Time-space tradeoffs for branching programs

Paul Beame, T. S. Jayram, Michael Saks

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


We obtain the first non-trivial time-space tradeoff lower bound for functions f:{0,1}n → {0,1} on general branching programs by exhibiting a Boolean function f that requires exponential size to be computed by any branching program of length (1 + ε) n, for some constant ε > 0. We also give the first separation result between the syntactic and semantic read-k models (A. Borodin et al., Comput. Complexity 3 (1993), 1-18) for k > 1 by showing that polynomial-size semantic read-twice branching programs can compute functions that require exponential size on any semantic read-k branching program. We also show a time-space tradeoff result on the more general R-way branching program model (Borodin et al., 1993): for any k, we give a function that requires exponential size to be computed by length kn q-way branching programs, for some q = q(k). This result gives a similar tradeoff for RAMs, and thus provides the first nontrivial time-space tradeoff for decision problems in this model.

Original languageEnglish (US)
Pages (from-to)542-572
Number of pages31
JournalJournal of Computer and System Sciences
Issue number4
StatePublished - Dec 2001

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science
  • Applied Mathematics
  • Computer Networks and Communications
  • Computational Theory and Mathematics


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