Graph models for reachability analysis of concurrent programs

Reachability analysis is an attractive technique for analysis of concurrent programs because it is simple and relatively straightforward to automate, and can be used in conjunction with model-checking procedures to check for application-specific as well as general properties. Several techniques have been proposed differing mainly on the model used; some of these propose the use of flowgraph based models, some others of Petri nets.This paper addresses the question: What essential difference does it make, if any, what sort of finite-state model we extract from program texts for purposes of reachability analysis? How do they differ in expressive power, decision power, or accuracy? Since each is intended to model synchronization structure while abstracting away other features, one would expect them to be roughly equivalent.We confirm that there is no essential semantic difference between the most well known models proposed in the literature by providing algorithms for translation among these models. This implies that the choice of model rests on other factors, including convenience and efficiency.Since combinatorial explosion is the primary impediment to application of reachability analysis, a particular concern in choosing a model is facilitating divide-and-conquer analysis of large programs. Recently, much interest in finite-state verification systems has centered on algebraic theories of concurrency. Yeh and Young have exploited algebraic structure to decompose reachability analysis based on a flowgraph model. The semantic equivalence of graph and Petri net based models suggests that one ought to be able to apply a similar strategy for decomposing Petri nets. We show this is indeed possible through application of category theory

Petri Nets and Other Models of Concurrency

This paper retraces, collects, and summarises contributions of the authors --- in collaboration with others --- on the theme of Petri nets and their categorical relationships to other models of concurrency

Between quantum logic and concurrency

We start from two closure operators defined on the elements of a special kind of partially ordered sets, called causal nets. Causal nets are used to model histories of concurrent processes, recording occurrences of local states and of events. If every maximal chain (line) of such a partially ordered set meets every maximal antichain (cut), then the two closure operators coincide, and generate a complete orthomodular lattice. In this paper we recall that, for any closed set in this lattice, every line meets either it or its orthocomplement in the lattice, and show that to any line, a two-valued state on the lattice can be associated. Starting from this result, we delineate a logical language whose formulas are interpreted over closed sets of a causal net, where every line induces an assignment of truth values to formulas. The resulting logic is non-classical; we show that maximal antichains in a causal net are associated to Boolean (hence "classical") substructures of the overall quantum logic.Comment: In Proceedings QPL 2012, arXiv:1407.842

The Geometry of Concurrent Interaction: Handling Multiple Ports by Way of Multiple Tokens (Long Version)

We introduce a geometry of interaction model for Mazza's multiport interaction combinators, a graph-theoretic formalism which is able to faithfully capture concurrent computation as embodied by process algebras like the $\pi$-calculus. The introduced model is based on token machines in which not one but multiple tokens are allowed to traverse the underlying net at the same time. We prove soundness and adequacy of the introduced model. The former is proved as a simulation result between the token machines one obtains along any reduction sequence. The latter is obtained by a fine analysis of convergence, both in nets and in token machines

Application of an Exact Transversal Hypergraph in Selection of SM-Components

Part 9: Embedded Systems and Petri NetsInternational audienceThe paper deals with the application of the hypergraph theory in selection of State Machine Components (SM-Components) of Petri nets [1,2].As it is known, Petri nets are widely used for modeling of concurrency processes. However, in order to implement the concurrent automaton, an initial Petri net ought to be decomposed into sequential automata (SM-Components), which can be easily designed as an Finite-State-Machine (FSM) or Microprogrammed Controller [3]. The last step of the decomposition process of the Petri nets is selection of SM-Components. This stage is especially important because it determines the final number of sequential automata. In the article we propose a new idea of SM-Components selection. The aim of the method is reduction of the computational complexity from exponential to polynomial. Such a reduction can be done if the selection hypergraph belongs to the exact transversal hypergraphs (xt-hypergraphs) class. Since the recognition and generation of the first transversal in the xt-hypergraphs are both polynomial, the complete selection process can be performed in polynomial time. The proposed ideas are an extension of the concept presented in [1].The proposed method has been verified experimentally. The conducted investigations have shown that for more than 85% of examined Petri nets the selection process can be done via xt-hypergraphs

A review of information flow diagrammatic models for product-service systems

A product-service system (PSS) is a combination of products and services to create value for both customers and manufacturers. Modelling a PSS based on function orientation offers a useful way to distinguish system inputs and outputs with regards to how data are consumed and information is used, i.e. information flow. This article presents a review of diagrammatic information flow tools, which are designed to describe a system through its functions. The origin, concept and applications of these tools are investigated, followed by an analysis of information flow modelling with regards to key PSS properties. A case study of selection laser melting technology implemented as PSS will then be used to show the application of information flow modelling for PSS design. A discussion based on the usefulness of the tools in modelling the key elements of PSS and possible future research directions are also presented

An Operational Petri Net Semantics for the Join-Calculus

We present a concurrent operational Petri net semantics for the join-calculus, a process calculus for specifying concurrent and distributed systems. There often is a gap between system specifications and the actual implementations caused by synchrony assumptions on the specification side and asynchronously interacting components in implementations. The join-calculus is promising to reduce this gap by providing an abstract specification language which is asynchronously distributable. Classical process semantics establish an implicit order of actually independent actions, by means of an interleaving. So does the semantics of the join-calculus. To capture such independent actions, step-based semantics, e.g., as defined on Petri nets, are employed. Our Petri net semantics for the join-calculus induces step-behavior in a natural way. We prove our semantics behaviorally equivalent to the original join-calculus semantics by means of a bisimulation. We discuss how join specific assumptions influence an existing notion of distributability based on Petri nets.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244