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Time–Space Tradeoffs for Branching Programs

✍ Scribed by Paul Beame; T.S. Jayram; Michael Saks

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
265 KB
Volume
63
Category
Article
ISSN
0022-0000

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✦ Synopsis

We obtain the first non-trivial time-space tradeoff lower bound for functions f: {0, 1} n Q {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+e) n, for some constant e > 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 : 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 tradedoff for decision problems in this model.

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