Compressibility and Resource Bounded Measure
نویسندگان
چکیده
منابع مشابه
Resource-Bounded Measure
A general theory of resource-bounded measurability and measure is developed. Starting from any feasible probability measure ν on the Cantor space C (the set of all decision problems) and any suitable complexity class C ⊆ C, the theory identifies the subsets of C that are ν-measurable in C and assigns measures to these sets, thereby endowing C with internal measure-theoretic structure. Classes C...
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We prove that the following classes have resource-bounded measure zero: the class of self-reducible sets. the class of commitable sets. the class of sets that are non-adaptively autoreducible with a linear number of queries. the class of disjunctively autoreducible sets. 2
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Supported by the Human Capital and Mobility Program of the European Community under grant CHRX-CT93-0415 (COLORET). Mathematisches Institut, Universit at Heidelberg, D-69120 Heidelberg, Germany Universidad de Zaragoza, Dept. Inform atica, CPS, Mar a del Luna 3, E-50015 Zaragoza, Spain We survey recent results on resource-bounded measure and randomness in structural complexity theory. In partic...
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Most research on resource-bounded measure and randomness has focused on the uniform probability density, or Lebesgue measure, on {0, 1}∞; the study of resource-bounded measure theory with respect to a nonuniform underlying measure was recently initiated by Breutzmann and Lutz [1]. In this paper we prove a series of fundamental results on the role of nonuniform measures in resource-bounded measu...
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In this paper we extend a key result of Nisan and Wigderson NW94] to the nondeterministic setting: for all > 0 we show that if there is a language in E = DTIME(2 O(n)) that is hard to approximate by nondeterministic circuits of size 2 n , then there is a pseudorandom generator that can be used to derandomize BP NP (in symbols, BP NP = NP). By applying this extension we are able to answer some o...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2001
ISSN: 0097-5397,1095-7111
DOI: 10.1137/s0097539797317123