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An Event Structure Semantics for General Petri Nets
 Theoretical Computer Science
, 1993
"... In this paper we address the following question: What type of event structures are suitable for representing the behaviour of general Petri nets? As a partial answer to this question we define a new class of event structures called local event structures and identify a subclass called ULevent stru ..."
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In this paper we address the following question: What type of event structures are suitable for representing the behaviour of general Petri nets? As a partial answer to this question we define a new class of event structures called local event structures and identify a subclass called ULevent structures. We propose that ULevent structures are appropriate for capturing the behaviour of general Petri nets. Our answer is a partial one in that in the proposed event structure semantics, autoconcurrency is filtered out from the behaviour of Petri nets. It turns out that this limited event structure semantics for Petri nets is nevertheless a nontrivial and conservative extension of the (prime) event structure semantics of 1safe Petri nets provided in [NPW]. We also show that the strong relationship between prime event structures and 1safe Petri nets established in a categorical framework in [W3] can be extended to the present setting, provided we restrict our attention to the subclass ...
On the Structure of Highlevel Nets
 Helsinki University of Technology
, 1995
"... : The structure of Highlevel nets is studied from an algebraic and a logical point of view using Algebraic nets as an example. First the category of Algebraic nets is defined and the semantics given through an unfolding construction. Other kinds of Highlevel net formalisms are then presented. It is ..."
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: The structure of Highlevel nets is studied from an algebraic and a logical point of view using Algebraic nets as an example. First the category of Algebraic nets is defined and the semantics given through an unfolding construction. Other kinds of Highlevel net formalisms are then presented. It is shown that nets given in these formalisms can be transformed into equivalent Algebraic nets. Then the semantics of nets in terms of universal constructions is discussed. A definition of Algebraic nets in terms of structured transition systems is proposed. The semantics of the Algebraic net is then given as a free completion of this structured transition system to a category. As an alternative also a sheaf semantics of nets is examined. Here the semantics of the net arises as a limit of a diagram of sheaves. Next Algebraic nets are characterized as encodings of special morphisms called foldings. Each algebraic net gives rise to a surjective morphism between Petri nets and conversely each sur...
Aggregation of transitions in marking graph generation based on maximality semantics for Petri nets (extended version
, 2008
"... In this paper, we propose an operational semantics to build maximalitybased labeled transition systems (MLTS) from Place/Transition Petri nets while performing aggregation of equivalent derivations of transitions according to maximality bisimulation relation. We show that generated MLTS are equival ..."
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Cited by 5 (4 self)
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In this paper, we propose an operational semantics to build maximalitybased labeled transition systems (MLTS) from Place/Transition Petri nets while performing aggregation of equivalent derivations of transitions according to maximality bisimulation relation. We show that generated MLTS are equivalent to MLTS generated without aggregation. As illustration, we apply results on a ticket reservation system.
ZeroSafe Nets: Composing Nets via Transition Synchronization
 Proceedings Int. Colloquium on Petri Net Technologies for Modelling Communication Based Systems
, 1999
"... Zerosafe nets have been introduced to extend classical Petri nets with a primitive notion of transition synchronization. To this aim, besides ordinary places, called stable, zerosafe nets are equipped with zero places, which cannot contain any token in a stable marking . An evolution between two s ..."
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Cited by 4 (3 self)
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Zerosafe nets have been introduced to extend classical Petri nets with a primitive notion of transition synchronization. To this aim, besides ordinary places, called stable, zerosafe nets are equipped with zero places, which cannot contain any token in a stable marking . An evolution between two stable markings is called transaction and can be a complex computation that involves zero places, with the restriction that no stable token generated in a transaction can be reused in the same transaction. The abstract counterpart of a generic zerosafe net B consists of an ordinary pt net whose places are the stable places of B, and whose transitions are the transactions of B. The two nets offer the refined and the abstract model of the same system, where the former can be much smaller than the latter, because of the transition synchronization mechanism. Depending on the chosen approach  collective vs individual token philosophy  two notions of transaction may be defined, each leading ...
Petri Nets, Discrete Physics, and Distributed Quantum Computation
"... This paper is dedicated to Ugo Montanari on the occasion of his 65th birthday. Abstract. We shall describe connections between Petri nets, quantum physics and category theory. The view of Net theory as a kind of discrete physics has been consistently emphasized by CarlAdam Petri. The connections be ..."
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This paper is dedicated to Ugo Montanari on the occasion of his 65th birthday. Abstract. We shall describe connections between Petri nets, quantum physics and category theory. The view of Net theory as a kind of discrete physics has been consistently emphasized by CarlAdam Petri. The connections between Petri nets and monoidal categories were illuminated in pioneering work by Ugo Montanari and José Meseguer. Recent work by the author and Bob Coecke has shown how monoidal categories with certain additional structure (dagger compactness) can be used as the setting for an effective axiomatization of quantum mechanics, with striking applications to quantum information. This additional structure matches the extension of the MontanariMeseguer approach by MartiOliet and Meseguer, motivated by linear logic. 1
Algebraic Structures of Directed Acyclic Graphs: Application to Concurrent Calculus
 Depart. of Computer Science, University of Ia��si
, 1998
"... The paper defines an algebraic tool for manipulating directed acyclic graphs (on short dags). The approach we propose combines two mathematical tools  category theory and universal algebra  and it allows an unitary treating of dags transformations. We show that the specification, implementation ..."
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The paper defines an algebraic tool for manipulating directed acyclic graphs (on short dags). The approach we propose combines two mathematical tools  category theory and universal algebra  and it allows an unitary treating of dags transformations. We show that the specification, implementation and programming of concurrent systems can be achieved by using this theory. 1 Introduction Graph transformation have been studied and applied in many fields of computer science: formal languages theory, software engineering, concurrent and distributed systems, etc. The intrinsic complexity of graphs does not allowed to find up to now an uniform formalism for studying graph transformation which to be universal accepted. In the present great efforts are doing to unify the theory of graph grammars and rewriting in order to demonstrate the potential of graph transformation to serve as a unifying paradigm for specification, implementation and programming sequential, parallel and distributed syst...
IOS Press Causal Semantics of Algebraic Petri Nets distinguishing Concurrency
"... Abstract. In this paper, we show how to obtain causal semantics distinguishing ”earlier than ” and ”not later than ” causality between events from algebraic semantics of Petri nets. Janicki and Koutny introduced so called stratified order structures (sostructures) to describe such causal semantics. ..."
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Abstract. In this paper, we show how to obtain causal semantics distinguishing ”earlier than ” and ”not later than ” causality between events from algebraic semantics of Petri nets. Janicki and Koutny introduced so called stratified order structures (sostructures) to describe such causal semantics. To obtain algebraic semantics, we redefine our own algebraic approach generating rewrite terms via partial operations of synchronous composition, concurrent composition and sequential composition. These terms are used to produce sostructures which define causal behavior consistent with the (operational) step semantics. For concrete Petri net classes with causal semantics derived from processes minimal sostructures obtained from rewrite terms coincide with minimal sostructures given by processes. This is demonstrated for elementary nets with inhibitor arcs.
IOS Press Causal Semantics of Algebraic Petri Nets distinguishing Concurrency
, 2016
"... Abstract. In this paper, we show how to obtain causal semantics distinguishing ”earlier than ” and ”not later than ” causality between events from algebraic semantics of Petri nets. Janicki and Koutny introduced so called stratified order structures (sostructures) to describe such causal semantics. ..."
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Abstract. In this paper, we show how to obtain causal semantics distinguishing ”earlier than ” and ”not later than ” causality between events from algebraic semantics of Petri nets. Janicki and Koutny introduced so called stratified order structures (sostructures) to describe such causal semantics. To obtain algebraic semantics, we redefine our own algebraic approach generating rewrite terms via partial operations of synchronous composition, concurrent composition and sequential composition. These terms are used to produce sostructures which define causal behavior consistent with the (operational) step semantics. For concrete Petri net classes with causal semantics derived from processes minimal sostructures obtained from rewrite terms coincide with minimal sostructures given by processes. This is demonstrated for elementary nets with inhibitor arcs.
IOS Press Characterising Concurrent Histories
"... © the authors, 2015. DOI link to article: ..."
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