Compositional semantics for open Petri nets based on deterministic processes (original) (raw)
Open Petri nets: Non-deterministic processes and compositionality
2008
We introduce ranked open nets, a reactive extension of Petri nets which generalises a basic open net model introduced in a previous work by allowing for a refined notion of interface. The interface towards the external environment of a ranked open net is given by a subset of places designated as open and used for composition. Additionally, a bound on the number of connections which are allowed on an open place can be specified.
Acta Informatica, 1998
This paper describes a high-level Petri net model called M-nets (for modular multilabelled nets). A distinctive feature of this model is that it allows both: unfolding, as do most other high-level net models; and composition -in particular, synchronisation -in a process algebraic style, turning the set of M-nets into an algebraic domain. It turns out that the composition operations of this domain have various algebraic properties. Moreover, the model is such that composition operations are coherent with unfolding, in the sense that the unfolding of a composite high-level net is the composition of the unfoldings of its components.
“Truly concurrent” and nondeterministic semantics of discrete-time Petri nets
Programming and Computer Software, 2016
In the paper, a "truly concurrent" and nondeterministic semantics is defined in terms of branching processes of discrete-time Petri nets (DTPNs). These nets may involve infinite numbers of transitions and places, infinite number of tokens in places, and (maximal) steps of concurrent transitions, which allows us to consider this class of DTPNs to be the most powerful class of Petri nets. It is proved that the unfolding (maximal branching process) of the DTPN is the greatest element of a complete lattice constructed on branching processes of DTPNs with step semantics. Moreover, it is shown that this result is true also in the case of maximal transition steps if additional restrictions are imposed on the structure and behavior of the DTPN.
Semantics of petri nets: A comparison
2007 Winter Simulation Conference, 2007
In this paper, we investigate results on relationship between different semantics of place/transition Petri nets based on labelled partial orders. We also discuss relationships between so called commutative processes representing collective token philosophy and individual process semantics of place/transition nets.
Process Semantics of Petri Nets over Partial Algebra
Lecture Notes in Computer Science, 2000
Petri nets are monoids" is the title and the central idea of the paper . It provides an algebraic approach to define both nets and their processes as terms. A crucial assumption for this concept is that arbitrary concurrent composition of processes is defined, which holds true for place/transition Petri nets where places can hold arbitrarily many tokens. This paper defines a similar concept for elementary Petri nets, which are elementary net systems with arbitrary initial marking. Since markings of elementary nets cannot be added arbitrarily, some operators are only defined partially; hence we employ concepts of partial algebra. The main result of the paper states that the semantics based on process terms agrees with the classical partial-order process semantics for elementary net systems. More precisely, we provide a syntactic equivalence notion for process terms and a bijection from according equivalence classes of process terms to isomorphism classes of partially ordered processes.
A Comparison of Petri Net Semantics under the Collective Token Philosophy
Lecture Notes in Computer Science, 1998
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.
Application and Theory of Petri Nets and Concurrency
Lecture Notes in Computer Science, 2013
These are the proceedings of the International Workshop on Petri Nets and Software Engineering (PNSE'13) in Milano, Italy, June 24-25, 2013. It is a co-located event of Petri Nets 2013, the 34th international conference on Applications and Theory of Petri Nets and Concurrency. More information about the workshop can be found at http://www.informatik.uni-hamburg.de/TGI/events/pnse13/ For the successful realisation of complex systems of interacting and reactive software and hardware components the use of a precise language at different stages of the development process is of crucial importance. Petri nets are becoming increasingly popular in this area, as they provide a uniform language supporting the tasks of modelling, validation, and verification. Their popularity is due to the fact that Petri nets capture fundamental aspects of causality, concurrency and choice in a natural and mathematically precise way without compromising readability. The use of Petri Nets (P/T-Nets, Coloured Petri Nets and extensions) in the formal process of software engineering, covering modelling, validation, and verification, will be presented as well as their application and tools supporting the disciplines mentioned above.
Encoding asynchronous interactions using open Petri nets
2009
Abstract. We present an encoding for (bound) processes of the asynchronous CCS with replication into open Petri nets: ordinary Petri nets equipped with a distinguished set of open places. The standard token game of nets models the reduction semantics of the calculus; the exchange of tokens on open places models the interactions between processes and their environment.
Propositional dynamic logic for Petri Nets
Logic Journal of IGPL, 2014
Propositional Dynamic Logic (PDL) is a multi-modal logic used for specifying and reasoning on sequential programs. Petri Net is a widely used formalism to specify and to analyse concurrent programs with a very nice graphical representation. In this work, we propose a PDL to reasoning about Petri Nets. First we define a compositional encoding of Petri Nets from basic nets as terms. Second, we use these terms as PDL programs and provide a compositional semantics to PDL Formulas. Finally, we present an axiomatization and prove completeness w.r.t. our semantics. The advantage of our approach is that we can do reasoning about Petri Nets using our dynamic logic and we do not need to to translate it to other formalisms. Moreover our approach is compositional allowing for construction of complex nets using basic ones.