Showing papers on "Petri net published in 1979"
02 Jul 1979
TL;DR: The general aim of the paper is to find a theory of concurrency combining the approaches of Petri and Scott, and to connect the abstract ideas of events and domains of information, by showing how causal nets induce certain kinds of domains where the information points are certain sets of events.
Abstract: The general aim of the paper is to find a theory of concurrency combining the approaches of Petri and Scott (and other workers) [Pet 1,2],ESeo ~,3],[Sto]. To connect the abstract ideas of events and domains of information, we show how causal nets induce certain kinds of domains where the information points are certain sets of events. This allows translations between the languages of net theory and domain theory. Following the idea that events of causal nets are occurrences we generalise causal nets to occurrence nets, by adding forwards conflict; just as infinite flow chartsunfold finite ones [Sco 2], so transition nets can be unfolded into occurrence nets. Next we extend the above connections between nets and domains to these new nets. Event structures, which are intermediate between nets and domains play an important part in all our work.
521 citations
TL;DR: If the firing of a Transition in a Petri net is considered non instantaneous, it becomes possible to replace a transition in a net B by another net 8’, which allows the description and the analysis of a control structure by stepwise refinements.
310 citations
Book•
01 Jan 1979
TL;DR: A number of Petri Net problems are shown to be recursively equivalent to the Reachability Problem for Vector Addition Systems, and the equality of Reachability Sets and the equivalence of two Petri Nets in terms of their language-generating capability are recursive undecidable.
Abstract: An understanding of the mathematical properties of Petri Nets is essential when one wishes to use Petri Nets as an abstract model for concurrent systems The decidability of various problems which arise in this context is an important aspect of this question The fact that these problems also arise in the context of other mathematical theories, such as commutative semigroups, closure under linear relations, Matrix Context-Free grammars, or Weak Counter Automata, provides further motivation The Reachability Problem for Vector Addition Systems - whose decidability is still an open question - is of central importance We show that a number of Petri Net problems are recursively equivalent to this problem These include the Liveness Problem (eg can a system reach a deadlocked state?), the persistence problem (can a given transition ever be disabled by the firing of another transition?), and the membership and emptiness problems for certain classes of languages generated by Petri Nets The power of the unrestricted Petri Net model is illustrated by various undecidable equivalence results In particular, we show that the equality of Reachability Sets and the equivalence of two Petri Nets in terms of their language-generating capability are recursive undecidable It is hoped that the constructions used to prove our results will shed some light on the source of the complexities of the unrestricted Petri Net model, and may eventually permit us to achieve an optimal balance between representational transparency and analytical power of the Petri Net model
258 citations
IBM1
TL;DR: Today's modeling tools, appropriate for conventional sequential systems, will be inadequate for the complex concurrent systems of the 80's, and petri nets may offer a solution.
Abstract: Today's modeling tools, appropriate for conventional sequential systems, will be inadequate for the complex concurrent systems of the 80's. Petri nets may offer a solution.
174 citations
02 Jul 1979
TL;DR: Within the framework of net-semantics of models of dynamic systems, a new standard interpretation of nets are introduced called predicate/transition-nets (Pr/T-nets), which are schemes of ‘ordinary’ Petri nets.
Abstract: Within the framework of net-semantics of models of dynamic systems, the present paper introduces a new standard interpretation of nets called predicate/transition-nets (Pr/T-nets). These nets are schemes of ‘ordinary’ Petri nets. The places (circles) of Pr/T-nets represent changing properties of, or relations between, individuals; they are ‘predicates’ with variable extension. A current case of a system modelled by a Pr/T-net is denoted by marking the places with those tuples of individual symbols for which the respective predicates hold in that case. The transitions (boxes) are schemes of elementary changes of markings constituting the processes carried by the system. Instances of these schemes are generated by means of consistent substitution of individual variables by symbols.
151 citations
08 Oct 1979
TL;DR: The results give properties of marking graphs, provide insight into the computational complexity of several decision procedures, show the initimate relation of reachability sets to Presburger formulas, and deal with state-machine composition and the deadlock-trap property.
Abstract: Definitions and theorems fundamental for the study of general Petri nets or place/transition nets are presented. The results give properties of marking graphs, provide insight into the computational complexity of several decision procedures, show the initimate relation of reachability sets to Presburger formulas, and deal with state-machine composition and the deadlock-trap property.
98 citations
TL;DR: The above resuit shows that Pétri nets without X-labeled transitions are less powerful thon gênerai nets as regards their firing séquences since the class S£\ is identical with Aî^D'?
Abstract: — We prove Jtn {D[*) £ M (£>!*), where I>î* is the one-sided Dyck language, and discuss some old and new resuits concerning Pétri net languages. The above resuit shows that Pétri nets without X-labeled transitions are less powerful thon gênerai nets as regards their firing séquences since the class S£\ of gênerai Pétri net languages {Hack [13]) is identical with Aî^D'?), and the class ^Sf^ of computation séquence sets (Peterson [21]) equals ^ n ( D j * ) .
70 citations
Journal Article•
55 citations
TL;DR: A random Petri net model is presented and analyzed that has application to systems involving concurrency and is suitable for solving the problem of distributed systems.
Abstract: A random Petri net model is presented and analyzed. The model has application to systems involving concurrency.
22 citations
08 Oct 1979
TL;DR: Petri nets are used to illustrate statements and dependencies in a lucid and precise way as mentioned in this paper, and examples are given to indicate how this graphical representation can be used to convey information.
Abstract: Petri nets are used to illustrate statements and dependencies in a lucid and precise way. Examples are given to indicate how this graphical representation can be used.
21 citations
08 Oct 1979
TL;DR: In this paper, the authors propose a Petri Nets language for expressing the complexities of actual computing systems, and deal with performance questions typically asked about them, by using a higher level modeling language.
Abstract: Place/Transition nets, or Petri Nets, have an appealing mix of simplicity and power for expressing essential interactions in concurrent systems. Yet, when one wishes to express the complexities of actual computing systems, and deal with performance questions typically asked about them, one needs further capabilities that are attuned to the application — a higher level modeling language.
IBM1
TL;DR: By the inclusion of markings and the corresponding standard definitions, the full modelling power of Extended Control Structure Nets is introduced in respect to the dynamical behaviour of parallel programs.
Abstract: A new subclass of Petri Nets is presented called the "Extended Control Structure Nets". The control structure of arbitrarily structured parallel programs can be represented by nets of this class, even if they include operations on general semaphores. First of all, the purely statical structure of the Extended Control Structure Nets is dealt with, i.e. the graph of these nets. It is defined, in which way these nets are recursively generated by a composition of connected state machines which in turn represent the control structure of sequential parts of a parallel program or event variables resp. semaphores. Various properties of these graphs of Extended Control Structure Nets are stated. In addition, some special paths in these graphs are defined which are meaningful in respect to the underlying interpretation and thus are important for the later structural analysis. By the inclusion of markings and the corresponding standard definitions, the full modelling power of Extended Control Structure Nets is introduced in respect to the dynamical behaviour of parallel programs. The notion of liveness is given in terms of reachable markings. Finally, necessary and sufficient conditions are given for the liveness of Extended Control Structure Nets. This result offers the conceptual framework for the following proposal: o Represent the control structure of parallel programs by Extended Control Structure Nets. o Check (at compile-time) if all the seven liveness conditions are satisfied for a parallel program. o If they are satisfied the analyzed program will be deadlock-free.
02 Jul 1979
TL;DR: In the paper algebraic properties of symmetric and irreflexive relations (called sir-relations) are discussed and are of importance in the Petri nets theory.
Abstract: In the paper algebraic properties of symmetric and irreflexive relations (called sir-relations) are discussed. Such relations are of importance in the Petri nets theory (Best[1], Petri[11,12], Mazurkiewicz[7]).
TL;DR: Three graphical method families are investigated and compared in terms of their representability in production control problems and put PERT networks and their extensions in GANs before the same comparison basis as Petri nets and the new GRAI nets suggested by the authors.
Abstract: Three graphical method families are investigated and compared in terms of their representability in production control problems. The confrontation put PERT networks and their extensions in GANs before the same comparison basis as Petri nets and the new GRAI nets suggested by one of the authors.
02 Jul 1979
TL;DR: The semantic model is an extension of Petri nets with a data part and with expressions attached to transitions and to places, and the language is based on Delta.
Abstract: This paper introduces a language for the description of systems with concurrency, and presents a formal definition of its semantics. The language is based on Delta and the semantic model is an extension of Petri nets with a data part and with expressions attached to transitions and to places.
06 Nov 1979
TL;DR: Predicate/transition-nets, a first-order extension of Petri nets, are shown to provide suitable means for concise representation of complex decentralized systems and for their rigorous formal analysis.
Abstract: In this paper a net model for decentralized control of user accesses to a distributed database is proposed and devel oped in detail for a restricted case. Predicate/transition-nets, a first-order extension of Petri nets, are shown to provide suitable means for concise representa tion of complex decentralized systems and for their rigorous formal analysis. It will be demonstrated in the present paper how these net models can be constructed and in terpreted in a quite natural manner and how they can be analyzed by linear algebraic methods. by this, it will be shown that the modelled distributed database system is deadlockfree and guarantees a consistent database as well as a fair and effective service to the users.
02 Jul 1979
TL;DR: After having recalled some basic definitions and properties of the Petri nets, some algebraic results are synthesized based upon a theorem of compatibility of linear inequalities systems (near of the Farkas lemma).
Abstract: After having recalled some basic definitions and properties of the Petri nets, we synthesize some algebraic results, based upon a theorem of compatibility of linear inequalities systems (near of the Farkas lemma).
Journal Article•
TL;DR: A single formal tool that allows one to treat different aspects of the real time control algorithm decomposition, data flow, concurrency, error propagation, execution time, interprocess communication and performance problems is developed: Time Valued Petri Nets.
08 Oct 1979
TL;DR: The Component-Net is a special form corresponding to the state-machine-concept of the Automata-Theory, for the simulation of hardware systems, for instance for the problems of Switching Algebra.
Abstract: In lecture I the different aspects of Theoreticians and Engineers are discussed. The Component-Net is a special form corresponding to the state-machine-concept of the Automata-Theory. Some special symbols are suggested. Side-conditions and side effects are well appropriate for the simulation of hardware systems, for instance for the problems of Switching Algebra.
Book•
01 Jun 1979
TL;DR: The temporal semantics of concurrent programs, including the absence of livelocks in parallel programs, and an approach to fair applicative multiprogramming are studied.
Abstract: The temporal semantics of concurrent programs.- Modal logic of concurrent nondeterministic programs.- Non-deterministic system specification.- On properties preserved by contractions of concurrent systems.- Static analysis of concurrent processes for dynamic properties using Petri Nets.- Notion de Dualite et de Symetrie dans les Reseaux de Petri.- A characterization of concurrency-like relations.- The analysis of distributed systems by means of predicate/transition-nets.- On describing the behavior and implementation of distributed systems.- On the absence of livelocks in parallel programs.- Denotational semantics of parallelism.- An approach to fair applicative multiprogramming.- Modeling a solution for a control problem in distributed systems by restrictions.- Adequate path expressions.- Petri nets, event structures and domains.- An extensional treatment of dataflow deadlock.- On achieving distributed termination.- Specifying and proving properties of guardians for distributed systems.- Principles for distributing programs.- A Petri net definition of a system description language.
08 Oct 1979
01 Mar 1979
TL;DR: A formal semantics for Delta is defined and analysed using Petri nets, and a number of proposals for changes in Delta are reported here, whereas anumber of extensions to the Petri net formalism may be found in [Jensen 78] (DAIMI TR-5).
Abstract: Delta is a language designed for general system description. It is partly built upon Simula, but is more than a programming language, since it contains several features, which cannot be implemented on a computer system. E.g. a continuous time concept, concurrency between an unbounded number of components and the possibility of using predicates to specify state changes. In this paper a formal semantics for Delta is defined and analysed using Petri nets. Petri nets were chosen because the ideas behind Petri nets and Delta coincide on several points. A number of proposals for changes in Delta, which resulted from this work, are also reported here, whereas a number of extensions to the Petri net formalism may be found in [Jensen 78] (DAIMI TR-5). Revised version. 137 pp DELTA Project Report No, 12
TL;DR: This letter describes a hardware implementation of generalized Petri nets, Bounded nets with arcs having positive integer weights and with labelled transitions are considered.
Abstract: Cette lettre presente une realisation materielle des reseaux de Petri generalises. On considere ici des reseaux bornes dont les arcs entre places et transitions et transitions et places sont ponderes par des entiers positifs, et dont lea transitions peuvent etre etiquetees. This letter describes a hardware implementation of generalized Petri nets. Bounded nets with arcs having positive integer weights and with labelled transitions are considered.
06 Nov 1979
TL;DR: The extended timed Petri net model is used to model clearly the synchronization involved in these systems and it is found that the computational complexity involved increases in the same order as they are listed above.
Abstract: Some analysis techniques for real time asynchronous concurrent sysLems are presented. In order to model clearly the synchronization involved in these systems, the extended timed Petri net model is used. The system to be studied is first modelled by a Petri net. Based on the Petri net model, the system is classified into either: (1) consistent system; or (2) inconsistent system. Most real-world systems fall into the first class which is further subclassified into; (i) decision-free system; (ii) safe persistent system; (iii) general system. Procedures for predicting and verifying the system performance of all three types are presented. It is found that the computational complexity involved increases in the same order as they are listed above.
03 Sep 1979
01 Aug 1979
TL;DR: A new computer performance evaluation structure called the time-extended Petri net is developed which retains logical synchronization and concurrency characteristics of systems and is used to determine the automatic data processing dollar's efficiency.
Abstract: : This thesis develops a new computer performance evaluation structure called the time-extended Petri net which retains logical synchronization and concurrency characteristics of systems. Cost effectiveness is one of the important considerations together with an evaluation of how it works. The overall objective is to obtain a model to determine the automatic data processing dollar's efficiency. (Author)