/ 06 11 05 4 v 2 2 4 A pr 2 00 7 Negative weights make adversaries stronger
نویسندگان
چکیده
The quantum adversary method is one of the most successful techniques for proving lower bounds on quantum query complexity. It gives optimal lower bounds for many problems, has application to classical complexity in formula size lower bounds, and is versatile with equivalent formulations in terms of weight schemes, eigenvalues, and Kolmogorov complexity. All these formulations rely on the principle that if an algorithm successfully computes a function then, in particular, it is able to distinguish between inputs which map to different values. We present a stronger version of the adversary method which goes beyond this principle to make explicit use of the stronger condition that the algorithm actually computes the function. This new method, which we call ADV, has all the advantages of the old: it is a lower bound on bounded-error quantum query complexity, its square is a lower bound on formula size, and it behaves well with respect to function composition. Moreover ADV is always at least as large as the adversary method ADV, and we show an example of a monotone function for which ADV(f) = Ω(ADV(f)1.098). We also give examples showing that ADV does not face limitations of ADV like the certificate complexity barrier and the property testing barrier.
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متن کاملnt - p h / 06 11 05 4 v 1 5 N ov 2 00 6 Negative weights makes adversaries stronger
The quantum adversary method is one of the most successful techniques for proving lower bounds on quantum query complexity. It gives optimal lower bounds for many problems, has application to classical complexity in formula size lower bounds, and is versatile with equivalent formulations in terms of weight schemes, eigenvalues, and Kolmogorov complexity. All these formulations are information-t...
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The cosmological evolution in Nonlinear Born-Infeld(hereafter NLBI) scalar field theory with negative potentials was investigated. The cosmological solutions in some important evolutive epoches were obtained. The different evolutional behaviors between NLBI and linear(canonical) scalar field theory have been presented. A notable characteristic is that NLBI scalar field behaves as ordinary matte...
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