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:
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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.
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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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Hromkovič, J. (1986). A new approach to defining the communication complexity for VLSI. In: Gruska, J., Rovan, B., Wiedermann, J. (eds) Mathematical Foundations of Computer Science 1986. MFCS 1986. Lecture Notes in Computer Science, vol 233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0016268
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DOI: https://doi.org/10.1007/BFb0016268
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