Functorial Semantics for Petri Nets under the Individual Token Philosophy

Although the algebraic semantics of place/transition Petri nets under the collective token philosophy has been fully explained in terms of (strictly) symmetric (strict) monoidal categories, the analogous construction under the individual token philosophy is not completely satisfactory because it lacks universality and also functoriality. We introduce the notion of pre-net to recover these aspects, obtaining a fully satisfactory categorical treatment centered on the notion of adjunction. This allows us to present a purely logical description of net behaviours under the individual token philosophy in terms of theories and theory morphisms in partial membership equational logic, yielding a complete match with the theory developed by the authors for the collective token view of net

A Comparison of Petri Net Semantics under the Collective Token Philosophy

In recent years, several semantics for place/transition Petri nets have been proposed that adopt the collective token philosophy. We investigate distinctions and similarities between three such models, namely configuration structures, concurrent transition systems, and (strictly) symmetric (strict) monoidal categories. We use the notion of adjunction to express each connection. We also present a purely logical description of the collective token interpretation of net behaviours in terms of theories and theory morphisms in partial membership equational logic

On Modelling and Analysis of Dynamic Reconfiguration of Dependable Real-Time Systems

This paper motivates the need for a formalism for the modelling and analysis of dynamic reconfiguration of dependable real-time systems. We present requirements that the formalism must meet, and use these to evaluate well established formalisms and two process algebras that we have been developing, namely, Webpi and CCSdp. A simple case study is developed to illustrate the modelling power of these two formalisms. The paper shows how Webpi and CCSdp represent a significant step forward in modelling adaptive and dependable real-time systems.Comment: Presented and published at DEPEND 201

TAPAs: A Tool for the Analysis of Process Algebras

Process algebras are formalisms for modelling concurrent systems that permit mathematical reasoning with respect to a set of desired properties. TAPAs is a tool that can be used to support the use of process algebras to specify and analyze concurrent systems. It does not aim at guaranteeing high performances, but has been developed as a support to teaching. Systems are described as process algebras terms that are then mapped to labelled transition systems (LTSs). Properties are verified either by checking equivalence of concrete and abstract systems descriptions, or by model checking temporal formulae over the obtained LTS. A key feature of TAPAs, that makes it particularly suitable for teaching, is that it maintains a consistent double representation of each system both as a term and as a graph. Another useful didactical feature is the exhibition of counterexamples in case equivalences are not verified or the proposed formulae are not satisfied

Life of occam-Pi

This paper considers some questions prompted by a brief review of the history of computing. Why is programming so hard? Why is concurrency considered an “advanced” subject? What’s the matter with Objects? Where did all the Maths go? In searching for answers, the paper looks at some concerns over fundamental ideas within object orientation (as represented by modern programming languages), before focussing on the concurrency model of communicating processes and its particular expression in the occam family of languages. In that focus, it looks at the history of occam, its underlying philosophy (Ockham’s Razor), its semantic foundation on Hoare’s CSP, its principles of process oriented design and its development over almost three decades into occam-? (which blends in the concurrency dynamics of Milner’s ?-calculus). Also presented will be an urgent need for rationalisation – occam-? is an experiment that has demonstrated significant results, but now needs time to be spent on careful review and implementing the conclusions of that review. Finally, the future is considered. In particular, is there a future

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

Elastic bundles :modelling and architecting asynchronous circuits with granular rigidity

PhD ThesisIntegrated Circuit (IC) designs these days are predominantly System-on-Chips (SoCs). The complexity of designing a SoC has increased rapidly over the years due to growing process and environmental variations coupled with global clock distribution di culty. Moreover, traditional synchronous design is not apt to handle the heterogeneous timing nature of modern SoCs. As a countermeasure, the semiconductor industry witnessed a strong revival of asynchronous design principles. A new paradigm of digital circuits emerged, as a result, namely mixed synchronous-asynchronous circuits. With a wave of recent innovations in synchronous-asynchronous CAD integration, this paradigm is showing signs of commercial adoption in future SoCs mainly due to the scope for reuse of synchronous functional blocks and IP cores, and the co-existence of synchronous and asynchronous design styles in a common EDA framework. However, there is a lack of formal methods and tools to facilitate mixed synchronousasynchronous design. In this thesis, we propose a formal model based on Petri nets with step semantics to describe these circuits behaviourally. Implication of this model in the veri cation and synthesis of mixed synchronous-asynchronous circuits is studied. Till date, this paradigm has been mainly explored on the basis of Globally Asynchronous Locally Synchronous (GALS) systems. Despite decades of research, GALS design has failed to gain traction commercially. To understand its drawbacks, a simulation framework characterising the physical and functional aspects of GALS SoCs is presented. A novel method for synthesising mixed synchronous-asynchronous circuits with varying levels of rigidity is proposed. Starting with a high-level data ow model of a system which is intrinsically asynchronous, the key idea is to introduce rigidity of chosen granularity levels in the model without changing functional behaviour. The system is then partitioned into functional blocks of synchronous and asynchronous elements before being transformed into an equivalent circuit which can be synthesised using standard EDA tools