2,986 research outputs found
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
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
Read Operators and their Expressiveness in Process Algebras
We study two different ways to enhance PAFAS, a process algebra for modelling
asynchronous timed concurrent systems, with non-blocking reading actions. We
first add reading in the form of a read-action prefix operator. This operator
is very flexible, but its somewhat complex semantics requires two types of
transition relations. We also present a read-set prefix operator with a simpler
semantics, but with syntactic restrictions. We discuss the expressiveness of
read prefixes; in particular, we compare them to read-arcs in Petri nets and
justify the simple semantics of the second variant by showing that its
processes can be translated into processes of the first with timed-bisimilar
behaviour. It is still an open problem whether the first algebra is more
expressive than the second; we give a number of laws that are interesting in
their own right, and can help to find a backward translation.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407
Formal and efficient verification techniques for Real-Time UML models
The real-time UML profile TURTLE has a formal semantics expressed by translation into a timed process algebra: RT-LOTOS. RTL, the formal verification tool developed for RT-LOTOS, was first used to check TURTLE models against design errors. This paper opens new avenues for TURTLE
model verification. It shows how recent work on translating RT-LOTOS specifications into Time Petri net model may be applied to TURTLE. RT-LOTOS to TPN translation patterns are presented. Their formal proof is the subject of another paper. These patterns have been implemented in a RT-LOTOS to TPN translator which has been interfaced with TINA, a Time Petri Net Analyzer which implements several reachability analysis procedures depending on the class of property to be verified. The paper illustrates the benefits of the TURTLE->RT-LOTOS->TPN transformation chain on an avionic case study
Algebraic Models for Contextual Nets
We extend the algebraic approach of Meseguer and Montanari from ordinary place/transition Petri nets to contextual nets, covering both the collective and the individual token philosophy uniformly along the two interpretations of net behaviors
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
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
Process versus Unfolding Semantics for Place/Transition Petri Nets
In the last few years, the semantics of Petri nets has been investigated in several different ways. Apart from the classical "token game," one can model the behaviour of Petri nets via non-sequential processes, via unfolding constructions, which provide formal relationships between nets and domains, and via algebraic models, which view Petri nets as essentially algebraic theories whose models are monoidal categories. In this paper we show that these three points of view can be reconciled. In our formal development a relevant role is played by DecOcc, a category of occurrence nets appropriately decorated to take into account the history of tokens. The structure of decorated occurrence nets at the same time provides natural unfoldings for Place/Transition (PT) nets and suggests a new notion of processes, the decorated processes, which induce on Petri nets the same semantics as that of unfolding. In addition, we prove that the decorated processes of a net can be axiomatized as the arrows of a symmetric monoidal category which, therefore, provides the aforesaid unification
Flux Analysis in Process Models via Causality
We present an approach for flux analysis in process algebra models of
biological systems. We perceive flux as the flow of resources in stochastic
simulations. We resort to an established correspondence between event
structures, a broadly recognised model of concurrency, and state transitions of
process models, seen as Petri nets. We show that we can this way extract the
causal resource dependencies in simulations between individual state
transitions as partial orders of events. We propose transformations on the
partial orders that provide means for further analysis, and introduce a
software tool, which implements these ideas. By means of an example of a
published model of the Rho GTP-binding proteins, we argue that this approach
can provide the substitute for flux analysis techniques on ordinary
differential equation models within the stochastic setting of process algebras
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