On the power of randomized branching programs

Abstract

We define the notion of a randomized branching program in the natural way similar to the definition of a randomized circuit. We exhibit an explicit function f _n for which we prove that:

• 1) f_n can be computed by polynomial size randomized read-once ordered branching program with a small one-sided error;

• 2) f_n cannot be computed in polynomial size by deterministic read-once branching programs;

• 3) f_n cannot be computed in polynomial size by deterministic read-κ-times ordered branching program for k = o(n/log n) (the required deterministic size is exp (Ω (n/k))).

Keywords

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Research partially supported by the Volkswagen-Stiftung and the Basic Research Grant 96-01-01962

Research partially supported by DFG Grant K A 673/4-1, by the ESPRIT BR Grants 7097 and EC-US 030, and by the Volkswagen-Stiftung.