1,694 research outputs found
A Forward Reachability Algorithm for Bounded Timed-Arc Petri Nets
Timed-arc Petri nets (TAPN) are a well-known time extension of the Petri net
model and several translations to networks of timed automata have been proposed
for this model. We present a direct, DBM-based algorithm for forward
reachability analysis of bounded TAPNs extended with transport arcs, inhibitor
arcs and age invariants. We also give a complete proof of its correctness,
including reduction techniques based on symmetries and extrapolation. Finally,
we augment the algorithm with a novel state-space reduction technique
introducing a monotonic ordering on markings and prove its soundness even in
the presence of monotonicity-breaking features like age invariants and
inhibitor arcs. We implement the algorithm within the model-checker TAPAAL and
the experimental results document an encouraging performance compared to
verification approaches that translate TAPN models to UPPAAL timed automata.Comment: In Proceedings SSV 2012, arXiv:1211.587
A Congruence for Petri Nets
We introduce a way of viewing Petri nets as open systems. This is done by considering a bicategory of cospans over a category of p/t nets and embeddings. We derive a labelled transition system (LTS) semantics for such nets using GIPOs and characterise the resulting congruence. Technically, our results are similar to the recent work by Milner on applying the theory of bigraphs to Petri Nets. The two main differences are that we treat p/t nets instead of c/e nets and we deal directly with a category of nets instead of encoding them into bigraphs
A coalgebraic semantics for causality in Petri nets
In this paper we revisit some pioneering efforts to equip Petri nets with
compact operational models for expressing causality. The models we propose have
a bisimilarity relation and a minimal representative for each equivalence
class, and they can be fully explained as coalgebras on a presheaf category on
an index category of partial orders. First, we provide a set-theoretic model in
the form of a a causal case graph, that is a labeled transition system where
states and transitions represent markings and firings of the net, respectively,
and are equipped with causal information. Most importantly, each state has a
poset representing causal dependencies among past events. Our first result
shows the correspondence with behavior structure semantics as proposed by
Trakhtenbrot and Rabinovich. Causal case graphs may be infinitely-branching and
have infinitely many states, but we show how they can be refined to get an
equivalent finitely-branching model. In it, states are equipped with
symmetries, which are essential for the existence of a minimal, often
finite-state, model. The next step is constructing a coalgebraic model. We
exploit the fact that events can be represented as names, and event generation
as name generation. Thus we can apply the Fiore-Turi framework: we model causal
relations as a suitable category of posets with action labels, and generation
of new events with causal dependencies as an endofunctor on this category. Then
we define a well-behaved category of coalgebras. Our coalgebraic model is still
infinite-state, but we exploit the equivalence between coalgebras over a class
of presheaves and History Dependent automata to derive a compact
representation, which is equivalent to our set-theoretical compact model.
Remarkably, state reduction is automatically performed along the equivalence.Comment: Accepted by Journal of Logical and Algebraic Methods in Programmin
Formal Relationships Between Geometrical and Classical Models for Concurrency
A wide variety of models for concurrent programs has been proposed during the
past decades, each one focusing on various aspects of computations: trace
equivalence, causality between events, conflicts and schedules due to resource
accesses, etc. More recently, models with a geometrical flavor have been
introduced, based on the notion of cubical set. These models are very rich and
expressive since they can represent commutation between any bunch of events,
thus generalizing the principle of true concurrency. While they seem to be very
promising - because they make possible the use of techniques from algebraic
topology in order to study concurrent computations - they have not yet been
precisely related to the previous models, and the purpose of this paper is to
fill this gap. In particular, we describe an adjunction between Petri nets and
cubical sets which extends the previously known adjunction between Petri nets
and asynchronous transition systems by Nielsen and Winskel
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 -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
Open Petri Nets
The reachability semantics for Petri nets can be studied using open Petri
nets. For us an "open" Petri net is one with certain places designated as
inputs and outputs via a cospan of sets. We can compose open Petri nets by
gluing the outputs of one to the inputs of another. Open Petri nets can be
treated as morphisms of a category , which
becomes symmetric monoidal under disjoint union. However, since the composite
of open Petri nets is defined only up to isomorphism, it is better to treat
them as morphisms of a symmetric monoidal double category
. We describe two forms of semantics
for open Petri nets using symmetric monoidal double functors out of
. The first, an operational semantics,
gives for each open Petri net a category whose morphisms are the processes that
this net can carry out. This is done in a compositional way, so that these
categories can be computed on smaller subnets and then glued together. The
second, a reachability semantics, simply says which markings of the outputs can
be reached from a given marking of the inputs.Comment: 30 pages, TikZ figure
Two Algebraic Process Semantics for Contextual Nets
We show that the so-called 'Petri nets are monoids' approach initiated by Meseguer and Montanari can be extended from ordinary place/transition Petri nets to contextual nets by considering suitable non-free monoids of places. The algebraic characterizations of net concurrent computations we provide cover both the collective and the individual token philosophy, uniformly along the two interpretations, and coincide with the classical proposals for place/transition Petri nets in the absence of read-arcs
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