Showing papers on "Petri net published in 1981"
TL;DR: To connect the abstract ideas of events and domains of information, it is shown how casual nets induce certain kinds of domains where the information points are certain sets of events, which allows translations between the languages of net theory and domain theory.
987 citations
TL;DR: A linear-algebraic techniques for verifying invariant assertions are used, yielding a calculus of S-invariants for PrT-nets, and these modelling and analysis techniques are applied to a scheme for organizing a distributed data base taken from literature.
682 citations
TL;DR: It is shown how Petri nets can be generalized to allow processes to be described by a common subnet, without losing the ability to distinguish between them.
639 citations
11 May 1981
TL;DR: An algorithm is presented for the general Petri net reachability problem based on a generalization of the basic reachability construction which is symmetric with respect to the initial and final marking.
Abstract: An algorithm is presented for the general Petri net reachability problem based on a generalization of the basic reachability construction which is symmetric with respect to the initial and final marking. Sets of transition sequences described by finite automata are used for approximations to firing sequences, and the approximation error is assessed by uniformly constructable Presburger expressions. The approximation algorithm is iterated until a sufficient criterion for reachability can be given, not-withstanding the remaining uncertainty.
226 citations
TL;DR: It is shown that the regularity problem for firing sequence sets of Petri nets is decidable and L0λ is shown to be not closed under complementation without reference to the reachability problem.
129 citations
TL;DR: The complexity of decision procedures for these two problems are investigated and it is shown by reducing a bounded version of Hilbert''s Tenth problem to the finite containment problem that these two problem are extremely hard, that the complexity of each decision procedure exceeds any primitive recursive function infinitely often.
Abstract: If the reachability set of a Petri net (or, equivalently, vector addition system) is finite it can be effectively constructed. Furthermore, the finiteness is decidable. Thus, the containment and equality problem for finite reachability sets become solvable. We investigate the complexity of decision procedures for these two problems and show by reducing a bounded version of Hilbert''s Tenth problem to the finite containment problem that these two problems are extremely hard, that, in fact, the complexity of each decision procedure exceeds any primitive recursive function infinitely often. The finite containment and quality problem are thus the first uncontrived, decidable problems with provably non-primitive recursive complexity.
110 citations
TL;DR: An algorithm is presented which allows to decide whether an arbitrary VRS is persistent or not, and if so, to construct a semilinear representation of the set of states reachable in the system.
Abstract: In a persistent vector replacement system (VRS) or Petri net, an enabled transition can become disabled only by firing itself. Here, an algorithm is presented which allows to decide whether an arbitrary VRS is persistent or not, and if so, to construct a semilinear representation of the set of states reachable in the system.
83 citations
TL;DR: A simplification of flow expressions, an extension of the regular expressions designed to model concurrency, is examined, and grammars for all shuffle languages are generated and shown to be context-sensitive.
Abstract: Flow expressions have been proposed as an extension of the regular expressions designed to model concurrency. We examine a simplification of these flow expressions which we call shuffle expressions. We introduce two types of machines to aid in recognizing shuffle languages and show that one such machine may be equivalent to a Petri Net. In addition, closure and containment properties of the related language classes are investigated, and we show that one machine type recognizes at least a restricted class of shuffle languages. Finally, grammars for all shuffle languages are generated, and the shuffle languages are shown to be context-sensitive.
77 citations
31 Aug 1981
TL;DR: A set of transformation rules are defined, which can be used to transform the incidence matrix, without changing the set of invariants, for coloured Petri Nets.
Abstract: This paper shows how invariants can be found for coloured Petri Nets. We define a set of transformation rules, which can be used to transform the incidence matrix, without changing the set of invariants.
69 citations
TL;DR: The tool presented presented processes characteristics which should make it attractive for general use in modeling simulation designs, and their use as guidelines for coding is illustrated.
Abstract: Simulation graphs, a general language-independent tool for modeling simulation designs, is presented. Simulation graphs are an extension of Petri net graphs. The modifications to ordinary Petri net...
31 Aug 1981
TL;DR: An overview of some formal models of concurrent systems, that are derived from the classical Petri net model, and a more formal definition of self-modifying nets together with a new presentation.
Abstract: In this paper we give an overview of some formal models of concurrent systems, that are derived from the classical Petri net model. Since several of these models are introduced by Petri and his group within General Net Theory [4] they can also be called 'high-level Petri nets'. We discuss the motivation and usefulness of such extensions, as well as some of their disadvantages. While many of these models are only informally presented, we give a more formal definition of self-modifying nets together with a new presentation. On the other hand we do not consider such models that are combinations of Petri nets with other models, such as the program schemata of Roucairol f213 or evaluation nets of Noe [19~ .
Journal Article•
TL;DR: This paper defines weakly per.
01 Mar 1981
TL;DR: This paper surveys the current state of the art in protocol specification and verification, and describes methods for specification such as abstract machines, Petri nets, formal languages, abstract data types, and programs.
Abstract: Interest in more rigorous definition and analysis of communication protocols is increasing. This paper surveys the current state of the art in protocol specification and verification. Methods for specification such as abstract machines, Petri nets, formal languages, abstract data types, and programs are described and compared. Verification methods including state exploration, symbolic execution, structural induction, and program proof are discussed. Work is progressing rapidly in many of these areas, and no clearly superior method has emerged yet. At least in the area of specification, some of these methods are ready for use by a wider community of protocol designers and users.
TL;DR: It is shown that flow languages for some restricted class of flow expressions are equivalent to Petri net languages.
01 Apr 1981
TL;DR: Some techniques for the determination of Σ's for various classes of ΔM's are suggested, which finds a variety of applications in the area of computers.
Abstract: Murata has given state space representation of Petri nets (PN) in the form ATΣ=ΔM. The present paper suggests some techniques for the determination of Σ's for various classes of ΔM's. This finds a variety of applications in the area of computers.
TL;DR: The complexity evaluation of a program utilizing the reachability concept of a Petri net (PN) and a PN representation of a particular program is given, which does not require matrix multiplication.
Abstract: The complexity evaluation of a program utilizing the reachability concept of a Petri net (PN) is proposed. A PN representation of a particular program is also given. Three measures of complexity namely (i) cyclomatic number (ii) number of simple paths and (iii) execution time are discussed. Unlike other methods for the determination of number of paths as a complexity measure, the proponed technique does not require matrix multiplication. Only vector additions on the columns of a single matrix is needed. This alleviates the computational effort, and it is simple and easily computerized.
01 Apr 1981
TL;DR: With the proposed state equation, all the logic operations hitherto not covered, can be conveniently represented using general form and this makes it possible to analyze the Petri net model of a computer.
Abstract: The representation of a Petri net is given with state equations more general than those described by Murata. With the proposed state equation, all the logic operations hitherto not covered, can be conveniently represented using general form. This makes it possible to analyze the Petri net model of a computer.
TL;DR: In the proposed technique all maximal compatible classes of microoperations for a given ROM and all the irredundant solutions of CM cover table proposed by Das et al. are determined.
TL;DR: Two new net operators, motivated by the phenomena of growth, learning and brain damage are introduced and compared with Boolean operators.
Abstract: Motivated by the cell-assemblies theory of the brain, we propose a new formal model of threshold nets (TN). TN are patterned after Petri nets, with a very different firing rule, which removes all tokens upon firing of a transition. The generative power of threshold nets, with and without inhibition, is compared with traditional families of languages. Excitatory TN languages are included by the noncounting regular languages and form an infinite hierarchy for increasing values of threshold. Inhibitory nets are included by the context-sensitive languages. Two new net operators, motivated by the phenomena of growth, learning and brain damage are introduced and compared with Boolean operators.
29 Jun 1981
TL;DR: It is finally shown how to interpret the generated control structure which serves as a basis for algorithms generating a controlled system structure which exactly performs the functions specified.
Abstract: The approach presented is intended to help solve design problems above the logical level. It is based on the use of a special class of PETRI nets to model system components and data flows. Instead of describing an already existing design the functions to be implemented are introduced by a specification program. This serves as a basis for algorithms generating a controlled system structure which exactly performs the functions specified. So, no further verification is necessary. It is finally shown how to interpret the generated control structure.
19 Apr 1981
01 Jan 1981
TL;DR: The ECMA transport protocol allows correction of the errors signaled by the network level, by using a window mechanism and control frames for acknowledgments and rejections, and the correctness of the data transfer is demonstrated using invariants.
Abstract: After a brief introduction to the theory of Petri nets, the ECMA transport protocol is presented. Then a model of the connection and disconnection phases is developed. Properties of correctness are demonstrated, using Petri net theory results, namely, reductions and linear invariants techniques. Predicate/transition nets are introduced and the underlying network service is modeled. Then a model of the data transfer phase is described. It allows correction of the errors signaled by the network level, by using a window mechanism and control frames for acknowledgments and rejections. The correctness of the data transfer is demonstrated using invariants. The service provided to the upper level is thus validated.
01 Nov 1981
TL;DR: A new framework to compare the descriptive power of different types of Petri nets is proposed, and in the proposed framework, it is shown that this extension has the same descriptive power as condition/event-nets.
Abstract: This paper proposes a new framework to compare the descriptive power of different types of Petri nets. An extension of condition/event-nets is defined, and in the proposed framework, it is shown that this extension has the same descriptive power as condition/event-nets.This paper proposes a new framework to compare the descriptive power of different types of Petri nets. An extension of condition/event-nets is defined, and in the proposed framework, it is shown that this extension has the same descriptive power as condition/event-nets.
01 Jan 1981
TL;DR: A method for approximating the time required to execute a data flow program (assuming adequate computing resources) is described and this method is applied to the static program graph at compile time and yields a parameterized equation for execution time performance.
Abstract: The computer systems of the eighties are expected to be designed using powerful low-cost distributed parts to achieve increases in computing power and concurrency. The resulting complexity due to the interaction and communication between these parts requires new methods for the analysis of the behavior of these systems. One such class of architectures, based on the concept of data flow, is designed to exploit the inherent parallelism within a program. In these computers, traditional sequencing constraints are removed and an operation is enabled for execution as soon as its operands are available.
A method for approximating the time required to execute a data flow program (assuming adequate computing resources) is described. This method is applied to the static program graph at compile time and yields a parameterized equation for execution time performance. Based on a Petri net analysis and combined with more traditional approaches, this method is recursively applied to abstract operations in the program graph using a top-down approach. While this approach may introduce approximations at each stage, the major benefit is a significant reduction over other techniques in the time required for the analysis.
TL;DR: A technique utilizing the concept of reachability in a Petri net is proposed to enumerate all maximal compatible classes in ROM bit optimization of microprocessors and microprogrammed computers.
Abstract: A technique utilizing the concept of reachability in a Petri net is proposed to enumerate all maximal compatible classes in ROM bit optimization of microprocessors and microprogrammed computers. It is simple, requires less computation and is easily implemented on computers.