Advertisement

An Upper Bound for a Communication Game Related to Time-Space Tradeoffs

  • Pavel PudlákEmail author
  • Jiří Sgall
Chapter

Summary.

We prove an unexpected upper bound on a communication game proposed by Jeff Edmonds and Russell Impagliazzo [2, 3] as an approach for proving lower bounds for time-space tradeoffs for branching programs. Our result is based on a generalization of a construction of Erdős, Frankl and Rödl [5] of a large 3-hypergraph with no 3 distinct edges whose union has at most 6 vertices.

Notes

Acknowledgements

We would like to thank Russell Impagliazzo and Jeff Edmonds for many fruitful discussions. We are grateful to Vojta Rödl for pointing to us the literature on the related extremal problems.

Bibliography

  1. 1.
    F.A. Behrend, On sets of integers which contain no three in arithmetic progression, Proc. Nat. Acad. Sci. 23 (1946), 331–332.MathSciNetCrossRefGoogle Scholar
  2. 2.
    J. Edmonds and R. Impagliazzo Towards time-space lower bounds on branching programs, manuscript.Google Scholar
  3. 3.
    J. Edmonds and R. Impagliazzo About time-space bounds for st-connectivity on branching programs, manuscript.Google Scholar
  4. 4.
    J. Edmonds and R. Impagliazzo A more general communication game related to time-space tradeoffs, manuscript.Google Scholar
  5. 5.
    P. Erdős, P. Frankl, and V. Rödl, The asymptotic number of graphs not containing a fixed subgraph, Graphs and Combinatorics 2, 113–121 (1986)MathSciNetCrossRefGoogle Scholar
  6. 6.
    R.L. Graham and V. Rödl, Numbers in Ramsey Theory, In: Surveys in combinatorics (ed. I. Anderson), London Mathematical Society lecture note series 103, pp. 111–153,1985.Google Scholar
  7. 7.
    D.R. Heath-Brown, Integer sets containing no arithmetic progressions, preprint, 1986.Google Scholar
  8. 8.
    I.Z. Rusza and E. Szemerédi, Triple systems with no six points carrying three triangles, Coli. Math. Soc. Janos Bolyai 18 (1978), pp. 939–945.Google Scholar
  9. 9.
    E. Szemerédi, Regular partitions of graphs, In : Proc. Coloq. Int. CNRS, Paris, CNRS, 1976, 399–401.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Academy of SciencesInstitute of MathematicsPragueCzech Republic
  2. 2.Computer Science Institute of Charles UniversityPragueCzech Republic

Personalised recommendations