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On the Power of Randomized Branching Programs

Electronic Colloquium on Computational Complexity (ECCC) 01/1995; 2.
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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 fn 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) fn cannot be computed in polynomial size by deterministic readonce branching programs; 3) fn cannot be computed in polynomial size by deterministic read- k-times ordered branching program for k = o(n= log n) (the required deterministic size is exp GammaOmega Gamma n k DeltaDelta ). 1 Preliminaries Different models of branching programs introduced in [13, 15], have been studied extensively in the last decade (see for example [19]). A survey of known lower bounds for different models of branching programs can be found in [17]. Developments in the field of digital design and verification have led to the introduction of restricted forms of branching programs. In parti...

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    ABSTRACT: We present several results on comparative complexity for di?erent variants of OBDD models. - We present some results on comparative complexity of classical and quantum OBDDs. We consider a partial function depending on pa- rameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2 but any classical OBDD (deter- ministic or stable bounded error probabilistic) needs width 2k+1. - We consider quantum and classical nondeterminism. We show that quantum nondeterminism can be more e?cient than classical one. In particular, an explicit function is presented which is computed by a quantum nondeterministic OBDD with constant width but any clas- sical nondeterministic OBDD for this function needs non-constant width. - We also present new hierarchies on widths of deterministic and non- deterministic OBDDs. We focus both on small and large widths.

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