Abstract
The approach of characterising certain properties of concurrent structures by traces, i.e. partial orders of event occurrences has already been used by several authors in particular by S. Patil, A.W. Holt, P.E. Lauer. The approach also has a close connection to causal-nets introduced by C.A. Petri.
As to the formal linguistic approaches to Petri nets, the aspects of (string-) languages and commutative grammars have already been carefully investigated, e.g. by M. Hack and S. Crespi Reghizzi respectively. The interconnections between Petri nets and traces have been studied by F. Furtek, and later in particular by A. Mazurkiewicz who proved that the behaviour of 1-safe nets can always be characterised by regular languages of traces.
This paper is inspired by an interest in whether the converse statement is true, that is, whether regular trace languages can always be represented by 1-safe nets. An affirmative answere is given for a simple special class which, however, has a number of practical applications.
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References
Mazurkiewicz, A.: Concurrent program schemes and their interpretations, Aarhus Workshop on Verification of Parallel Processes, June 1977.
Lauer, P.E., Best, E. and Shields, M.W.: On the problem of achieving adequacy of concurrent programs, Proc. of the IFIP Work. Conf. on Formal Desc. of Prog. Concepts, North Holland, August 1977.
Lauer, P.E. and Campbell, R.H.: Formal semantics of a class of highlevel primitives for co-ordinating concurrent processes, Acta Informatica, 5, pp. 297–332 /1975/.
Petri, C.A.: Nichtsequentielle Processe, GMD-ISF, Internal Report 76-6, Bonn 1976.
Hack, M.: Petri net languages, MIT Memo 124, June 1975.
Crespi Reghizzi, S. and Mandrioli, D.: Petri nets and commutative grammars. Inst. di Elettrotecnica ed Elettronica del Politechnico di Milano, Internal Report 74-5, March 1974.
Patil, S.S.: Co-ordination of asynchronous events, MIT MAC TR-72, 1970.
Holt, A.W.: Information system theory project, Final Report, TR-68-305, New York, 1968.
Furtek, F.: A new approach to Petri Nets, MIT Computation Structures group Memo 123, 1975.
Shields, M.W. and Lauer, P.E.: On the abstract specification and formal analysis of synchronisation properties of concurrent systems, to appear in the Proc. of the Int. Conf. on Mathematical Studies of Information Processing. RIMS Kyoto, Japan, 1978.
Knuth, E.: Petri nets and regular trace languages. University of Newcastle upon Tyne Computing Laboratory ASM/47, April, 1978.
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Knuth, E. (1978). Cycles of partial orders. In: Winkowski, J. (eds) Mathematical Foundations of Computer Science 1978. MFCS 1978. Lecture Notes in Computer Science, vol 64. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-08921-7_79
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DOI: https://doi.org/10.1007/3-540-08921-7_79
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