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21
Relations in Concurrency
"... The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the seman ..."
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Cited by 263 (33 self)
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The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the semantics of nondeterministic dataflow. Profunctors are shown to play a key role in relating models for concurrency and to support an interpretation as higherorder processes (where input and output may be processes). Two recent directions of research are described. One is concerned with a language and computational interpretation for profunctors. This addresses the duality between input and output in profunctors. The other is to investigate general spans of event structures (the spans can be viewed as special profunctors) to give causal semantics to higherorder processes. For this it is useful to generalise event structures to allow events which “persist.”
Stubborn Sets for Reduced State Space Generation
 Proceedings of the Tenth International Conference on Application and Theory of Petri Nets
, 1989
"... ABSTRACT The "stubborn set " theory and method for generating reduced state spaces is presented. The theory takes advantage of concurrency, or more generally, of the lack of interaction between transitions, captured by the notion of stubborn sets. The basic method preserves all terminal states and t ..."
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Cited by 155 (1 self)
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ABSTRACT The "stubborn set " theory and method for generating reduced state spaces is presented. The theory takes advantage of concurrency, or more generally, of the lack of interaction between transitions, captured by the notion of stubborn sets. The basic method preserves all terminal states and the existence of nontermination. A more advanced version suited to the analysis of properties of reactive systems is developed. It is shown how the method can be used to detect violations of invariant properties. The method preserves the liveness (in Petri net sense) of transitions, and livelocks which cannot be exited. A modification of the method is given which preserves the language generated by the system. The theory is developed in an abstract variable/transition framework and adapted to elementary
Generalized stochastic Petri nets: A definition at the net level and its implications
 IEEE Transactions on Software Engineering
, 1993
"... Abstmct The original proposals of several stochastic Petri net modeling techniques and of generalized stochastic Petri nets (GSPN) in particular were based mainly on the characteristics of their underlying stochastic processes. This led to the use of GSPN only as a shortened notation for the descri ..."
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Cited by 55 (9 self)
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Abstmct The original proposals of several stochastic Petri net modeling techniques and of generalized stochastic Petri nets (GSPN) in particular were based mainly on the characteristics of their underlying stochastic processes. This led to the use of GSPN only as a shortened notation for the description of stochastic models. Although already quite useful in practice, this approach did not fully exploit the benefits of a Petri net description; in particular, it did not use any of the results of classical net theory. The integration of qualitative net theory results, together with the probabilistic analysis approach, requires a deep structural foundation of the GSPN definition. In this paper, the class of Petri nets obtained by eliminating timing from GSPN models while preserving the qualitative behavior is identified. Structural results for those nets are also derived, thus obtaining the first structural analysis of Petri nets with priority and inhibitor arcs. A revision of the GSPN definition based on the structural properties of the models is then presented. The main advantage is that for a (wide) class of nets, the definition of firing probabilities of conflicting immediate transitions does not require the information on reachable markings (which was, instead, necessary with the original definition). Identification of the class of models for which the netlevel specification is possible is also based on the structural analysis results. The new procedure for the model specification is illustrated by means of an example, which shows the usefulness of the new approach. A net level specification of the model associated with efficient structural analysis techniques can have a substantial impact on model analysis as well. Index TermsConflicts and concurrency, Markovian models, performance modeling, probabilistic specification, stochastic Petri nets, structural Petri net analysis, timed and immediate transitions, transition priorities. I.
Complexity Results for 1safe Nets
, 1993
"... We study the complexity of several standard problems for 1safe Petri nets and some of its subclasses. We prove that reachability, liveness, and deadlock are all PSPACEcomplete for 1safe nets. We also prove that deadlock is NPcomplete for freechoice nets and for 1safe freechoice nets. Finally, ..."
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Cited by 44 (7 self)
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We study the complexity of several standard problems for 1safe Petri nets and some of its subclasses. We prove that reachability, liveness, and deadlock are all PSPACEcomplete for 1safe nets. We also prove that deadlock is NPcomplete for freechoice nets and for 1safe freechoice nets. Finally, we prove that for arbitrary Petri nets, deadlock is equivalent to reachability and liveness. This paper is to be presented at FST&TCS 13, Foundations of Software Technology & Theoretical Computer Science, to be held 1517 December 1993, in Bombay, India. A version of the paper with most proofs omitted is to appear in the proceedings. 1 Introduction Petri nets are one of the oldest and most studied formalisms for the investigation of concurrency [33]. Shortly after the birth of complexity theory, Jones, Landweber, and Lien studied in their classical paper [24] the complexity of several fundamental problems for Place/Transition nets (called in [24] just Petri nets). Some years later, Howell,...
Concurrent Transition Systems
 Theoretical Computer Science
, 1989
"... : Concurrent transition systems (CTS's), are ordinary nondeterministic transition systems that have been equipped with additional concurrency information, specified in terms of a binary residual operation on transitions. Each CTS C freely generates a complete CTS or computation category C , whose ..."
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Cited by 40 (5 self)
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: Concurrent transition systems (CTS's), are ordinary nondeterministic transition systems that have been equipped with additional concurrency information, specified in terms of a binary residual operation on transitions. Each CTS C freely generates a complete CTS or computation category C , whose arrows are equivalence classes of finite computation sequences, modulo a congruence induced by the concurrency information. The categorical composition on C induces a "prefix" partial order on its arrows, and the computations of C are conveniently defined to be the ideals of this partial order. The definition of computations as ideals has some pleasant properties, one of which is that the notion of a maximal ideal in certain circumstances can serve as a replacement for the more troublesome notion of a fair computation sequence. To illustrate the utility of CTS's, we use them to define and investigate a dataflowlike model of concurrent computation. The model consists of machines, which ...
A Logical Study of Distributed Transition Systems
, 1995
"... We extend labelled transition systems to distributed transition systems by labelling the transition relation with a finite set of actions, representing the fact that the actions occur as a concurrent step. We design an actionbased temporal logic in which one can explicitly talk about steps. The log ..."
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Cited by 29 (5 self)
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We extend labelled transition systems to distributed transition systems by labelling the transition relation with a finite set of actions, representing the fact that the actions occur as a concurrent step. We design an actionbased temporal logic in which one can explicitly talk about steps. The logic is studied to establish a variety of positive and negative results in terms of axiomatizability and decidability. Our positive results show that the step notion is amenable to logical treatment via standard techniques. They also help us to obtain a logical characterization of two well known models for distributed systems: labelled elementary net systems and labelled prime event structures. Our negative results show that demanding deterministic structures when dealing with a "noninterleaved " notion of transitions is, from a logical standpoint, very expressive. They also show that another well known model of distributed systems called asynchronous transition systems exhibits a surprising a...
Time processes of time Petri nets
 IN APPLICATIONS AND THEORY OF PETRI NETS
, 1996
"... The objective of this thesis is to give time Petri nets a partial order semantics, like the nonsequential processes of untimed net systems. A time process of a time Petri net is defined as a traditionally constructed causal process with a valid timing. This means that the events of the process are l ..."
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Cited by 16 (1 self)
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The objective of this thesis is to give time Petri nets a partial order semantics, like the nonsequential processes of untimed net systems. A time process of a time Petri net is defined as a traditionally constructed causal process with a valid timing. This means that the events of the process are labeled with occurrence times which must satisfy specific validness criteria. An efficient algorithm for checking validness of known timings is presented. Interleavings of the time processes are defined as linearizations of the causal partial order of events where also the time order of events is preserved. The relationship between firing schedules of a time Petri net and the interleavings of the time processes of the net is shown to be bijective. Also, a sufficient condition is given for when the invalidity of timings for a process can be inferred from its initial subprocess. An alternative characterization for the validness of timings results in an algorithm for constructing the set of all vali...
Concurrency in Communicating Object Petri Nets
, 1999
"... : Objects are studied as higherlevel net tokens having an individual dynamical behaviour. In the context of Petri net research it is quite natural to also model such tokens by Petri nets. To distinguish them from the system net, they are called object nets. Object nets behave like tokens, i.e., the ..."
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Cited by 13 (2 self)
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: Objects are studied as higherlevel net tokens having an individual dynamical behaviour. In the context of Petri net research it is quite natural to also model such tokens by Petri nets. To distinguish them from the system net, they are called object nets. Object nets behave like tokens, i.e., they are lying in places and are moved by transitions. In contrast to ordinary tokens, however, they may change their state (i.e. their marking) when lying in a place or when being moved by a transition. By this approach an interesting and challenging twolevel system modelling technique is introduced. Similar to the objectoriented approach, complex systems are modelled close to their real appearance in a natural way to promote clear and reliable concepts. Applications in fields like workflow, agentoriented approaches (mobile agents and/or intelligent agents as in AI research) or open system networks are feasible. This paper gives a precise definition of the basic model together with a suitab...
Concurrent Transition System Semantics of Process Networks
 In Fourteenth ACM Symposium on Principles of Programming Languages
, 1987
"... Using concurrent transition systems [Sta86], we establish connections between three models of concurrent process networks, Kahn functions, input /output automata, and labeled processes. For each model, we define three kinds of algebraic operations on processes: the product operation, abstractio ..."
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Cited by 9 (7 self)
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Using concurrent transition systems [Sta86], we establish connections between three models of concurrent process networks, Kahn functions, input /output automata, and labeled processes. For each model, we define three kinds of algebraic operations on processes: the product operation, abstraction operations, and connection operations. We obtain homomorphic mappings, from input/output automata to labeled processes, and from a subalgebra (called "input/output processes") of labeled processes to Kahn functions. The proof that the latter mapping preserves connection operations amounts to a new proof of the "Kahn Principle." Our approach yields: (1) extremely simple definitions of the process operations; (2) a simple and natural proof of the Kahn Principle that does not require the use of "strategies" or "scheduling arguments"; (3) a semantic characterization of a large class of labeled processes for which the Kahn Principle is valid, (4) a convenient operational semantics...
Reasoning about Reactive Systems
, 1998
"... The main concern of this thesis is the formal reasoning about reactive systems, that is, systems that repeatedly act and react in interaction with their environment without necessarily terminating. When describing such systems the focus is not on what is computed but rather on the interaction capabi ..."
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Cited by 8 (0 self)
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The main concern of this thesis is the formal reasoning about reactive systems, that is, systems that repeatedly act and react in interaction with their environment without necessarily terminating. When describing such systems the focus is not on what is computed but rather on the interaction capabilities over time. Moreover, reactive systems are usually highly concurrent, typically spatially distributed, and often nondeterministic. Such systems include telecommunication protocols, telephone switches, airtra#c controllers, circuits, and many more. The goal of formal reasoning is to achieve system with provably correct behaviour. The task of formal reasoning is to specify systems and properties of systems as mathematical objects and to supply methodologies and techniques supporting formal proofs of properties of systems. Numerous semantic formalisms such as synchronisation trees, event structures, transition systems, temporal logics, Petri nets, and process algebras, to mention a few, have been proposed for the specification of reactive systems. In particular, formalisms vary in the sort of reasoning methodologies they support and encourage. Some methods have little practical pertinence, others have more. Some methods are decidable, others are not. Hence, numerous methods for reasoning about systems have been proposed; ranging from manual methods for the analysis of the most simple isolated aspects of systems to automatic methods for the synthesis of complex systems from succinct logical specifications.