Abstract
The framework of finite-state systems is used to investigate the relative power of three fundamental notions: nondeterminism and pure parallelism, the two facets of alternation, and cooperative concurrency, whereby configurations consist of states between which communication can occur. To formalize cooperative concurrency, which appears to be the closest finite-state analog to real-world distributed concurrency, we use the recent statecharts, though our results hold for many other approaches, such as Petri nets, CSP or CCS. We exhibit an exhaustive set of upper and lower bounds on the ability to inter-simulate these features over Σ*, and an almost exhaustive set for the Σω case, establishing that (a) each of the three features represents an exponential saving in succinctness of the representation, in a manner that is independent of the other two and additive with respect to them, and (b) of the three, cooperative concurrency is the strongest, representing a similar exponential saving when it is substituted for each of the others. For example, we prove an exponential lower bound on the simulation of deterministic statecharts by AFAs and a triple-exponential lower bound on the simulation of alternating statecharts by DFAs.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Book R. V. and S. A. Greibach, “Quasi-Realtime Languages”, Math. Systems Theory 4, (1970), 97–111.
Chandra A. K. and Stockmeyer L. J., “Alternation”, Proc. 17th IEEE Symp. on Found. of Computer Science, October 1976, pp. 98–108.
Chandra A.K., Kozen D. and Stockmeyer L.J., “Alternation”, J. Assoc. Comput. Mach. 28:1, (1981), 114–133
Choueka Y., “Theories of Automata on ω-tapes: A Simplified Approach”, J. Comput. and System Sci. 8, (1974), 117–141.
Drusinsky D., On Synchronized Statecharts, Ph.d Thesis, The Weizmann Institute of Science, Rehovot, Israel, 1988.
Garey M.R. and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman, 1979.
Harel, D., “Statecharts: A Visual Approach to Complex Systems”, Science of Comput. Prog. 8, (1987), 231–274. (Also, CS84-05, Weizmann Institute of Science, Rehovot, Israel, February 1984, and in revised form, CS86-02, March 1986.)
Harel, D., “On Visual Formalisms”, Comm. Assoc. Comput. Mach. 31:5, (1988), 514–530.
Harel D., A. Pnueli, J.P Schmidt, and R. Sherman, “On the Formal Semantics of Statecharts”, Proc. 2nd IEEE Symp. on Logic in Computer Science, June 1987, pp. 54–64.
Hoare C.A.R, “Communicating Sequential Processes”, Comm. Assoc. Comput. Mach. 21, (1978), 666–677.
Hopcroft, J. E. and Ullman, J. D., Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, 1979.
King K. N., “Alternating Multihead Finite Automata”, Lecture Notes in Computer Science 115, Springer-Verlag, New-York, pp. 506–520.
Kozen, D., “On Parallelism in Turing Machines”, Proc. 17th IEEE Symp. on Found. of Computer Science, October 1976, pp. 81–88.
Kozen D., “Lower Bounds for Natural Proof Systems”, 18'th IEEE Symp. on Foundations of Computer Science, October 1977, pp. 254–266.
McNaughton R., “Testing and Generating Infinite Sequences by a Finite Automaton”, Inf. and Cont., 9 (1966), pp. 521–530.
Meyer A. and Fischer M. J., “Economy of Description by Automata, Grammars, and Formal Systems”, Proc. 12th IEEE Symp. on Switching and Automata Theory, October 1971, pp. 188–191.
Milner, R., A Calculus of Communicating Systems, Lecture Notes in Computer Science, Springer-Verlag, New York, 1980.
Rabin M.O. and Scott D, “Finite Automata and Their Decision Problems”, IBM J. Res. 3:2 (1959), 115–125.
Reisig W., Petri Nets: An Introduction, Springer-Verlag, Berlin, 1985.
Savitch W.J., “Relationships Between Nondeterministic and Deterministic Tape Complexities”, J. Comput. Syst. Sci. 4, (1970), 177–192.
Sakoda W. and Sipser M., “Nondeterminism and the Size of Two Way Finite Automata”, Proc. 10th ACM Symp. on Theory of Computing, May 1978, pp. 275–286.
Streett R. S., “Propositional Dynamic Logic with Converse”, Inf. and Cont. 54, (1982), 121–141.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Drusinsky, D., Harel, D. (1988). On the power of cooperative concurrency. In: Vogt, F.H. (eds) CONCURRENCY 88. CONCURRENCY 1988. Lecture Notes in Computer Science, vol 335. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50403-6_34
Download citation
DOI: https://doi.org/10.1007/3-540-50403-6_34
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50403-0
Online ISBN: 978-3-540-45999-6
eBook Packages: Springer Book Archive