Advertisement

A new approach to defining the communication complexity for VLSI

  • Juraj Hromkovič
Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 233)

Abstract

We define the S-communication complexity which squared gives lower bounds on AT2, i.e. it has the same relation to AT2 as the original communication complexity. The reasons to define it are the following ones:
  1. 1,

    S-communication complexity gives the strongest lower bounds Ω(n2) on AT2 in many cases when the communication complexity grants only constant lower bounds on AT2.

     
  2. 2,

    Proving lower bounds for S-communication complexity is technically not so hard as obtaining lower bounds for communication complexity.

     

It is shown that almost all languages recognizable within sublinear communication complexity require linear S-communication complexity. A specific language having constant communication complexity and linear S-communication complexity is constructed. The basic hierarchy of S-communication complexity, exponential gap between deterministic and nondeterministic S-communication complexity, and further basic results concerning the properties of S-communication complexity are established. New, linear lower bounds on S-communication complexity for the recognition of specific languages are obtained.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abelson, H.: Lower bounds on information transfer in distributed computations. Proc. 19th Annual IEEE FOCS, 1978, pp.151–158Google Scholar
  2. 2.
    Aho,A.V. — Ullman, J.D. — Yanakakis,M.: On notions of information transfer in VLSI circuits. Proc. 14th Annual ACM STOC, 1983, pp.133–139.Google Scholar
  3. 3.
    Ďuriš,P. — Galil,Z. — Schnitger,G.: Lower bounds on communication complexity. Proc. 15th Annual ACM STOC, 1984, pp.81–91.Google Scholar
  4. 4.
    Hromkovič, J.: Communication complexity. Proc. 11th ICALP, Lecture Notes in Computer Science 172, Springer-Verlag 1984, pp.235–246Google Scholar
  5. 5.
    Hromkovič,J.: Relation between Chomsky hierarchy and communication complexity hierarchy. Acta Mathematica Universtatis Comenianae 1986, to appearGoogle Scholar
  6. 6.
    Hromkovič, J.: Normed protocol and communication complexity. Computers and Artificial Intelligence 3, No.5, 1984, 415–422.Google Scholar
  7. 7.
    Lipton,R.J. — Sedgewick,R.: Lower bounds for VLSI. Proc. 13th Annual ACM STOC, 1981, 300–307.Google Scholar
  8. 8.
    Melhorn,K. — Schmidt,E.M.: Las Vegas is better than determinism in VLSI and distributed computing. Proc. 14th Annual ACM STOC, 1979, pp.209–213Google Scholar
  9. 9.
    Papadimitriou, C.H. — Sipser, M.: Communication complexity. Journal of Computer and System Sciences 28, 1984, 260–269.Google Scholar
  10. 10.
    Paturi,R. — Simon,J.: Probabilistic communication complexity. Proc. 25th Annual IEEE FOCS, 1984, pp.118–126Google Scholar
  11. 11.
    Škalikova,N.A.: Kletočnyje avtomaty in Russian. Ph.D. thesis, Moscow State University, Dept. of Mathematical Cybernetics, 1979Google Scholar
  12. 12.
    Thompson,C.D.: Area-time complexity for VLSI. Proc. 11th Annual ACM STOC, 1979, pp.209–213Google Scholar
  13. 13.
    Yao,A.C.: The entropic limitation on VLSI computations. Proc. 13th Annual ACM STOC, 1979, pp.209–213Google Scholar
  14. 14.
    Yao,A.C.: Some complexity question related to distributed computing. Proc. 11th Annual ACM STOC, 1979, pp.209–213Google Scholar
  15. 15.
    Yao,A.C.: Lower bounds by probabilistic arguments. Proc. 24th Annual IEEE FOCS, 1983, pp.420–428.Google Scholar
  16. 16.
    Gubáš,X. — Vaczulík,J.: Closure properties of the families of languages defined by communication complexity. ŠVOČ 1986, Komenský University, Bratislava, Dept. of Theoretical Cybernetics and Mathematical Informatics 1986 (in Slovak)Google Scholar
  17. 17.
    Kurcabová,V.: Communication complexity. Diplom thesis, Komenský University, Bratislava, Dept. of Theoretical Cybernetics and Mathematical Informatics 1986 (in Slovak)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Juraj Hromkovič
    • 1
  1. 1.Department of Theoretical Cybernetics and Mathematical InformaticsKomenský UniversityBratislavaCzechoslovakia

Personalised recommendations