Abstract
The paper consists of two parts. In the first part, three different groups of models for concurrent systems and processes are surveyed: 1) the models representing concurrency as nondeterministic interleaving of atomic actions; 2) the models representing concurrency as interleaving of multisets of actions; and 3) the models describing true concurrency. A number of algebras and algebraic calculi axiomatizing these models are discussed. Different equivalence relations introduced in these models are compared.
In the second part, the algebra of finite (generalized) processes AFP is introduced. The semantics of a process specified by a formula of AFP is characterized by a set of partial orders. The complete set of axioms and inference rules for deduction of partial and total properties of processes is presented.
In conclusion, the primitives of proposed algebra AFP are compared with those of CSP, and the directions of further developments are outlined.
Preview
Unable to display preview. Download preview PDF.
References
Austry D., Boudol G. Algebre de Processus et Synchronization. Theoret. Comput. Sci. Vol. 30, No 1, North Holland, Amsterdam, 1984.
Aceto L., De Nicola R., Fantechi A. Testing Equivalences for Event Structures. LNCS, Vol. 280, p. 1–20, 1987.
Baeten J., Bergstra J., Klop J. An operational semantics for process algebra. Report CS-R8522 Centrum voor Wiskunde en Informatica, 1985.
Brookes S.D., Hoare C.A.R., Roscoe A.D. A Theory of Communicating Sequential Processes. Journal of ACM, Vol. 31, No 3, pp. 560–599, 1984.
Bergstra J., Klop G. Process Algebra for Synchronous Communication. — Information and Control, Vol. 60, pp. 109–137, North Holland, Amsterdam, 1984.
Boudol G., Castellani I. On the semantics of Concurrency: Partial Orders and Transition System. LNCS, Vol. 249, p. 123–137, 1987.
Campbell R.H., Haberman A.N. The Specification of Process Synchronization by Path Experissions. LNCS, Vol. 16, p. 89–102, 1974.
Cherkasova L., Kotov V. Descriptive and Analytical process algebras. Will appear in proceedings of 9-th European workshop on Theory and Applications of Petri Nets.
Degano P., De Nicola R., Montanari U. CCS is an (Augmented) Contact-Free C/E Systems. LNCS, Vol. 280, p. 144–165, 1987.
Goltz U., Mycroft A. On the relationship of CCS and Petri Nets. LNCS, Vol. 172, p. 196–208, 1984.
Goltz U., Mycroft A. Processes of Place-Transitions Nets. LNCS, Vol. 154, p. 264–177, 1983.
Hoare C.A.R A model for Communicating Sequential Processes. Technical Monograph Prg-22, Computing Laboratory, University of Oxford, 1982.
Hoare C.A.R. Communicating Sequential Processes. Prentice Hall, 1985.
Kotov V.E. An algebra for parallelism based on Petri Nets. LNCS, Vol. 64, p. 39–55, 1978.
Kotov V.E., Cherkasova L.A. On structural properties of generalized processes. LNCS, Vol. 188, p. 288–306, 1984.
Lauer P.E., Torrigiani P.R., Shields M.W. COSY — A System Specification Language Based on Paths and Processes. Acta Informatica, vol. 12, p. 109–158, 1979.
Milner R. Calculus of Communicating Systems. LNCS, Vol. 92, 1980.
Milner R. Calculi for Synchrony and Asynchrony Theoret. Comput. Sci. Vol. 25, North Holland, p. 267–310, 1983.
Nielsen M., Plotkin G., Winskel G. Petri Nets, Event Structures and Domains. Theoret. Comp. Sci. 13, p. 85–108, 1981.
Olderog E.R. TCSP: Theory of Communicating Sequential Processes. LNCS, Vol. 255, p. 441–465, 1987.
Petri C.A. Non-sequential Processes, GMD-ISF, Rep. 77-05, 1977.
Pomello L. Some equivalenve notions for concurrent systems. An overview. LNCS, Vol. 222, p. 381–400, 1986.
Pratt V.R. Modelling Concurrency with Partial Orders. International Journal of Parallel Programming. Vol. 15, No 1, p. 33–71, 1987.
Reizig W. Petri Nets: An Introduction, Springer-Verlag, 1985.
Shields M.W. Adequate Path Expressions. LNCS, Vol. 70, p. 249–265, 1979.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cherkasova, L.A. (1988). On models and algebras for concurrent processes. In: Chytil, M.P., Koubek, V., Janiga, L. (eds) Mathematical Foundations of Computer Science 1988. MFCS 1988. Lecture Notes in Computer Science, vol 324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017129
Download citation
DOI: https://doi.org/10.1007/BFb0017129
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50110-7
Online ISBN: 978-3-540-45926-2
eBook Packages: Springer Book Archive