computational complexity

, Volume 3, Issue 1, pp 1–18 | Cite as

On lower bounds for read-k-times branching programs

  • A. Borodin
  • A. Razborov
  • R. Smolensky


A syntactic read-k-times branching program has the restriction that no variable occurs more thank times on any path (whether or not consistent) of the branching program. We first extend the result in [31], to show that the “n/2 clique only function”, which is easily seen to be computable by deterministic polynomial size read-twice programs, cannot be computed by nondeterministic polynomial size read-once programs, although its complement can be so computed. We then exhibit an explicit Boolean functionf such that every nondeterministic syntactic read-k-times branching program for computingf has size exp
$$\left( {\Omega \left( {\frac{n}{{4^k k^3 }}} \right)} \right).$$

Subject classifications

68Q05 68Q25 


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Copyright information

© Birkhäuser Verlag 1993

Authors and Affiliations

  • A. Borodin
    • 1
  • A. Razborov
    • 2
  • R. Smolensky
    • 1
  1. 1.Department of Computer ScienceUniversity of TorontoTorontoCANADA
  2. 2.Steklov Mathematical InstituteMoscowRUSSIA

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