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ResourceBounded Measure and Randomness
"... We survey recent results on resourcebounded measure and randomness in structural complexity theory. In particular, we discuss applications of these concepts to the exponential time complexity classes and . Moreover, we treat timebounded genericity and stochasticity concepts which are weaker than ..."
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Cited by 43 (6 self)
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We survey recent results on resourcebounded measure and randomness in structural complexity theory. In particular, we discuss applications of these concepts to the exponential time complexity classes and . Moreover, we treat timebounded genericity and stochasticity concepts which are weaker than
Resourcebounded Measure on Probabilistic Classes
"... We extend Lutz’s resourcebounded measure to probabilistic classes, and obtain notions of resourcebounded measure on probabilistic complexity classes such as BPE and BPEXP. Unlike former attempts, our resource bounded measure notions satisfy all three basic measure properties, that is every singlet ..."
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We extend Lutz’s resourcebounded measure to probabilistic classes, and obtain notions of resourcebounded measure on probabilistic complexity classes such as BPE and BPEXP. Unlike former attempts, our resource bounded measure notions satisfy all three basic measure properties, that is every
Results on ResourceBounded Measure
, 1997
"... . We construct an oracle relative to which NP has pmeasure 0 but D p has measure 1 in EXP. This gives a strong relativized negative answer to a question posed by Lutz [Lut96]. Secondly, we give strong evidence that BPP is small. We show that BPP has pmeasure 0 unless EXP = MA and thus the polyn ..."
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Cited by 3 (0 self)
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the polynomialtime hierarchy collapses. This contrasts with the work of Regan et. al. [RSC95], where it is shown that P=poly does not have pmeasure 0 if exponentially strong pseudorandom generators exist. 1 Introduction Since the introduction of resourcebounded measure by Lutz [Lut92], many researchers
ResourceBounded Measure and Autoreducibility
, 1996
"... We prove that the following classes have resourcebounded measure zero: ffl the class of selfreducible sets. ffl the class of commitable sets. ffl the class of sets that are nonadaptively autoreducible with a linear number of queries. ffl the class of disjunctively autoreducible sets. 1 Intro ..."
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We prove that the following classes have resourcebounded measure zero: ffl the class of selfreducible sets. ffl the class of commitable sets. ffl the class of sets that are nonadaptively autoreducible with a linear number of queries. ffl the class of disjunctively autoreducible sets. 1
Twelve Problems in ResourceBounded Measure
"... A significant segment of the complexity theory community has taken up the study of resourcebounded measure as a tool in understanding complexity classes. For many theoreticians, however, the central problems and accomplishments of this area remain unknown. In this edition of the Column, two leader ..."
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A significant segment of the complexity theory community has taken up the study of resourcebounded measure as a tool in understanding complexity classes. For many theoreticians, however, the central problems and accomplishments of this area remain unknown. In this edition of the Column, two
On Pseudorandomness and ResourceBounded Measure
 Theoretical Computer Science
, 1997
"... In this paper we extend a key result of Nisan and Wigderson [17] to the nondeterministic setting: for all ff ? 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 ffn , then there is a pseudorandom generator that can be u ..."
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Cited by 43 (3 self)
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for ZPP NP . 1 Introduction In recent years, following the development of resourcebounded meas...
Resourcebounded measure
 In Proceedings of the 13th IEEE Conference on Computational Complexity
, 1998
"... ar ..."
Resource Bounded Measure and Learnability
 IN PROC. 13TH ANNUAL IEEE CONFERENCE ON COMPUTATIONAL COMPLEXITY
, 1998
"... We consider the resource bounded measure of polynomialtime learnable subclasses of polynomialsize circuits. We show that if EXP 6= MA, then every PAClearnable subclass of P=poly has EXPmeasure zero. We introduce a nonuniformly computable variant of resource bounded measure and show that, for eve ..."
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Cited by 2 (0 self)
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We consider the resource bounded measure of polynomialtime learnable subclasses of polynomialsize circuits. We show that if EXP 6= MA, then every PAClearnable subclass of P=poly has EXPmeasure zero. We introduce a nonuniformly computable variant of resource bounded measure and show that
Two Results on ResourceBounded Measure
, 1996
"... We construct an oracle relative to which NP has pmeasure 0 but D p has measure 1 in EXP. This gives a strong relativized negative answer to a question posed by Lutz [Lut96]. Secondly, we give strong evidence that BPP is small. We show that BPP has pmeasure 0 unless EXP = MA and the polynomialti ..."
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time hierarchy collapses. This contrasts the work of Regan et al. [RSC95], where it is shown that P=poly does not have pmeasure 0 unless strong pseudorandom generators do not exist. 1 Introduction Since the introduction of resourcebounded measure by Lutz [Lut92], many researchers investigated the size
Contributions to the Study of ResourceBounded Measure
, 1994
"... r of other people have contributed with different ideas, among others Peter Miltersen, Eric Allender, and Martin Strauss. Thanks to all the people that helped me during my visits to Iowa State University, the University of Ulm, the University of California at Santa Barbara and the University of Aarh ..."
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r of other people have contributed with different ideas, among others Peter Miltersen, Eric Allender, and Martin Strauss. Thanks to all the people that helped me during my visits to Iowa State University, the University of Ulm, the University of California at Santa Barbara and the University of Aarhus. I specially appreciate the hospitality of Robyn Lutz and Celia Wrathall. The Spanish Ministerio de Educacion y Ciencia supported this work through grant FPIPN90 25434951. I received partial support from Acci'on Integrada HA047, by the ESPRIT EC project 3075 (ALCOM) and by National Science Foundation Grant CCR9157382. The people in the Department de Llenguatges i Sistemes Inform`atics have given me their friendship and help through these years. In the section of Theoretical Computer Science I found lots of interesting discussions and people that listened to my often still incoherent ideas. Finally, I thank my family for being there. And Juanjo, for his love and support. Conten
Results 1  10
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