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Relativized Worlds without Worst-Case to Average-Case Reductions for NP
[chapter]

2010
*
Lecture Notes in Computer Science
*

We prove that relative

doi:10.1007/978-3-642-15369-3_56
fatcat:6nedksj2j5gnpigavopxrjho34
*to*an oracle, there is no*worst*-*case**to**average*-*case**reduction**for**NP*. ... In fact, we prove that relative*to*an oracle, there is no*worst*-*case**to*errorless-*average*-*case**reduction*from*NP**to*BPP*NP*. ... Acknowledgments First and foremost, I thank Luca Trevisan*for*suggesting the research topic. I thank Luca Trevisan, Dieter van Melkebeek, Ronen Shaltiel, and anonymous reviewers*for*helpful comments. ...##
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Relativized Worlds without Worst-Case to Average-Case Reductions for NP

2012
*
ACM Transactions on Computation Theory
*

We prove that relative

doi:10.1145/2355580.2355583
fatcat:32ecj6wnlndyvdo7iw6plbn3fq
*to*an oracle, there is no*worst*-*case**to**average*-*case**reduction**for**NP*. ... In fact, we prove that relative*to*an oracle, there is no*worst*-*case**to*errorless-*average*-*case**reduction*from*NP**to*BPP*NP*. ... Acknowledgments First and foremost, I thank Luca Trevisan*for*suggesting the research topic. I thank Luca Trevisan, Dieter van Melkebeek, Ronen Shaltiel, and anonymous reviewers*for*helpful comments. ...##
###
If NP Languages are Hard on the Worst-Case, Then it is Easy to Find Their Hard Instances

2007
*
Computational Complexity
*

This is the first

doi:10.1007/s00037-007-0235-8
fatcat:x2ubi7gojzdlzdrpudwyuvwvd4
*worst*-*case**to**average*-*case**reduction**for**NP*of any kind. ... (unless*NP*is easy in the*worst**case*). ... We also thank Salil and Rahul Santhanam*for*valuable comments on an earlier version of the manuscript. We thank the anonymous referees*for*helpful comments. ...##
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New connections between derandomization, worst-case complexity and average-case complexity
[article]

2006
*
Electronic colloquium on computational complexity
*

Thus our techniques show a way

dblp:journals/eccc/GutfreundT06
fatcat:a34uuphxkndbti3rzsrzje2ke4
*to*bypass black-box impossibility arguments regarding*worst*-*case**to**average*-*case**reductions*. ... There has been a long line of research trying*to*explain our failure in proving worstcase*to**average*-*case**reductions*within*NP*[FF93, Vio03, BT03, AGGM06]. ... Andrej Bogdanov*for*pointing out*to*us that Theorem 5.2 follows directly from a generalization of [BT03] (i.e. Theorem 5.1). Previously we had a more complicated and weaker statement. Charlie ...##
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Structural Average Case Complexity

1996
*
Journal of computer and system sciences (Print)
*

A new notion of \real polynomial-time computations" is introduced based on

doi:10.1006/jcss.1996.0024
fatcat:muvu7uuxiva2rfo2p4ygv7zpdy
*average*polynomial-time computations*for*arbitrary distributions from a xed set, and it is used*to*characterize the*worst*-*case*...*for*Random-*NP*are Turing self-reducible. ... Acknowledgments The authors would like*to*thank Professor Jos e Balc azar and Professor Uwe S c h oning*for*organizing workshops in Barcelona and Ulm in 1991 where many discussions on*average*-*case*complexity ...##
###
Structural average case complexity
[chapter]

1992
*
Lecture Notes in Computer Science
*

A new notion of \real polynomial-time computations" is introduced based on

doi:10.1007/3-540-56287-7_100
fatcat:rcfbjdt24rfjpav36znuhiyfke
*average*polynomial-time computations*for*arbitrary distributions from a xed set, and it is used*to*characterize the*worst*-*case*...*for*Random-*NP*are Turing self-reducible. ... Acknowledgments The authors would like*to*thank Professor Jos e Balc azar and Professor Uwe S c h oning*for*organizing workshops in Barcelona and Ulm in 1991 where many discussions on*average*-*case*complexity ...##
###
Finding Pessiland
[chapter]

2006
*
Lecture Notes in Computer Science
*

Introduction Pessiland, coined by Impagliazzo [I95], is a

doi:10.1007/11681878_22
fatcat:rilppn3n3zfb3ikgtiq74ljucu
*world*in which there are hard-on-*average*languages in*NP*but no one-way functions. ...*For*2-round argument systems, it is known that a relaxation of hard-on-*average*languages in*NP*is necessary [W05] (also, Appendix A.2). ... In addition, I thank Lance Fortnow and Russell Impagliazzo*for*pointing out previous constructions of Pessiland, and the anonymous referees*for*their helpful and constructive feedback. ...##
###
Towards Non-Black-Box Lower Bounds in Cryptography
[chapter]

2011
*
Lecture Notes in Computer Science
*

We consider

doi:10.1007/978-3-642-19571-6_35
fatcat:gd4qwcndgzfihe7xnuv373p354
*average*-*case*strengthenings of the traditional assumption that coNP is not contained in AM. ... ., one-way permutations, collision-resistant hash-functions, constant-round statistically hiding commitments, and constant-round black-box zero-knowledge proofs*for**NP*) from one-way functions, assuming ... Acknowledgements We are thankful*to*the anonymous TCC-reviewers*for*their insightful comments. ...##
###
Structure vs. Hardness Through the Obfuscation Lens
[chapter]

2017
*
Lecture Notes in Computer Science
*

There is no fully black-box

doi:10.1007/978-3-319-63688-7_23
fatcat:tw76c3gqnvetvfburf4ttppsza
*reduction*of any (even*worst*-*case*) hard problem in SZK*to*IO and OWPs. Corollary 1.2 (from [SW14, Wat15], Informal). ... The existence of one-way permutations (OWPs) requires a hard problem in*NP*∩ coNP [Bra79]; the same holds*for*restricted*cases*of public-key encryption schemes satisfying specific structural properties ... We also thank the anonymous FOCS'16 reviewers*for*their valuable comments. ...##
###
On the Existence of Weak One-Way Functions
[article]

2017
*
arXiv
*
pre-print

of the decision problem (language) L_0 (however,

arXiv:1609.01575v3
fatcat:va2sg7kmv5c3jjk4dvleta6bb4
*without*any auxiliary information that could ease the decision like a polynomial witness). ... well-known discrete time-hierarchy theorem from complexity theory), we construct another intractable decision problem L⊆{0,1}^* that has its words scattered across {0,1}^ℓ at a relative frequency p(ℓ),*for*... Acknowledgment The author is indebted*to*Sandra König from the Austrian Institute of Technology,*for*spotting some errors, as well as*to*Patrick Horster,*for*valuable discussions about earlier versions ...##
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The status of the P versus NP problem

2009
*
Communications of the ACM
*

Acknowledgments Thanks

doi:10.1145/1562164.1562186
fatcat:gxquaagohnc7jdxdhaaexzof44
*to*Rahul Santhanam*for*many useful discussions and comments. Josh Grochow wrote an early draft of Section 9. The anonymous referees provided critical advice. ... Whether similar*worst*-*to*-*average**reductions*hold*for**NP*-complete sets is an important open problem. ... Heuristics and*Average*-*Case*Complexity The study of*NP*-completeness focuses on how algorithms perform on the*worst*possible inputs. ...##
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An Atypical Survey of Typical-Case Heuristic Algorithms
[article]

2012
*
arXiv
*
pre-print

How close can heuristic algorithms get

arXiv:1210.8099v1
fatcat:g52yqzbgtjd4bb2jypg6fw6txa
*to*always giving the right answer,*without*inducing seismic complexity-theoretic consequences? ... Heuristic approaches often do so well that they seem*to*pretty much always give the right answer. ... Acknowledgments We are grateful*to*Paul Beame*for*providing helpful SAT references. References ...##
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One-way Functions and Partial MCSP
[article]

2021
*
Electronic colloquium on computational complexity
*

It remained an open problem

dblp:journals/eccc/AllenderCMTV21
fatcat:og52i7xvhbbadpwpz7ex7r2egq
*to*establish such an equivalence*for*the*average*-*case*hardness of some natural*NP*-complete problem. ... Thus the existence of OWFs is inextricably linked*to*the*average*-*case*hardness of this*NP*-complete problem. ... Acknowledgements We would like*to*thank Russell Impagliazzo*for*explaining his work [IL90]*to*us, and Ján Pich and Ninad Rajgopal*for*illuminating discussions. ...##
###
The P versus NP Problem
[article]

2010
*
arXiv
*
pre-print

See http://gauss.claymath.org:8888/millennium/P_vs_NP/pvsnp.pdf

arXiv:1001.3816v2
fatcat:ghl35v6tdjfkdmvqgl5g6cb53i
*for*the original text. ... This article was plagiarized directly from Stephen Cook's description of the problem*for*the Clay Mathematics Institute. ... at least steps in the*worst**case*,*for*some . ...##
###
The NP-completeness column

2007
*
ACM Transactions on Algorithms
*

Garey and I used in our book "Computers and Intractability: A Guide

doi:10.1145/1240233.1240247
fatcat:2rnecxy6ufcihmva53od5i6234
*to*the Theory of*NP*-Completeness," W. H. Freeman & Co., New York, 1979, hereinafter referred*to*as " [G&J]." ... This is the 26th edition of a column that covers new developments in the theory of*NP*-completeness. The presentation is modeled on that which M. R. ... Each could turn out*to*be in P*without*implying that*NP*∩ co-*NP*equals P. ...
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