Showing papers on "Petri net published in 1977"

Petri Nets

Abstract: Over the last decade, the Petr i net has gamed increased usage and acceptance as a basic model of systems of asynchronous concurrent computation. This paper surveys the basic concepts and uses of Petm nets. The structure of Petr i nets, thei r markings and execution, several examples of Petm net models of computer hardware and software, and research into the analysis of Petm nets are presented, as are the use of the reachabil i ty tree and the decidability and complexity of some Petr i net problems. Petr i net languages, models of computation related to Petm nets, and some extensions and subclasses of the Petri net model are also bmefly discussed

State equation, controllability, and maximal matchings of petri nets

Abstract: Petri nets are a versatile modeling device for studying the structure and control of concurrent systems. Petri nets and related graph models have been used for modeling a wide variety of systems from computers to social systems. In order to introduce this interesting modeling device to the researcher in control theory, this paper discusses Petri nets in the context of the state equation for a linear discrete-time system. The controllability concept of dynamic systems is applied to Petri nets for the first time. It is also shown that the controllability and reachability of a Petri net are related to maximal matchings of its bipartite graph.

Use of production systems for modeling asynchronous, concurrent processes

Abstract: Because of the event-driven, nature of asynchronous, concurrent processes, production systems (PS's) are an attractive modeling tool. The system of interest can be modeled with a large number of independent states, with independent actions, and tile knowledge base can be conveniently encoded declaratively. However, asynchronous, concurrent processes normally have strict requirements for inter-process communication and coordination; this requires a substantial degree of inter-rule communication in the PS. The result of this is that a complex control structure is embedded in the short term memory (STM); this is generally considered unattractive for a number of reasons. This paper proposes a separate, explicit control structure for modeling asynchronous, concurrent processes With PS's. Specifically, the use of a Petri net is addressed. A system of asynchronous, concurrent processes can be modeled using 'PS's to model the individual processes or events and using a Petri net to model the relationships between the processes. Furthermore, a hierarchy of such networks is proposed; an allowable production rule action is the instantiation of another network. This is supported with a structured, hierarchial STM.

Model, Design, and Evaluation of a Compiler for a Parallel Processing Environment

Abstract: The problem of designing compilers for a multiprocessing environment is approached. We show that by modeling an existing sequential compiler, we gain an understanding of the modifications necessary to transform the sequential structure into a pipeline of processes. The pipelined compiler is then evaluated through measurements and simulation. Properties of the model, a generalized Petri Net, are also discussed.

Petri nets and szilard languages

Abstract: We investigate the properties of firing sequences (f.s.) of Petri nets and relate' them to other well-known families of formal languages. We prove in particular that the complement of the f.s. set is context free, and consequently neither the class of f.s. sets (according to some definition) nor Szilard languages are closed with respect to the complement. After introducing new normal forms for Petri nets, we prove that the reachability problem is equivalent to the emptiness problem for the intersection of Szilard languages. 1. INTRODUCTION The focus of this paper is on the formal properties of Petri nets, but the methodology presented should also apply to related models for representing parallel processes such as those by Karp and Miller (1969) and Gostelow

Hardware Description Languages: Voices from the Tower of Babel*

Abstract: A hardware description language can be used to describe the logic gates, the sequential machines, and the functional modules, along with their interconnection and their control, in a digital system. In a general sense, Boolean equations, logic diagrams, programrning languages, and Petri nets are hardware description languages: they can be used to describe some aspect of hardware and they have definable syntax and semantics. Specifically, what is more commonly referred to as a hardware description language is a variation of a programming language tuned to the overall needs of describing hardware. This article will discuss the rationale for using such languages in the first place, identify the problems attendant upon their proliferation, and describe the measures being taken to achieve a solution.

Modeling for synthesis - the gap between intent and behavior

Abstract: Aside from the continuing critical inputs of UCLA faculty and students SARA has been affected by [CLE74]; the work of the MIT Information Structures Group, Carnegie-Mellon studies, the Case-Western Reserve LOGOS project, Petri Net studies, the growing literature on structured programming and work on program verification. The body of this paper presents the highlights of our synthesis methodology, the set of primitives used by modeling tools in SARA and a fast look at the design procedure proposed to support the methodology.

Addenda and corrigenda

Abstract: 11. Lautenbach, K., Schmid, H. A. : Use of Petri nets for proving correctness of concurrent process systems. Proc. I F I P Congress 74, Stockholm, pp. 187-191. Amsterdam: North-Holland 1974 12. Best, E., Schmid, H. A. : Systems of open paths in Petr i nets. In : J. Be6v~i" (ed.), Mathematical foundations of computer science 1975. Lecture Notes in Computer Science 32. Berlin-Heidelberg-New York: Springer 1975 13. Schmid, H. A., Best, E. : A further step towards a solution of the liveness problem in Petr i nets. Submit ted a t the Conference on Petri Nets and Related Methods, MIT, Boston, Ju ly 1975

Colored Petri Nets: Their Properties and Applications.

Abstract: : The problem of representing reentrancy, recursivity and pipe-lining of control in asynchronous structures is examined with the intention of eliminating some of the drawbacks of the other solutions to their problems known so far. A model of concurrent systems having the capability of handling colored representations of control flow has been defined as an extension of an already existing model of parallel systems, the Petri Net Model. The structure and execution rules of Petri Nets have been modified in order to handle the colored tokens. (Author)

A Note on Petri Net Languages

Abstract: It is shown that there is no effective procedure to construct a labeled Petri Net whose language is the complement of the language generated by a given labeled Petri Net.

A Graph Theoretic Approach to Fault Tolerant Computing.

Abstract: : This report describes the results of an initial effort to identify properties of labelled graphs which are useful for the representation and analysis of fault tolerant digital systems. It builds on the results of previous work, where the feasibility of using LOGOS and Petri Nets to represent fault tolerant systems was assessed. The properties of conventional directed graphs were reviewed to identify any properties relevant to fault tolerance. Concepts such as balanced graphs, strongly connected graphs, cut sets, circuits, and reachability were identified as useful and shown to be applicable to labelled graphs. Next the fault phenomena commonly seen in digital systems were classified, both from the viewpoint of their observable effects on the faulty system and from the more conventional viewpoint of their sources. Six functional Fault Classes were defined which accurately describe virtually all the common control related fault phenomena. The existing labelled graph theory was then examined for properties related to the Functional Fault Classes. Concepts such as liveness, boundedness, siphons, traps, and invariants among others were identified as useful. A taxonomy of structural and dynamic properties useful for fault tolerant analysis is given. The relationship between these properties and their application to fault tolerant system analysis is described. Finally, limitations of this approach and directions for future work are described. (Author)

Petri-net based description, analysis and simulation of concurrent processes

Abstract: 1.1 The language CAPWhile there are a couple of programming languages which allow the representation of parallelism /1,2,5/ there is a lack for languages which allow in an as well disciplined as general manner the description of concurrency.A well defined mathematical description method for concurrent processes is given by the Petri net model /3,7,9/. It fulfils the above requirements and in addition is widely used and extremely easy to understand.This concept is integrated into the language CAP in a very elegant way: Lables are used as places, where one has in mind that a labelled statement puts a token into its label(s) after it has been processed. On the other hand the processability of a statement is controlld by "On-conditions" on labels. Every statement is processed if and only if its "On-condition" has become true. At this time, in accordance with the firing-rule (="On-condition"), "tokens" are withdrawn from certain labels used within the "On-condition" and placed into the labels of the statement.In addition various parameters may be associated to transitions thus offering a description power similar to the Macro-E-Nets /8/. On the other hand there are a lot of language-constructs to support structured programming.1.2 The analysis of CAP-programs at compile-timeSince a couple of years Petri nets are object of research. For some rather restricted subclasses of Petri nets sufficiant an necessary conditions for the topology of a net to be well-formed are known /3,4,7/. Under a well-formed net we understand a net without dead-locks being safe (no loss of information) and residue-free (independent from a certain history). Related to results by Herzog an Yoeli /4/ for a subclass of Petri nets we prove that there are six conditions for the topology of a net of the subclass of Petrinets which are used to describe the control-structure of CAP-programs so that the net is well-formed.By this we can decide at compile-time without simulation whether a CAP-program describes a life, safe and residue-free system (i. e. a useful one) or not. After having defined, what we mean ba a "Structured CAP-program" we will have the fine result that every structured CAP-program is well-formed.1.3 The simulation of systems described in CAPAs CAP allows the description of systems down to a level of specification which is comparable with the bit-level of digital systems inclusive the detailled description of the real-time-behaviour, for the processing of CAP one needs a system similar to a simulator for digital circuits. On the other hand also very global descriptions on a high level of abstraction are possible.This implies that the run-time system for CAP must be extremely adaptive. We tried to solve this problem by a very flexible and powerful table driven and event oriented simulator with the event-mechanism being directly adopted from the Petri net concept of CAP.