Abstract
We present an intuitive preorder for a simple CCS-like language whose semantic theory allows us to relate concurrency and nondeterminism without reducing the former to the latter. The preorder over processes is induced by using an equationally defined preorder over computations in a bisimulation-like protocol. The relationships of the proposed preorder with pomset bisimulation and standard strong bisimulation equivalence are studied in detail. Moreover, we give an axiomatization of the preorder over recursion-free processes.
This work has been supported by a grant from the United Kingdom Science and Engineering Research Council and by the Esprit BRA project CEDISYS.
Preview
Unable to display preview. Download preview PDF.
References
S. Abramsky, Observation Equivalence as a Testing Equivalence, TCS 53, pp. 225–241, 1987
S. Abramsky, A Domain Equation for Bisimulation, Imperial College Technical Report, 1987
S. Abramsky; Causal Semantics in Process Algebra, draft paper, 1990
G. Boudol and I. Castellani, On the Semantics of Concurrency: Partial Orders and Transition Systems, in Proc. TAPSOFT 87, LNCS 249, pp. 122–137, Springer Verlag, 1987
G. Boudol and I. Castellani, Concurrency and Atomicity, TCS 59, pp. 25–84, 1988
S. D. Brookes, C. A. R. Hoare and A. W. Roscoe, A Theory of Communicating Sequential Processes, J. ACM 31, 3, pp. 560–599, 1984
J. A. Bergstra and J. W. Klop, Algebra of Communicating Processes with Abstraction, TCS 37, 1, pp. 77–121, 1985
I. Castellani, Bisimulations for Concurrency, Ph. D. Thesis CST-51-88, University of Edinburgh, April 1988
I. Castellani and M. Hennessy, Distributed Bisimulations, J. ACM, October 1989
R. Cleaveland, J. Parrow and B. Steffen, The Concurrency Workbench: A Semantics-Based Verification Tool for Finite-State Systems, Report ECS-LFCS-89-83, University of Edinburgh, 1989
P. Degano, R. de Nicola and U. Montanari, Observational Equivalences for Concurrency Models, in Proc. IFIP TC2 Workshop on Formal Description of Programming Concepts IV (M. Wirsing ed.), pp. 105–137, North-Holland, 1987
R. de Nicola and M. Hennessy, Testing Equivalences for Processes, TCS 34, 1, pp. 83–134, 1984
J. L. Gischer, Partial Orders and the Axiomatic Theory of Shuffle, Ph. D. Thesis, Stanford University, 1984
J. Grabowski, On Partial Languages, Fundamenta Informaticae IV.2, pp. 427–498, 1981
R. van Glabbeek and F. Vaandrager, Petri Net Models for Algebraic Theories of Concurrency, in Proc. PARLE Conference 1987 (J. de Bakker et al. eds.), LNCS 259, Springer Verlag, 1987
M. Hennessy, Algebraic Theory of Processes, MIT Press, 19988
M. Hennessy, Axiomatising Finite Concurrent Processes, SIAM Journal on Computing, October 1988
M. Hennessy and R. Milner, Algebraic Laws for Nondeterminism and Concurrency, J. ACM 32, 1, pp. 137–161, 1985
C. A. R. Hoare, Communicating Sequential Processes, Prentice-Hall, 1985
R. Keller, Formal Verification of Parallel Programs, C. ACM 19, 7, pp. 561–572, 1976
R. Milner, A Calculus of Communicating Systems, LNCS 92, Springer Verlag, 1980
R. Milner, Communication and Concurrency, Prentice-Hall, 1989
D. Park, Concurrency and Automata on Infinite Sequences, LNCS 104, Springer Verlag, 1981
G. Plotkin, A Structural Approach to Operational Semantics, Report DAIMI FN-19, Computer Science Dept., Aarhus University, 1981
V. Pratt, Modelling Concurrency with Partial Orders, International Journal of Parallel Programming 15, pp. 37–71, 1986
W. Reisig, Petri Nets, EATCS Monographs on Theoretical Computer Science, Springer Verlag, 1985
B. Thomsen, An Extended Bisimulation Induced by a Preorder on Actions, M.Sc. Thesis in Computer Science, Aalborg University Centre, 1987
G. Winskel, Event Structures, in Advances in Petri Nets 1986, LNCS 255, pp. 325–392, Springer Verlag, 1987
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aceto, L. (1992). On relating concurrency and nondeterminism. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Semantics. MFPS 1991. Lecture Notes in Computer Science, vol 598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55511-0_19
Download citation
DOI: https://doi.org/10.1007/3-540-55511-0_19
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55511-7
Online ISBN: 978-3-540-47194-3
eBook Packages: Springer Book Archive