Results 1 - 10 of 57

Hardness vs. randomness

by Noam Nisan, Avi Wigderson - JOURNAL OF COMPUTER AND SYSTEM SCIENCES , 1994
"... We present a simple new construction of a pseudorandom bit generator, based on the constant depth generators of [N]. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (eg P, NC, PSPACE,...) using an arbitrary function tha ..."
Abstract - Cited by 298 (27 self) - Add to MetaCart
that is hard for C. This construction reveals an equivalence between the problem of proving lower bounds and the problem of generating good pseudorandom sequences. Our construction has many consequences. The most direct one is that efficient deterministic simulation of randomized algorithms is possible under

Pseudorandomness from shrinkage

by Russell Impagliazzo, Raghu Meka, David Zuckerman - In Proceedings of the Fifty-Third Annual IEEE Symposium on Foundations of Computer Science , 2012
"... One powerful theme in complexity theory and pseudorandomness in the past few decades has been the use lower bounds to give pseudorandom generators (PRGs). However, the general results using this hardness vs. randomness paradigm suffer a quantitative loss in parameters, and hence do not give nontrivi ..."
Abstract - Cited by 15 (1 self) - Add to MetaCart
One powerful theme in complexity theory and pseudorandomness in the past few decades has been the use lower bounds to give pseudorandom generators (PRGs). However, the general results using this hardness vs. randomness paradigm suffer a quantitative loss in parameters, and hence do not give

Nondeterministic Circuit Lower Bounds from Mildly Derandomizing Arthur-merlin Games

by Dieter van Melkebeek , et al. , 2012
"... In several settings derandomization is known to follow from circuit lower bounds that them-selves are equivalent to the existence of pseudorandom generators. This leaves open the question whether derandomization implies the circuit lower bounds that are known to imply it, i.e., whether the ability t ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
In several settings derandomization is known to follow from circuit lower bounds that them-selves are equivalent to the existence of pseudorandom generators. This leaves open the question whether derandomization implies the circuit lower bounds that are known to imply it, i.e., whether the ability

Quantum circuit complexity of one dimensional topological phases

by Yichen Huang, Xie Chen , 2014
"... Topological quantum states cannot be created from a product state with constant depth local unitary circuits and are in this sense more entangled than topologically trivial states. But how entangled are they? In this paper, we quantify the entanglement in one dimensional topological states by showin ..."
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by showing that a linear depth circuit is necessary to generate them from product states. We establish such a linear lower bound for both bosonic and fermionic topological phases and use symmetric circuits for phases with symmetry. On the other hand, we show that this linear lower bound can be saturated

Hardness vs. Randomness within Alternating Time

by Emanuele Viola , 2003
"... We study the complexity of building pseudorandom generators (PRGs) with logarithmic seed length from hard functions. We show that, starting from a function f: {0, 1} l → {0, 1} that is mildly hard on average, i.e. every circuit of size 2 Ω(l) fails to compute f on at least a 1/poly(l) fraction of in ..."
Abstract - Cited by 11 (0 self) - Add to MetaCart
We study the complexity of building pseudorandom generators (PRGs) with logarithmic seed length from hard functions. We show that, starting from a function f: {0, 1} l → {0, 1} that is mildly hard on average, i.e. every circuit of size 2 Ω(l) fails to compute f on at least a 1/poly(l) fraction

New constructions and applications . . .

by Gil Cohen , 2015
"... Pseudorandomness is the subfield of theoretical computer science which studies explicit constructions of objects that share desired properties with random objects. Results and techniques from pseudorandomness have found applications in many research fields, such as privacy, cryptography, coding theo ..."
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results from the field for solving fundamental problems in other research areas, such as secure multiparty computation, privacy amplification, and circuit lower bounds. In some cases, a priori, the connection to pseudorandomness is unclear. Acknowledgements Towards the end of my undergraduate studies

On the complexity of parallel hardness amplification for one-way functions

by Chi-jen Lu - In 3rd Theory of Cryptography Conference (TCC , 2006
"... Abstract. We prove complexity lower bounds for the tasks of hardness amplification of one-way functions and construction of pseudo-random generators from one-way functions, which are realized non-adaptively in black-box ways. First, we consider the task of converting a one-way function f: {0, 1} n → ..."
Abstract - Cited by 4 (0 self) - Add to MetaCart
Abstract. We prove complexity lower bounds for the tasks of hardness amplification of one-way functions and construction of pseudo-random generators from one-way functions, which are realized non-adaptively in black-box ways. First, we consider the task of converting a one-way function f: {0, 1} n

Almost-natural proofs

by Timothy Y. Chow - In IEEE Symposium on Foundations of Computer Science (FOCS , 2008
"... Razborov and Rudich have shown that so-called natural proofs are not useful for separating P from NP unless hard pseudorandom number generators do not exist. This famous result is widely regarded as a serious barrier to proving strong lower bounds in circuit complexity theory. By definition, a natur ..."
Abstract - Cited by 4 (0 self) - Add to MetaCart
Razborov and Rudich have shown that so-called natural proofs are not useful for separating P from NP unless hard pseudorandom number generators do not exist. This famous result is widely regarded as a serious barrier to proving strong lower bounds in circuit complexity theory. By definition, a

Randomness buys depth for approximate counting

by Emanuele Viola , 2010
"... We show that the promise problem of distinguishing n-bit strings of hamming weight ≥ 1/2 + Ω(1 / lg d−1 n) from strings of weight ≤ 1/2 − Ω(1 / lg d−1 n) can be solved by explicit, randomized (unbounded-fan-in) poly(n)-size depth-d circuits with error ≤ 1/3, but cannot be solved by deterministic pol ..."
Abstract - Cited by 9 (2 self) - Add to MetaCart
circuits we combine the switching lemma with an earlier depth-3 lower bound by the author (Comp. Complexity 2009). To exhibit randomized circuits we combine recent analyses by Amano (ICALP ’09) and Brody and Verbin (FOCS ’10) with derandomization. To make these circuits explicit – which we find important

On the complexity of hardness amplification

by Chi-jen Lu, Shi-chun Tsai, Hsin-lung Wu - In Proceedings of the 20th Annual IEEE Conference on Computational Complexity , 2005
"... We study the task of transforming a hard function f, with which any small circuit disagrees on (1 − δ)/2 fraction of the input, into a harder function f ′ , with which any small circuit disagrees on (1 − δ k)/2 fraction of the input, for δ ∈ (0, 1) and k ∈ N. We show that this process can not be car ..."
Abstract - Cited by 8 (1 self) - Add to MetaCart
. Finally, we derive similar lower bounds for any black-box construction of pseudorandom generators from hard functions.
Results 1 - 10 of 57