On the complexity of branching programs and decision trees for clique functions

  • Authors:
  • Ingo Wegener

  • Affiliations:
  • Univ. Dortmund, Dortmund, Federal Republic of Germany

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1988

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Abstract

Exponential lower bounds on the complexity of computing the clique functions in the Boolean decision-tree model are proved. For one-time-only branching programs, large polynomial lower bounds are proved for k-clique functions if k is fixed, and exponential lower bounds if k increases with n. Finally, the hierarchy of the classes BPd(P) of all sequences of Boolean functions that may be computed by d-times only branching programs of polynomial size is introduced. It is shown constructively that BP1(P) is a proper subset of BP2(P).