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M.Koutny and F.Pommereau. An Algebra of Nonsafe Petri Boxes
 AMAST’02, LNCS 2422
, 2002
"... Abstract. We define an algebraic framework based on nonsafe Petri nets, which allows one to express operations such as iteration, parallel composition, and transition synchronisation. This leads to an algebra of process expressions, whose constants and operators directly correspond to those used in ..."
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Abstract. We define an algebraic framework based on nonsafe Petri nets, which allows one to express operations such as iteration, parallel composition, and transition synchronisation. This leads to an algebra of process expressions, whose constants and operators directly correspond to those used in Petri nets, and so we are able to associate nets to process expressions compositionally. The semantics of composite nets is then used to guide the definition of a structured operational semantics of process expressions. The main result is that an expression and the corresponding net generate isomorphic transition systems. We finally discuss a partial order semantics of the two algebras developed in this paper.
An Algebraic Semantics for Hierarchical P/T Nets (Extended Abstract)
 Application and Theory of Petri Nets 1995, 16th. International Conference, Proceedings, volume 935 of Lecture Notes in Computer Science
, 1995
"... . The first part of this paper gives an algebraic semantics for Place/Transition nets in terms of an algebra which is based on the process algebra ACP. The algebraic semantics is such that a P/T net and its term representation have the same operational behavior. As opposed to other approaches in the ..."
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. The first part of this paper gives an algebraic semantics for Place/Transition nets in terms of an algebra which is based on the process algebra ACP. The algebraic semantics is such that a P/T net and its term representation have the same operational behavior. As opposed to other approaches in the literature, the actions in the algebra do not correspond to the firing of a transition, but to the consumption or production of tokens. Equality of P/T nets can be determined in a purely equational way. The second part of this paper extends the results to hierarchical P/T nets. It gives a compositional algebraic semantics for both their complete operational behavior and their highlevel, observable behavior. By means of a nontrivial example, the AlternatingBit Protocol, it is shown that the notions of abstraction and verification in the process algebra ACP can be used to verify in an equational way whether a hierarchical P/T net satisfies some algebraic specification of its observable beha...
Asynchronous Box Calculus
"... The starting point of this paper is an algebraic Petri net framework allowing one to express net compositions, such as iteration and parallel composition, as well as transition synchronisation and restriction. We enrich the original model by introducing new constructs supporting asynchronous interpr ..."
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The starting point of this paper is an algebraic Petri net framework allowing one to express net compositions, such as iteration and parallel composition, as well as transition synchronisation and restriction. We enrich the original model by introducing new constructs supporting asynchronous interprocess communication. Such a communication is made possible thanks to special `buer' places where dierent transitions (processes) may deposit and remove tokens. We also provide an abstraction mechanism, which hides buer places, eectively making them private to the processes communicating through them. We then provide a characterisation of the operational step sequence semantics of composite nets. These developments lead to an algebra of process expressions, whose constants and operators directly correspond to those used in the Petri net framework. Such a correspondence is used to associate nets to process expressions in a fully compositional way. Moreover, a structural characterisation of the Petri net semantics of composite nets guides the denition of a structured operational semantics of process expressions. That the resulting algebra of expressions is consistent with the net algebra is demonstrated by showing that an expression and the corresponding net generate isomorphic transition systems. This results in the (or ABC), which is a coherent dual model, based on Petri nets and process expressions, suitable for modelling and analysing distributed systems whose components can interact using both synchronous and asynchronous communication.
APC Semantics for Petri Nets
, 2007
"... The paper deals with an algebraic semantics for Petri nets, based on a process algebra APC (Algebra of Process Components) by the authors. APC is tailored especially for describing processes in Petri nets. This is done by assigning special variables (called Evariables here) to every place of given ..."
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The paper deals with an algebraic semantics for Petri nets, based on a process algebra APC (Algebra of Process Components) by the authors. APC is tailored especially for describing processes in Petri nets. This is done by assigning special variables (called Evariables here) to every place of given Petri net, expressing processes initiated in those places. Algebraic semantics is then given as a parallel composition of all the variables, whose corresponding places hold token(s) within the initial marking. Resulting algebraic specification preserves operational behavior of the original netbased specification. Povzetek: Članek opisuje algebro semantike za Petri mreže. 1