An Application of Hindman's Theorem to a Problem on Communication Complexity

  • Authors:

  • Pavel Pudlák

  • Affiliations:

  • Mathematical Institute, Academy of Sciences, Prague, Czech Republic (e-mail: pudlak@math.cas.cz)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2003

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Abstract

We consider the $k$-party communication complexity of the problem of determining if a word $w$ is of the form $w_0a_1w_1a_2\dots w_{k-1}a_kw_k$, for fixed letters $a_1,\dots,a_k$. Using the well-known theorem of Hindman (a Ramsey-type result about finite subsets of natural numbers), we prove that for $k=4$ and $5$ the communication complexity of the problem increases with the length of the word $w$.