We introduce a complexity measure r for the class F of read-once formulas over the basis {AND,OR,NOT, XOR, MUX} and show that for any Boolean formula F in the class F, r(F) is a lower bound on the quantum query complexity of the Boolean function that F represents. We also show that for any Boolean function f represented by a formula in F, the deterministic query complexity of f is only quadratically larger than the quantum query complexity of f. Thus, the paper gives further evidence for the conjecture that there is an only quadratic gap for all functions.
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Hideaki FUKUHARA, Eiji TAKIMOTO, "Lower Bounds on Quantum Query Complexity for Read-Once Formulas with XOR and MUX Operators" in IEICE TRANSACTIONS on Information,
vol. E93-D, no. 2, pp. 280-289, February 2010, doi: 10.1587/transinf.E93.D.280.
Abstract: We introduce a complexity measure r for the class F of read-once formulas over the basis {AND,OR,NOT, XOR, MUX} and show that for any Boolean formula F in the class F, r(F) is a lower bound on the quantum query complexity of the Boolean function that F represents. We also show that for any Boolean function f represented by a formula in F, the deterministic query complexity of f is only quadratically larger than the quantum query complexity of f. Thus, the paper gives further evidence for the conjecture that there is an only quadratic gap for all functions.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E93.D.280/_p
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@ARTICLE{e93-d_2_280,
author={Hideaki FUKUHARA, Eiji TAKIMOTO, },
journal={IEICE TRANSACTIONS on Information},
title={Lower Bounds on Quantum Query Complexity for Read-Once Formulas with XOR and MUX Operators},
year={2010},
volume={E93-D},
number={2},
pages={280-289},
abstract={We introduce a complexity measure r for the class F of read-once formulas over the basis {AND,OR,NOT, XOR, MUX} and show that for any Boolean formula F in the class F, r(F) is a lower bound on the quantum query complexity of the Boolean function that F represents. We also show that for any Boolean function f represented by a formula in F, the deterministic query complexity of f is only quadratically larger than the quantum query complexity of f. Thus, the paper gives further evidence for the conjecture that there is an only quadratic gap for all functions.},
keywords={},
doi={10.1587/transinf.E93.D.280},
ISSN={1745-1361},
month={February},}
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TY - JOUR
TI - Lower Bounds on Quantum Query Complexity for Read-Once Formulas with XOR and MUX Operators
T2 - IEICE TRANSACTIONS on Information
SP - 280
EP - 289
AU - Hideaki FUKUHARA
AU - Eiji TAKIMOTO
PY - 2010
DO - 10.1587/transinf.E93.D.280
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E93-D
IS - 2
JA - IEICE TRANSACTIONS on Information
Y1 - February 2010
AB - We introduce a complexity measure r for the class F of read-once formulas over the basis {AND,OR,NOT, XOR, MUX} and show that for any Boolean formula F in the class F, r(F) is a lower bound on the quantum query complexity of the Boolean function that F represents. We also show that for any Boolean function f represented by a formula in F, the deterministic query complexity of f is only quadratically larger than the quantum query complexity of f. Thus, the paper gives further evidence for the conjecture that there is an only quadratic gap for all functions.
ER -