Petri Nets and Marked Graphs–Mathematical Models of Concurrent Computation
TL;DR: In this paper, Petri nets and Marked Graphs are used to model concurrent computations in the model of concurrent computation, and a Petri net is used to represent a graph.
Abstract: (1982). Petri Nets and Marked Graphs–Mathematical Models of Concurrent Computation. The American Mathematical Monthly: Vol. 89, No. 8, pp. 552-566.
Citations
More filters
Patent•
14 Apr 1987
TL;DR: A system and method for controlling operation of a plurality of elements in an automated process, such as a production process, and indicating error conditions as they occur is presented in this paper.
Abstract: A system and method for controlling operation of a plurality of elements in an automated process, such as a production process, and indicating error conditions as they occur. Each unique set of input and output conditions of the various system elements defines a unique logic state or zone. Thus, there are defined a multiplicity of valid system logic states or zones, each having a unique input/output image. A predetermined sequence of zones, productive zones representing designed machine operations, is stored in a zone table. All zones not explicitly defined in the zone table are automatically treated as error zones. A zone engine automatically cycles to observe any change in input/output image. Any change in inputs from the various system elements automatically transfer action to the unique zone associated with such inputs, resulting in corresponding changes in control outputs to the system elements and/or display an error message as appropriate.
92 citations
07 Apr 2008
TL;DR: A model based software testing method for testing of the Web applications using StateCharts, which briefly describes the test coverage technique, editorial tools for drawing State Charts, modeling concurrency in Web applications, and test metrics.
Abstract: In this paper, we discuss a model based software testing method for testing of the Web applications using StateCharts. To this end, we briefly describe the test coverage technique, editorial tools for drawing StateCharts, modeling concurrency in Web applications, and test metrics. A simple Web application has been used to show the feasibility of our approach.
31 citations
Cites background from "Petri Nets and Marked Graphs–Mathem..."
...Petri nets are a model for visually representing concurrency in a system [8]....
[...]
Dissertation•
27 Jul 2016
25 citations
DOI•
30 Dec 1899TL;DR: The complexity of modern computer systems has made performance evaluation results more and more difficult to obtain this paper and the difficulty of representation and analysis of combination hardware/software systems has increased with the level of sophistication used in their design.
Abstract: The growing complexity of modern computer systems has made performance evaluation results more and more difficult to obtain. The difficulty of representation and analysis of combination hardware/software systems has increased with the level of sophistication used in their design. One popular approach that has been used for evaluating proposed computer systems is simulation.
21 citations
References
More filters
01 Jan 1962
TL;DR: The theory of automata is shown not capable of representing the actual physical flow of information in the solution of a recursive problem and a theory of communication is proposed that yields a means of representation that with equal rigor and simplicity accomplishes more than the theory of synchronous automata.
Abstract: Diese Arbeit befasst sich mit den begrifflichen Grundlagen einer Theorie der Kommunikation. Die Aufgabe dieser Theorie soll es sein, moglichst viele Erscheinungen bei der Informationsubertragung und Informationswandlung in einheitlicher und exakter Weise zu beschreiben.
The theory of automata is shown not capable of representing the actual physical flow of information in the solution of a recursive problem. The argument proceeds as follows:
1. We assume the following postulates:
a) there exists an upper bound on the speed of signals;
b) there exists an upper bound on the density with which information can be stored.
2. Automata of fixed, finite size can recognize, at best, only iteratively defined classes of input sequences. (See Kleene (11) and Copi, Elgot, and Wright (8).)
3. Recursively defined classes of input sequences that cannot be defined iteratively can be recognized only by automata of unbounded size.
4. In order for an automaton to solve a (soluble) recursive problem, the possibility must be granted that it can be extended unboundedly in whatever way might be required.
5. Automata (as actual hardware) formulated in accordance with automata theory will, after a finite number of extensions, conflict with at least one of the postulates named above.
Suitable conceptual structures for an exact theory of communication are then discussed, and a theory of communication proposed.
All of the really useful results of automata theory may be expressed by means of these new concepts. Moreover, the results retain their usefulness and the new nrocedure has definite advantages over the older ones.
The proposed representation differs from each of the presently known theories concerning information on at least one of the following essential points:
1. The existence of a metric is assumed for either space nor time nor for other physical magnitudes.
2. Time is introduced as a strictly local relation between states.
3. The objects of the theory are discrete, and they are combined and produced only by means of strictly finite techniques.
The following conclusions drawn from the results of this work may be cited as of some practical interest:
1. The tolerance requirements for the response characteristics of computer components can be substantially weakened if the computer is suitably structured.
2. It is possible to design computers structurally in such a way that they are asynchronous, all parts operating in parallel, and can be extended arbitrarily without interrupting their computation.
3. For complicated organizational processes of any given sort the theory yields a means of representation that with equal rigor and simplicity accomplishes more than the theory of synchronous automata.
2,523 citations
"Petri Nets and Marked Graphs–Mathem..." refers background in this paper
...Petri nets originated in C. A. Petri's dissertation [ 46 ]....
[...]
1,252 citations
Book•
01 Jan 1974
1,204 citations
Book•
01 Jan 1974
TL;DR: This outstanding introductory treatment of graph theory and its applications has had a long life in the instruction of advanced undergraduates and graduate students in all areas that require knowledge of this subject.
1,161 citations