On the Power of Randomized Branching Programs

Electronic Colloquium on Computational Complexity (ECCC) 01/1995; 2.
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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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Available from: Farid Ablayev, Oct 02, 2015
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    ABSTRACT: We investigate the relationship between probabilistic and nondeterministic complexity classes PP, BPP, NP and coNP with respect to ordered read-once branching programs (OBDDs). We exhibit two explicit Boolean functions qn; Rn such that: (1) qn : {0,1}n → { 0,1} belongs to BPP (NP (semi-circle up) coNP) in the context of OBDDs; (2) Rn : {0,1}n → {0,1} belongs to PP \ (BPP(semi-circle up) NP (semi-circle up) coNP) in the context of OBDDs. Both of these functions are not in AC0.
    Theoretical Computer Science 08/2001; 264(1):127-137. DOI:10.1016/S0304-3975(00)00216-4 · 0.66 Impact Factor
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    ABSTRACT: We show that the satisfiability problem for bounded-error probabilistic ordered branching programs is \NP -complete. If the error is very small, however (more precisely, if the error is bounded by the reciprocal of the width of the branching program), then we have a polynomial-time algorithm for the satisfiability problem.
    Theory of Computing Systems 11/2001; 34(5):471-487. DOI:10.1007/s00224-001-1011-9 · 0.53 Impact Factor
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    ABSTRACT: The complexity classes defined on the basis of branching programs are considered. Some basic relations are established between the complexity classes defined by the probabilistic and quantum branching programs (measure-once, as well as measure-many), computing with bounded or unbounded error. To prove these relations, we developed a method of “linear simulation” of a quantum branching program and a method of “quantum simulation” of a probabilistic branching program.
    Journal of Applied and Industrial Mathematics 02/2007; 1(1):33-44. DOI:10.1134/S1990478907010048
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