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Separating complexity classes related to bounded alternating ω-branching programs

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Abstract

We develop a theory of communication within branching programs that provides exponential lower bounds on the size of branching programs that are bounded alternating. Our theory is based on the algebraic concept of Ω-branching programs, ω: ℕ → ℝ, a semiring homomorphism, that generalizes ordinary branching programs, Ω-branching programs [M2] andMOD p-branching programs [DKMW].

Due to certain exponential lower and polynomial upper bounds on the size of bounded alternating ω-branching programs we are able to separate the corresponding complexity classesNℒ ba ,co-Nℒ ba ⊕ℒ ba , andMOD p -ℒ ba ,p prime, from each other, and from that classes corresponding to oblivious linear length-bounded branching programs investigated in the past.

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Authors and Affiliations

  1. FB IV-Informatik, Universität Trier, D-54286, Trier, Germany

    C. Meinel

  2. Institut für Numerisch und Angewandte Mathematik, Georg-August-Universität Göttingen, D-37083, Göttingen, Germany

    S. Waack

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  1. C. Meinel
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  2. S. Waack
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Meinel, C., Waack, S. Separating complexity classes related to bounded alternating ω-branching programs. Math. Systems Theory 28, 21–39 (1995). https://doi.org/10.1007/BF01294594

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