On sequential modelling of non-sequential processes
The aim of this paper is to answer the question whether all properties of discrete non-sequential processes can be expressed and proved in the framework of sequential descriptions of such processes. The paper deals only with the processes which can be defined in terms of Petri nets.
The rules according to which a process is running are represented by a Petri net. The process itself is identified with a Petri net of occurrences of conditions and events of this net. A characterization of these two nets, and of relationships between them, constitutes a theory of the process. Such a theory is objective in the sense of Petri.
A sequential description of a non-sequential process is a description of this process from the point of view of an external observer. The observer identifies the process with a sequence of occurrences of global states of the Petri net representing the rules of the process. A characterization of the last net, of the sequence of global net state occurrences, and of relationships between these two objects, is just a sequential description of the process, or a sequential theory of it. Such a theory is subjective in the sense of Petri.
The main result of the paper is that the objective theory of a process from a broad class of processes can be modelled in a subjective theory. It implies that the foundamental question of the paper may be answered positively for a class of processes.
KeywordsGlobal State Objective Theory External Observer Subjective Theory State Occurrence
Unable to display preview. Download preview PDF.
- 1.Baer, J.L., A Survey of Some Theoretical Aspects of Multiprogramming, Computing Surveys, Vol 5, No 1, March 1973Google Scholar
- 2.Brinch Hansen, P., Concurrent Programming Concepts, Computing Surveys, Vol 5, 1973Google Scholar
- 3.Genrich, H.J., Einfache nicht-sequentielle Prozesse, BMBW-GMD-37, Bonn, 1971Google Scholar
- 4.Genrich, H.J., Extended Simple Regular Expressions, in Proc. of MFCS'75 Symp., Marianske Lazne, Lecture Notes in Comp. Sc. 32, Springer-Verlag, 1975Google Scholar
- 5.Karp, R.M. and Miller, R.E., Parallel Program Schemata, JCSS 3(2)Google Scholar
- 6.Mazurkiewicz, A., Parallel Recursive Program Schemes, in Proc. of MFCS'75 Symp., Marianske Lazne, Lecture Notes in Comp. Sc. 32, Springer-Verlag, 1975Google Scholar
- 7.Mazurkiewicz, A., Invariants of Concurrent Programs, to appearGoogle Scholar
- 8.Milner, R., An Approach to the Semantics of Parallel Programs, Unpublished Memo, Computer Science Department, University of Edinburgh, 1973Google Scholar
- 9.Petri, C.A., Interpretations of Net Theory, GMD, Bonn, 1975, presented at MFCS'75 Symp., Marianske Lazne, 1975Google Scholar
- 10.Shapiro, R.M. and Saint, H., A New Approach to Optimization of Sequencing Decisions, Ann. Rev. in Aut.Prog., Vol 6, P 5, 1970Google Scholar
- 11.Winkowski, J., Formal Theories of Petri Nets and Net Simulations, CC PAS Reports 242, 1976Google Scholar
- 12.Winkowski, J., Towards an Understanding of Computer Simulation, CC PAS Reports 243, 1976Google Scholar
- 13.Winkowski, J., On Sequential Modelling of Parallel Processes, to appear in CC PAS ReportsGoogle Scholar