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122
Lowness for the class of Schnorr random reals
 SIAM Journal on Computing
, 2005
"... We answer a question of AmbosSpies and Kučera in the affirmative. They asked whether, when a real is low for Schnorr randomness, it is already low for Schnorr tests. ..."
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Cited by 19 (4 self)
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We answer a question of AmbosSpies and Kučera in the affirmative. They asked whether, when a real is low for Schnorr randomness, it is already low for Schnorr tests.
SCHNORR RANDOMNESS AND THE LEBESGUE DIFFERENTIATION THEOREM
, 2012
"... We exhibit a close correspondence between L1computable functions and Schnorr tests. Using this correspondence, we prove that a point x ∈ [0,1] d is Schnorr random if and only if the Lebesgue Differentiation Theorem holds at x for all L1computable functions f ∈ L1([0,1] d). ..."
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Cited by 13 (0 self)
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We exhibit a close correspondence between L1computable functions and Schnorr tests. Using this correspondence, we prove that a point x ∈ [0,1] d is Schnorr random if and only if the Lebesgue Differentiation Theorem holds at x for all L1computable functions f ∈ L1([0,1] d).
An integral test for Schnorr randomness and its applications
"... Abstract. The author proposed in the previous paper that a characterization of a randomness notion by integral tests is a useful tool to study the relation between algorithmic randomness and computable analysis. In this paper we give a version of Schnorr randomness. With this result we show the con ..."
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Cited by 1 (1 self)
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Abstract. The author proposed in the previous paper that a characterization of a randomness notion by integral tests is a useful tool to study the relation between algorithmic randomness and computable analysis. In this paper we give a version of Schnorr randomness. With this result we show
Truthtable Schnorr randomness and truthtable reducible randomness
 Mathematical Logic Quarterly
, 2011
"... Schnorr randomness and computably randomness are natural concepts of random sequences. However van Lambalgen’s Theorem fails for both randomnesses. In this paper we define truthtable Schnorr randomness (defined in [6] too only by martingales) and truthtable reducibly randomness, for which we prov ..."
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Cited by 9 (5 self)
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Schnorr randomness and computably randomness are natural concepts of random sequences. However van Lambalgen’s Theorem fails for both randomnesses. In this paper we define truthtable Schnorr randomness (defined in [6] too only by martingales) and truthtable reducibly randomness, for which we
Schnorr dimension
 IN EXPONENTIAL TIME, COMPUTATIONAL COMPLEXITY 2001, 210217, IEEE COMPUTER SOCIETY
, 2001
"... Following Lutz’s approach to effective (constructive) dimension, we define a notion of dimension for individual sequences based on Schnorr’s concept(s) of randomness. In contrast to computable randomness and Schnorr randomness, the dimension concepts defined via computable martingales and Schnorr t ..."
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Cited by 5 (2 self)
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Following Lutz’s approach to effective (constructive) dimension, we define a notion of dimension for individual sequences based on Schnorr’s concept(s) of randomness. In contrast to computable randomness and Schnorr randomness, the dimension concepts defined via computable martingales and Schnorr
Schnorr triviality is equivalent to being a basis for Schnorr
"... We present some new characterizations of Schnorr triviality. The wellknown notion of Ktriviality is dened using complexity K via a prexfree machine, with which MartinLof randomness has a characterization. In a similar manner, Schnorr triviality is dened using complexity via a computable measure ..."
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We present some new characterizations of Schnorr triviality. The wellknown notion of Ktriviality is dened using complexity K via a prexfree machine, with which MartinLof randomness has a characterization. In a similar manner, Schnorr triviality is dened using complexity via a computable
On the Importance of Checking Cryptographic Protocols for Faults
, 1997
"... We present a theoretical model for breaking various cryptographic schemes by taking advantage of random hardware faults. We show how to attack certain implementations of RSA and Rabin signatures. An implementation of RSA based on the Chinese Remainder Theorem can be broken using a single erroneous s ..."
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Cited by 405 (6 self)
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We present a theoretical model for breaking various cryptographic schemes by taking advantage of random hardware faults. We show how to attack certain implementations of RSA and Rabin signatures. An implementation of RSA based on the Chinese Remainder Theorem can be broken using a single erroneous
Schnorr triviality and its equivalent notions
 Theory of Computing Systems
"... We give some new characterizations of Schnorr triviality. In concrete terms, we introduce a reducibility related to decidable prefixfree machines and show the equivalence with Schnorr reducibility. We also give a uniformSchnorrrandomness version of the equivalence of LRreducibility and LKreduc ..."
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Cited by 3 (3 self)
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We give some new characterizations of Schnorr triviality. In concrete terms, we introduce a reducibility related to decidable prefixfree machines and show the equivalence with Schnorr reducibility. We also give a uniformSchnorrrandomness version of the equivalence of LRreducibility and LK
VAN LAMBALGEN’S THEOREM FOR UNIFORMLY RELATIVE SCHNORR AND COMPUTABLE RANDOMNESS
"... Abstract. We correct Miyabe’s proof of van Lambalgen’s theorem for truthtable Schnorr randomness (which we will call uniformly relative Schnorr randomness). An immediate corollary is one direction of van Lambalgen’s theorem for Schnorr randomness. It has been claimed in the literature that this cor ..."
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Abstract. We correct Miyabe’s proof of van Lambalgen’s theorem for truthtable Schnorr randomness (which we will call uniformly relative Schnorr randomness). An immediate corollary is one direction of van Lambalgen’s theorem for Schnorr randomness. It has been claimed in the literature
On Schnorr and computable randomness, martingales, and machines
 Mathematical Logic Quarterly
, 2004
"... examine the randomness and triviality of reals using notions arising from martingales and prefixfree machines. ..."
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Cited by 15 (5 self)
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examine the randomness and triviality of reals using notions arising from martingales and prefixfree machines.
Results 1  10
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122