## Equivalence of Measures of Complexity Classes (0)

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Citations: | 70 - 19 self |

### BibTeX

@MISC{Breutzmann_equivalenceof,

author = {Josef Breutzmann and Jack H. Lutz},

title = {Equivalence of Measures of Complexity Classes},

year = {}

}

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### Abstract

The resource-bounded measures of complexity classes are shown to be robust with respect to certain changes in the underlying probability measure. Specifically, for any real number ffi ? 0, any uniformly polynomial-time computable sequence ~ fi = (fi 0 ; fi 1 ; fi 2 ; : : : ) of real numbers (biases) fi i 2 [ffi; 1 \Gamma ffi], and any complexity class C (such as P, NP, BPP, P/Poly, PH, PSPACE, etc.) that is closed under positive, polynomial-time, truth-table reductions with queries of at most linear length, it is shown that the following two conditions are equivalent. (1) C has p-measure 0 (respectively, measure 0 in E, measure 0 in E 2 ) relative to the coin-toss probability measure given by the sequence ~ fi. (2) C has p-measure 0 (respectively, measure 0 in E, measure 0 in E 2 ) relative to the uniform probability measure. The proof introduces three techniques that may be useful in other contexts, namely, (i) the transformation of an efficient martingale for one probability measu...