644 research outputs found
General parameterised refinement and recursion for the M-net calculus
AbstractThe algebra of M-nets, a high-level class of labelled Petri nets, was introduced in order to cope with the size problem of the low-level Petri box calculus, especially when applied as semantical domain for parallel programming languages. General, unrestricted and parameterised refinement and recursion operators, allowing to represent the (possibly recursive and concurrent) procedure call mechanism, are introduced into the M-net calculus
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An algebra of high level petri nets
PhD ThesisPetri nets were introduced by C.A. Petri as a theoretical model of concurrency in which the causal
relationship between actions, rather than just their temporal ordering, can be represented. As
a theoretical model of concurrency, Petri nets have been widely successful. Moreover, Petri nets
are popular with practitioners, providing practical tools for the designer and developer of real
concurrent and distributed systems.
However, it is from this second context that perhaps the most widely voiced criticism of Petri
nets comes. It is that Petri nets lack any algebraic structure or modularity, and this results in
large, unstructured models of real systems, which are consequently often intractable. Although
this is not a criticism of Petri nets per se, but rather of the uses to which Petri nets are put, the
criticism is well taken.
We attempt to answer this criticism in this work. To do this we return to the view of Petri nets
as a model of concurrency and consider how other models of concurrency counter this objection.
The foremost examples are then the synchronisation trees of Milner, and the traces of Hoare,
(against which such criticism is rarely, if ever, levelled). The difference between the models is
clear, and is to be found in the richness of the algebraic characterisations which have been made
for synchronisation trees in Milner's Calculus of Communicating Systems (CCS), and for traces
in Hoare's Communicating Sequential Processes (CSP).
With this in mind we define, in this thesis, a class of high level Petri nets, High Level Petri Boxes,
and provide for them a very general algebraic description language, the High Level Petri Box
Algebra, with novel ideas for synchronisation, and including both refinement and recursion among
its operators. We also begin on the (probably open-ended task of the) algebraic characterisation
of High Level Petri Boxes.
The major contribution of this thesis is a full behavioural characterisation of the High Level Petri
Boxes which form the semantic domain of the algebra. Other contributions are: a very general
method of describing communication protocols which extend the synchronisation algebras of
Winskel; a recursive operator that preserves finiteness of state (the best possible, given the
generality of the algebra); a refinement operator that is syntactic in nature, and for which the
recursive construct is a behavioural fix-point; and a notion of behavioural equivalence which is
a congruence with respect to a major part of the High Level Petri Box Algebra
A Decidable Characterization of a Graphical Pi-calculus with Iterators
This paper presents the Pi-graphs, a visual paradigm for the modelling and
verification of mobile systems. The language is a graphical variant of the
Pi-calculus with iterators to express non-terminating behaviors. The
operational semantics of Pi-graphs use ground notions of labelled transition
and bisimulation, which means standard verification techniques can be applied.
We show that bisimilarity is decidable for the proposed semantics, a result
obtained thanks to an original notion of causal clock as well as the automatic
garbage collection of unused names.Comment: In Proceedings INFINITY 2010, arXiv:1010.611
Synthesis and axiomatisation for structural equivalences in the Petri Box Calculus
PhD ThesisThe Petri Box Calculus (PBC) consists of an algebra of box expressions, and
a corresponding algebra of boxes (a class of labelled Petri nets). A compo-
sitional semantics provides a translation from box expressions to boxes. The
synthesis problem is to provide an algorithmic translation from boxes to box
expressions. The axiomatisation problem is to provide a sound and complete
axiomatisation for the fragment of the calculus under consideration, which
captures a particular notion of equivalence for boxes.
There are several alternative ways of defining an equivalence notion for
boxes, the strongest one being net isomorphism. In this thesis, the synthesis
and axiomatisation problems are investigated for net semantic isomorphism,
and a slightly weaker notion of equivalence, called duplication equivalence,
which can still be argued to capture a very close structural similarity of con-
current systems the boxes are supposed to represent.
In this thesis, a structured approach to developing a synthesis algorithm
is proposed, and it is shown how this may be used to provide a framework
for the production of a sound and complete axiomatisation. This method is
used for several different fragments of the Petri Box Calculus, and for gener-
ating axiomatisations for both isomorphism and duplication equivalence. In
addition, the algorithmic problems of checking equivalence of boxes and box
expressions, and generating proofs of equivalence are considered as extensions
to the synthesis algorithm
Connector algebras for C/E and P/T nets interactions
A quite fourishing research thread in the recent literature on component based system is concerned with the algebraic properties of different classes of connectors. In a recent paper, an algebra of stateless connectors was presented that consists of five kinds of basic connectors, namely symmetry, synchronization, mutual exclusion, hiding and inaction, plus their duals and it was shown how they can be freely composed in series and in parallel to model sophisticated "glues". In this paper we explore the expressiveness of stateful connectors obtained by adding one-place buffers or unbounded buffers to the stateless connectors. The main results are: i) we show how different classes of connectors exactly correspond to suitable classes of Petri nets equipped with compositional interfaces, called nets with boundaries; ii) we show that the difference between strong and weak semantics in stateful connectors is reflected in the semantics of nets with boundaries by moving from the classic step semantics (strong case) to a novel banking semantics (weak case), where a step can be executed by taking some "debit" tokens to be given back during the same step; iii) we show that the corresponding bisimilarities are congruences (w.r.t. composition of connectors in series and in parallel); iv) we show that suitable monoidality laws, like those arising when representing stateful connectors in the tile model, can nicely capture concurrency aspects; and v) as a side result, we provide a basic algebra, with a finite set of symbols, out of which we can compose all P/T nets, fulfilling a long standing quest
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems
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