Bisimulation from Open Maps

SUMMARYWe propose a theoretical testing framework and a test generation algorithm for concurrent systems specified with true‐concurrency models, such as Petri nets or networks of automata. The semantic model of computation of such formalisms is labelled event structures, which allow to represent concurrency explicitly. We introduce the notions of strong and weak concurrency: strongly concurrent events must be concurrent in the implementation, while weakly concurrent ones may eventually be ordered. The ioco type conformance relations for sequential systems rely on the observation of sequences of actions and blockings; thus, they are not capable of capturing and exploiting concurrency of non‐sequential behaviours. We propose an extension of ioco for labelled event structures, named co‐ioco, allowing to deal with strong and weak concurrency. We extend the notions of test cases and test execution to labelled event structures and give a test generation algorithm building a complete test suite for co‐ioco. Copyright © 2014 John Wiley & Sons, Ltd.

Presheaf models for CCS-like languages

A systematic treatment of weak bisimulation and observational congruence on presheaf models is presented. The theory is developed with respect to a "hiding" functor from a category of paths to observable paths. Via a view of processes as bundles, we are able to account for weak morphisms (roughly only required to preserve observable paths) and to derive a saturation monad (on the category of presheaves over the category of paths). Weak morphisms may be encoded as strong ones via the Kleisli construction associated to the saturation monad. A general notion of weak open-map bisimulation is introduced, and results relating various notions of strong and weak bisimulation are provided. The abstract theory is accompanied by fine concrete study of two key models for concurrency, the interleaving model of synchronisation trees and the independence model of labelled event structures.

In this paper, we investigate transition systems of a class of Petri nets suitable for the modelling and behavioural analysis of globally asynchronous locally synchronous systems. The considered model of Elementary Net Systems with Localities (ENL-systems) is basically that of Elementary Net Systems (EN-systems) equipped with an explicit notion of locality. Each locality identifies a distinct set of events which may only be executed synchronously, i.e., in a maximally concurrent manner. For this reason, the overall behaviour of an ENL-system cannot be represented by an interleaved transition system, with arcs being labelled by single events, but rather by a suitable notion of a step transition system, with arcs being labelled by sets of events executed concurrently.We completely characterise transition systems which can be generated by Elementary Net Systems with Localities under their intended concurrency semantics. In developing a suitable characterisation, we follow the standard approach in which key relationships between a Petri net and its transition system are established via the regions of the latter defined as specific sets of states of the transition system. We argue that this definition is insufficient for the class of transition systems of ENL-systems, and then augment the standard notion of a region with some additional information, leading to the notion of a region with explicit input and output events (or io-region).We define, and show consistency of, two behaviour preserving translations between ENL-systems and their transition systems. As a result, we provide a solution to the synthesis problem of Elementary Net Systems with Localities, which consists in constructing an ENL-system for a given transition system in such a way that the transition system of the former is isomorphic to the latter.KeywordsTheory of concurrencyPetri netselementary net systemslocalitiesanalysis and synthesisstep sequence semanticsstructure and behaviour of netstheory of regionstransition systems

When a Petri net is synthesised from a labelled transition system, it is frequently desirable that certain additional constraints are fulfilled. For example, in circuit design, one is often interested in constructing safe Petri nets. Targeting such subclasses of Petri nets is not necessarily computationally more efficient than targeting the whole class. For example, targeting safe nets is known to be NP-complete while targeting the full class of place/transition nets is polynomial, in the size of the transition system. In this paper, several classes of Petri nets are examined, and their suitability for being targeted through efficient synthesis from labelled transition systems is studied and assessed. The focus is on choice-free Petri nets and some of their subclasses. It is described how they can be synthesised efficiently from persistent transition systems, summarising and streamlining in tutorial style some of the authors’ and their groups’ work over the past few years.

Event structures are a well-established model in concurrency theory.Two structurally dierent methods of associating transition system semantics to event-oriented models are distinguished in the literature.One of them is based on congurations (event sets), the other on residuals (model fragments).In this paper, we deal with a highly expressive model of event structures event structures for resolvable conict (RC-structures) and provide isomorphism results on these two types of transition systems constructed from RC-structures, in step and partial order semantics.

Modelling concurrent interactions

Pre-synthesis of Petri nets based on prime cycles and distance paths

This paper is a tutorial introduction to a general methodology, consisting of categorical constructions, for the definition of new algebraic semantics for transition-based formalisms. The methodology individuates three levels of semantic description: programs, structured transition systems, and models. The various formalisms differ for the structure on states and transitions, with respect to which all the categorical constructions of the methodology are parametric. These constructions generate in an automatic way the induced transition system and the free model of a program. One characterizing issue of the methodology is that structured transition systems have a (usually algebraic) structure on both the states and the transitions, while for example in Plotkin's SOS approach just the structure of states is relevant. The advantage of considering transition systems with an algebraic structure on transitions, too, resides in the fact that often the same structure can be automatically extended to the computations of the system. This yields to categories whose arrows are not simple sequences of elementary transitions, but are instead abstract computations, equipped with a rich algebraic structure. The methodology generalizes the algebraic treatment of Petri nets proposed in [MM88], and includes the main ideas of the algebraic semantics for Horn Clause Logic presented in [Co90, CM90], and of the algebraic treatment of Milner's CCS, reported in [Fe90, FM90].

We study the following problems for strong and weak bisimulation equivalence: given a labelled Petri net and a finite transition system, are they equivalent?; given a labelled Petri net, is it equivalent to some (unspecified) finite transition system? We show that both problems are decidable for strong bisimulation and undecidable for weak bisimulation.

A Fully Abstract Presheaf Semantics of SCCS with Finite Delay

The synthesis problem of concurrent systems is the problem of synthesizing a concurrent system model from sequential observations. The paper studies the synthesis problem for elementary Petri nets and transition systems. A characterization of the class of transition systems which correspond to elementary Petri nets is proven. It is shown how to generate all elementary Petri nets corresponding to a given transition system. If there is any such elementary Petri net, it is proven that there always exists a small one which has only polynomially many elements in the size of the transition system.

Elementary net systems with localities (enl-systems) is a class of Petri nets introduced to model globally asynchronous locally synchronous systems (gals), where some of the components can be considered as logically or physically close and acting synchronously, while others can be considered as loosely connected or residing at distant locations and communicating asynchronously with the rest of the system. The specification of the behaviour of a gals system comes very often in the form of a transition system. Automated synthesis based on the regions of transition systems is an approach that allows to construct Petri net models from their transition system specifications. In this paper we focus on developing algorithms and tool support for the synthesis of the enl-systems from transition systems, where transitions are labelled by steps (sets) of executed actions. We pay special attention to the subclass of enl-systems with localised conflicts where there is no conflict between events belonging to different localities. The algorithms are implemented within the workcraft framework.

Event Structures for Local Traces

Petri nets play a central role in the analysis of discrete, parallel and distributed systems. Reachability problem is one of the analysis of Petri nets. This paper address the analysis of reachable marking of petri nets using invariants. We translate Petri nets as transition systems. Then, through computing vanishing ideal of sample points, we present a new approach for constructing polynomial equation invariants of Petri nets. Our approach avoids first-order quantifier elimination and cylindrical algebraic decomposition. From the preliminary experiment results, we demonstrate the feasibility of our approach.