Abstract
We define and investigate new methods for the parallel composition of words and languages. The operation of parallel composition leads to new shuffle-like operations defined by syntactic constraints on the usual shuffle operation. The approach is applicable to concurrency, providing a method to define the parallel composition of processes. It is also applicable to parallel computation.
The syntactic constraints are introduced using a uniform method based on the notion of a trajectory. We obtain in a natural way a large class of semirings.
The approach is amazingly flexible. Diverse concepts from the theory of concurrency can be introduced and studied in this framework. For instance, we provide examples of applications to the fairness property and parallelization of non-context-free languages in terms of context-free and even regular languages.
Semantic constraints mean constraints applied to the symbols (atomic actions) that occur inside of processes. Such constraints provide methods to define the parallel composition of processes that have critical sections, priorities or re-entrant routines. They are also applicable for modelling the communication between processes.
The work reported here has been supported by the Project 11281 of the Academy of Finland, and the ESPRIT Basic Research Working Group ASMICS II.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
T. Axford, Concurrent Programming Fundamental Techniques for Real Time and Parallel Software Design, John Wiley &: Sons, New York, 1989.
J. C. M. Baeten and W. P. Weijland, Process Algebra, Cambridge University Press, 1990.
J. A. Bergstra and J. W. Klop, “Process Algebra for Synchronous Communication”, Information and Control, 60 (1984), 109–137.
W. Brauer, Automatentheorie, B.G. Teubner, Stuttgart, 1984.
J. S. Golan, A. Mateescu and D. Vaida, “Semirings and Parallel Composition of Processes”, Journal of Automata, Languages and Combinatorics, to appear.
L. Guo, K. Salomaa and S. Yu, Synchronization Expressions and Languages, The University of Western Ontario London, Dept. of Comp. Sci., Technical Report 368, 1993.
T. Harju, M. Lipponen and A. Mateescu, “Flatwords and Post Correspondence Problem”, Theoretical Computer Science, to appear.
M. Hennessy, Algebraic Theory of Processes, The MIT Press, Cambridge, Massachusetts, London, 1988.
G.H. Higman, “Ordering by divisibility in abstract algebras”, Proc. London Math. Soc., 3, (1952) 326–336.
L. Kari, On insertion and deletion in formal languages, PhD Thesis, University of Turku, Turku, Finland, 1991.
M. Kudlek and A. Mateescu, “Distributed Catenation and Chomsky Hierarchy”, FCT'95, Dresden, 1995, Lecture Notes in Computer Science, LNCS 965, Springer-Verlag, 1995, 313–322.
M. Kudlek and A. Mateescu, “Rational and Algebraic Languages with Distributed Catenation”, DLT'95, Magdeburg, 1995, in Developments in Language Theory II, eds. J. Dassow, G. Rozenberg and A. Salomaa, World Scientific, Singapore, 1996, 129–138.
W. Kuich and A. Salomaa, Semirings, Automata, Languages, EATCS Monographs on Theoretical Computer Science, Springer-Verlag, Berlin, 1986.
A. Mateescu, “On (Left) Partial Shuffle”, Results and Trends in Theoretical Computer Science, LNCS 812, Springer-Verlag, (1994) 264–278.
A. Mateescu and A. Salomaa, “Formal Languages: an Introduction and a Synopsis”, Chapter 1, in Handbook of Formal Languages, eds. G. Rozenberg and A. Salomaa, Springer-Verlag, to appear.
A. Mateescu and A. Salomaa, “Parallel Composition of Words with Re-entrant Symbols”, TUCS Technical Report, 15, 1996.
A. Mateescu, K. Salomaa and S. Yu, “Decidability of Fairness for Context-Free Languages”, submitted.
H. A. Maurer, G. Rozenberg and E. Welzl, “Using String Languages to Describe Picture Languages”, Information and Control, 3, 54, (1982) 155–185.
R. Milner; Communication and Concurrency, Prentice Hall International. 1989.
A. Salomaa, Formal Languages, Academic Press, New York, 1973.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Mateescu, A., Rozenberg, G., Salomaa, A. (1997). Syntactic and semantic aspects of parallelism. In: Freksa, C., Jantzen, M., Valk, R. (eds) Foundations of Computer Science. Lecture Notes in Computer Science, vol 1337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0052078
Download citation
DOI: https://doi.org/10.1007/BFb0052078
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63746-2
Online ISBN: 978-3-540-69640-7
eBook Packages: Springer Book Archive