# A new approach to defining the communication complexity for VLSI

## Abstract

^{2}, i.e. it has the same relation to AT

^{2}as the original communication complexity. The reasons to define it are the following ones:

- 1,
S-communication complexity gives the strongest lower bounds Ω(n

^{2}) on AT^{2}in many cases when the communication complexity grants only constant lower bounds on AT^{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.

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