PN), on the other side, are a central and intuitive formalism for concurrent or distributed systems, well supported by a number of analysis techniques/tools. Some PN classes have been shown to be instances of GTS. In this paper, we change perspective presenting an operational semantics of GTS in terms of Symmetric Nets, a well-known class of Coloured Petri nets featuring a structured syntax that outlines model symmetries. Some practical exploitations of the proposed operational semantics are discussed. In particular, a recently developed structural calculus for SN is used to validate graph rewriting rules in a symbolic way

A Category Theoretical Approach to the Concurrent Semantics of Rewriting: Adhesive Categories and Related Concepts

This thesis studies formal semantics for a family of rewriting formalisms that have arisen as category theoretical abstractions of the so-called algebraic approaches to graph rewriting. The latter in turn generalize and combine features of term rewriting and Petri nets. Two salient features of (the abstract versions of) graph rewriting are a suitable class of categories which captures the structure of the objects of rewriting, and a notion of independence or concurrency of rewriting steps – as in the theory of Petri nets. Category theoretical abstractions of graph rewriting such as double pushout rewriting encapsulate the complex details of the structures that are to be rewritten by considering them as objects of a suitable abstract category, for example an adhesive one. The main difficulty of the development of appropriate categorical frameworks is the identification of the essential properties of the category of graphs which allow to develop the theory of graph rewriting in an abstract framework. The motivations for such an endeavor are twofold: to arrive at a succint description of the fundamental principles of rewriting systems in general, and to apply well-established verification and analysis techniques of the theory of Petri nets (and also term rewriting systems) to a wide range of distributed and concurrent systems in which states have a "graph-like" structure. The contributions of this thesis thus can be considered as two sides of the same coin: on the one side, concepts and results for Petri nets (and graph grammars) are generalized to an abstract category theoretical setting; on the other side, suitable classes of "graph-like" categories which capture the essential properties of the category of graphs are identified. Two central results are the following: first, (concatenable) processes are faithful partial order representations of equivalence classes of system runs which only differ w.r.t. the rescheduling of causally independent events; second, the unfolding of a system is established as the canonical partial order representation of all possible events (following the work of Winskel). Weakly ω-adhesive categories are introduced as the theoretical foundation for the corresponding formal theorems about processes and unfoldings. The main result states that an unfolding procedure for systems which are given as single pushout grammars in weakly ω-adhesive categories exists and can be characetrised as a right adjoint functor from a category of grammars to the subcategory of occurrence grammars. This result specializes to and improves upon existing results concerning the coreflective semantics of the unfolding of graph grammars and Petri nets (under an individual token interpretation). Moreover, the unfolding procedure is in principle usable as the starting point for static analysis techniques such as McMillan’s finite complete prefix method. Finally, the adequacy of weakly ω-adhesive categories as a categorical framework is argued for by providing a comparison with the notion of topos, which is a standard abstraction of the categories of sets (and graphs)

fUML Activity Diagrams with RAG-controlled Rewriting -A RACR Solution of The TTC 2015 Model Execution Case

This paper summarises a RACR solution of The TTC 2015 Model Execution Case. RACR is a metacompiler library for Scheme. Its most distinguished feature is the seamless combination of reference attribute grammars and graph rewriting combined with incremental evaluation semantics. The presented solution sketches how these integrated analyses and rewriting facilities are used to transform fUML Activity Diagrams to executable Petri nets. Of particular interest are (1) the exploitation of reference attribute grammar analyses for Petri net generation and (2) the efficient execution of generated nets based on the incremental evaluation semantics of RACR

Two polygraphic presentations of Petri nets

This document gives an algebraic and two polygraphic translations of Petri nets, all three providing an easier way to describe reductions and to identify some of them. The first one sees places as generators of a commutative monoid and transitions as rewriting rules on it: this setting is totally equivalent to Petri nets, but lacks any graphical intuition. The second one considers places as 1-dimensional cells and transitions as 2-dimensional ones: this translation recovers a graphical meaning but raises many difficulties since it uses explicit permutations. Finally, the third translation sees places as degenerated 2-dimensional cells and transitions as 3-dimensional ones: this is a setting equivalent to Petri nets, equipped with a graphical interpretation.Comment: 28 pages, 24 figure

An Operational Semantics of Graph Transformation Systems Using Symmetric Nets

Graph transformation systems (GTS) have been successfully proposed as a general, theoretically sound model for concurrency. Petri nets (PN), on the other side, are a central and intuitive formalism for concurrent or distributed systems, well supported by a number of analysis techniques/tools. Some PN classes have been shown to be instances of GTS. In this paper, we change perspective presenting an operational semantics of GTS in terms of Symmetric Nets, a well-known class of Coloured Petri nets featuring a structured syntax that outlines model symmetries. Some practical exploitations of the proposed operational semantics are discussed. In particular, a recently developed structural calculus for SN is used to validate graph rewriting rules in a symbolic way

Reactive Systems over Cospans

The theory of reactive systems, introduced by Leifer and Milner and previously extended by the authors, allows the derivation of well-behaved labelled transition systems (LTS) for semantic models with an underlying reduction semantics. The derivation procedure requires the presence of certain colimits (or, more usually and generally, bicolimits) which need to be constructed separately within each model. In this paper, we offer a general construction of such bicolimits in a class of bicategories of cospans. The construction sheds light on as well as extends Ehrig and Konig’s rewriting via borrowed contexts and opens the way to a unified treatment of several applications

Adjunct hexagonal array token Petri nets and hexagonal picture languages

Adjunct Hexagonal Array Token Petri Net Structures (AHPN) are re- cently introduced hexagonal picture generating devices which extended the Hexag- onal Array Token Petri Net Structures . In this paper we consider AHPN model along with a control feature called inhibitor arcs and compare it with some ex- pressive hexagonal picture generating and recognizing models with respect to the generating power

Bisimilarity and Behaviour-Preserving Reconfigurations of Open Petri Nets

We propose a framework for the specification of behaviour-preserving reconfigurations of systems modelled as Petri nets. The framework is based on open nets, a mild generalisation of ordinary Place/Transition nets suited to model open systems which might interact with the surrounding environment and endowed with a colimit-based composition operation. We show that natural notions of bisimilarity over open nets are congruences with respect to the composition operation. The considered behavioural equivalences differ for the choice of the observations, which can be single firings or parallel steps. Additionally, we consider weak forms of such equivalences, arising in the presence of unobservable actions. We also provide an up-to technique for facilitating bisimilarity proofs. The theory is used to identify suitable classes of reconfiguration rules (in the double-pushout approach to rewriting) whose application preserves the observational semantics of the net.Comment: To appear in "Logical Methods in Computer Science", 41 page

Parallel Graph Transformation for Model Simulation applied to Timed Transition Petri Nets

Proceedings of the Workshop on Graph Transformation and Visual Modelling Techniques (GT-VMT 2004)This work discusses the use of parallel graph transformation systems for (multi-formalism) modeling and simulation and their implementation in the meta-modeling tool AToM3. As an example, a simulator for Timed Transition Petri Nets (TTPN) is modeled using parallel graph transformation.This work has been partially sponsored by the SEGRAVIS network and the Spanish Ministry of Science and Technology (TIC2002-01948)