Non-commutative arithmetic circuits: depth reduction and size lower bounds
نویسندگان
چکیده
منابع مشابه
Non-Commutative Arithmetic Circuits: Depth Reduction and Size Lower Bounds
We investigate the phenomenon of depth-reduction in commutative and non-commutative arithmetic circuits. We prove that in the commutative setting, uniform semi-unbounded arithmetic circuits of logarithmic depth are as powerful as uniform arithmetic circuits of polynomial degree (and unrestricted depth); earlier proofs did not work in the uniform setting. This also provides a uni ed proof of the...
متن کاملNon - Commutative Arithmetic Circuits : DepthReduction and Size Lower
We investigate the phenomenon of depth-reduction in commutative and non-commutative arithmetic circuits. We prove that in the commutative setting, uniform semi-unbounded arithmetic circuits of logarithmic depth are as powerful as uniform arithmetic circuits of polynomial degree; earlier proofs did not work in the uniform setting. This also provides a uni ed proof of the circuit characterization...
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Nisan (STOC 1991) exhibited a polynomial which is computable by linear-size non-commutative circuits but requires exponential-size non-commutative algebraic branching programs. Nisan’s hard polynomial is in fact computable by linear-size “skew circuits.” Skew circuits are circuits where every multiplication gate has the property that all but one of its children is an input variable or a scalar....
متن کاملSuperpolynomial Lower Bounds for General Homogeneous Depth 4 Arithmetic Circuits
In this paper, we prove superpolynomial lower bounds for the class of homogeneous depth 4 arithmetic circuits. We give an explicit polynomial in VNP of degree n in n variables such that any homogeneous depth 4 arithmetic circuit computing it must have size n . Our results extend the works of Nisan-Wigderson [NW95] (which showed superpolynomial lower bounds for homogeneous depth 3 circuits), Gup...
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We investigate the power of Non-commutative Arithmetic Circuits, which compute polynomials over the free non-commutative polynomial ring F〈x1, . . . ,xN〉, where variables do not commute. We consider circuits that are restricted in the ways in which they can compute monomials: this can be seen as restricting the families of parse trees that appear in the circuit. Such restrictions capture essent...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1998
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(97)00227-2