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