Abstract
String-equivalence, Behaviour-equivalence, Observation-equivalence, Exhibited-Behaviour-equivalence, Failure-equivalence and Testing equivalence are re-defined and discussed on Petri Net models of concurrent systems. Since the previous notions, being based on sequences of events, do not distinguish real concurrency from its sequential non-deterministic simulation, they are refined, in order to capture the concurrency degree of the systems, in terms of the subset languages approach. The equivalence notions introduced are then compared w.r.t. their strength.
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References
C. Andrè, P.Armand, F.Boeri, Synchronic Relations and Applications in Parallel Computation, Digital Processes 5, Georgi Pub. Comp. (1979).
C. Andrè, Behaviour of a Place-Transition Net on a Subset of Transitions, IFB 52, Springer Verlag, (1982).
C. Andrè, Use of The Behaviour Equivalence in Place-Transition Net Analysis, IFB 52, Springer Verlag, (1982).
W. Brauer ed., Net Theory and Applications, LNCS Lecture Notes in Computer Science, Springer Verlag 84, (1980).
J.A. Bergstra, J.W. Klop, An Abstraction mechanism for Process Algebras, Dep. of Computer Science Technical Report IW 231/83, Mathematisch Centrum, Amsterdam, (1983).
S.D. Brookes, On The Relationship of CCS and CSP, LNCS Lecture Notes in Computer Science, Springer Verlag 154,(1983).
S.D. Brookes, A Semantics and Proof System for Communicating Processes, Proc. '83 NSF/ONR Workshop on Logics of Programs, Pittsburgh, Springer Verlag.
S.D. Brookes, C.A.R. Hoare, A.W. Roscoe, A theory of Communicating Sequential Processes, ACM 31, N.3, July '84, (1984).
S.D. Brookes, W. Rounds, Behavioural Equivalences Relations Induced by Programming Logic, LNCS Lecture Notes in Computer Science, Springer Verlag 154, (1983).
I. Castellani, P. Franceschi, U. Montanari, Labeled Event Structures: A Model for Observable Concurrency, in Formal Description of Programming Concepts II, D.Bjorner (ed.) North-Holland Publ. Comp. IFIP (1983).
L. Castellano et al., Dual Notions of Equivalence for Petri Nets, I.C. Internal Report, (1985).
P. Darondeau, An enlarged Definition and complete Axiomatization of Observational Congruence of Finite Processes, LNCS Lecture Notes in Computer Science, Springer Verlag 137, (1982).
P. Darondeau, On the Observational Semantics of Fair Parallelism, LNCS Lecture Notes in Computer Science, Springer Verlag 154, (1983).
F. De Cindio, G. De Michelis, L. Pomello, C. Simone, Equivalence Notions For Concurrent Systems, IFB 66, Springer Verlag, (1983).
F. De Cindio, G. De Michelis, L. Pomello, C. Simone, Exhibited-Behaviour Equivalence as the basis for Concurrent System Design, I.C. Internal Report, (1984).
F. De Cindio, G. De Michelis, L. Pomello, C. Simone, Exhibited-Behaviour Equivalence and Organizational Abstraction in Concurrent System Design, Proc. 5th Int. Conf. on Distributed Computing, IEEE (1985).
F. De Cindio, G. De Michelis, L. Pomello, C. Simone, Milner's Communicating Systems and Petri Nets, IFB 66, Springer Verlag, (1983).
F. De Cindio, G. De Michelis, L. Pomello, C. Simone, A Petri Net Model of CSP, Proc. CIL '81, Barcelona, (1981).
F. De Cindio, G. De Michelis, C. Simone, Giving Back some Freedom to System Designer, System Research, to appear (1985).
G. De Michelis, L. Pomello, A Less Restrictive Observational Equivalence Notion, Proc. IV Workshop on Applications and Theory of Petri Nets, Toulose, (1983).
G. De Michelis, L. Pomello, C. Simone, Observing Nets, Proc. Int. Symp. on Circuits and Systems ISCAS '85, Kyoto, (1985).
R. De Nicola, M. Hennessy, Testing Equivalence for Processes, Technical Report CSR-123-82, University of Edinburg, (1982).
H.J. Genrich, K. Lautenbach, System Modelling with high-level Petri Nets, Theoretical Computer Science 13, (1981).
U. Goltz, A. Mycroft, On the Relationship of CCS and Petri Nets, Proc.ICALP '84, (1984).
U. Goltz, W. Reisig, CSP-Programs as Nets with Individual Tokens, Proc. V Workshop on Applications and Theory of Petri Nets, Aarhus, (1984)
M. Hennessy, Synchronous and Asynchronous Experiments on Processes, Proc. NATO ASI on Logics for Verification and Specification of Concurrent Systems, vol.2, La-Colle-sur-Loup (France), (1984).
M. Hennesy, R. Milner, On Observing non-determinism and concurrency Lecture Notes in Computer Science, Springer Verlag 85, (1980).
C.A.R. Hoare, Communicating Sequential Processes, CACM 21, Vol.8, (1978).
K. Jensen, Coloured Petri Nets and the Invariant-method, Theoretical Computer Science 14, (1981).
M. Yoeli, T. Etzion, Behavioural Equivalence of Concurrent Systems, IFB 66, Springer Verlag (1983).
A. Mazurkiewicz, Concurrent Programs Schemes and Their Interpretations, DAIMI PB 78, Aarhus Univ. Publ. (1977).
R. Milner, A Calculus for Communicating Systems, LNCS Lecture Notes in Computer Science, Springer Verlag 92, (1980).
M. Nielsen, P.S. Thiagarajan, Degrees of Non-determinism and Concurrency: A Petri Net View, DAIMI PB 180, Aarhus Univ. Publ. (1984).
L. Pomello, Some Equivalence Notions for Concurrent Systems, An Overview, GMD Report Nr.103, (1984).
W. Reisig, Petri Netze, Springer Verlag, (1982).
G. Rozenberg, R. Verraedt, Subset Languages of Petri Nets, IFB 66, Springer Verlag (1983).
E. Sirmen, An Equivalence Notion for Condition/Event Systems, IFB 52, Springer Verlag, (1982).
K. Voss, On the Notion of Interface in Condition/Event Systems, IFB 66, Springer Verlag (1983).
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© 1986 Springer-Verlag Berlin Heidelberg
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Pomello, L. (1986). Some equivalence notions for concurrent systems. An overview. In: Rozenberg, G. (eds) Advances in Petri Nets 1985. APN 1985. Lecture Notes in Computer Science, vol 222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016222
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DOI: https://doi.org/10.1007/BFb0016222
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