A read-once branching program lower bound of Ω(2n/4) for integer multiplication using universal hashing

  • Authors:

  • Beate Bollig;Philipp Woelfel

  • Affiliations:

  • FB Informatik, LS2, Univ. Dortmund, 44221 Dortmund, Germany;FB Informatik, LS2, Univ. Dortmund, 44221 Dortmund, Germany

  • Venue:
  • STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
  • Year:
  • 2001

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Abstract

Branching programs (BPs) are a well-established computation and representation model for Boolean functions. Especially read-once branching programs (BP1s) have been studied intensively. Exponential lower bounds on the BP1 complexity of explicit functions have been known for a long time. Nevertheless, the proof of exponential lower bounds on the read-once branching program size of selected functions is sometimes difficult. Motivated by the applications the BP1 complexity of fundamental functions is of interest. It took quite a long time until Ponzio [16, 17] was able to prove a bound of 2^{&OHgr;(\sqrt{n})} for integer multiplication. Combining results and methods for universal hashing with lower bound techniques for BP1s a lower bound of &OHgr;(2^{n/4}) on the size of BP1s for integer multiplication is presented in this paper.