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Depth-Independent Lower Bounds on the Communication Complexity of Read-Once Boolean Formulas

  • Rahul Jain
  • Hartmut Klauck
  • Shengyu Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6196)

Abstract

We show lower bounds of \(\Omega(\sqrt{n})\) and Ω(n 1/4) on the randomized and quantum communication complexity, respectively, of all n-variable read-once Boolean formulas. Our results complement the recent lower bound of Ω(n/8 d ) by Leonardos and Saks [LS09] and Ω(n/2 O(dlogd)) by Jayram, Kopparty and Raghavendra [JKR09] for randomized communication complexity of read-once Boolean formulas with depth d.

We obtain our result by “embedding” either the Disjointness problem or its complement in any given read-once Boolean formula.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Rahul Jain
    • 1
  • Hartmut Klauck
    • 2
  • Shengyu Zhang
    • 3
  1. 1.Centre for Quantum Technologies and Department of Computer ScienceNational University of Singapore 
  2. 2.Centre for Quantum Technologies and SPMSNanyang Technological University 
  3. 3.Department of Computer Science and EngineeringThe Chinese University of Hong Kong 

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