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The tale of the PCP theorem

2012
*
XRDS Crossroads The ACM Magazine for Students
*

In other words, it is a

doi:10.1145/2090276.2090286
fatcat:aim67yzrxrhsnjfs72dkfomzae
*PCP**Theorem*. This*PCP**Theorem*is slightly different from*the**PCP**theorem*we described before: X,*the*probability*of*rejecting a correct proof, is not 1. ...*The*Proof*of**the**PCP**Theorem**The**PCP**theorem*has a reputation for being difficult and complicated to prove, which, in*the*author's opinion, is unjustified. ...##
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Relativization: a Revisionistic Retrospective
[chapter]

1993
*
Current Trends in Theoretical Computer Science
*

We begin with

doi:10.1142/9789812794499_0040
dblp:series/wsscs/HartmanisCCRR93
fatcat:xi32jv2ukjg4lbvrk62gorwjyu
*the*twice-told*tale**of**the*relativization principle and ponder upon its possible demise. Then, we discuss whether usual assumptions are historically accurate. ... In this column we examine*the*role*of*relativization in complexity theory in light*of*recent non-relativizing results involving interactive protocols. ...*Theorem*3 Let A be any language complete for EXPSPACE. Then*PCP*A (log) =*PCP*A (poly). ...##
###
Page 2531 of Mathematical Reviews Vol. , Issue 83f
[page]

1983
*
Mathematical Reviews
*

A. 83£:68008
Fixed point

*theorems*and semantics: a folk*tale*. Inform. Process. Lett. 14 (1982), no. 3, 112-116. ... ISBN 3-88457-017-X From*the*foreword: “*The*volume collects abstracts*of*proceedings*of**the*workshop ‘Restricted principles*of*computing processes (*PCP*) and equations in free semigroups’ held in St. ...##
###
Balanced max 2-sat might not be the hardest

2007
*
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing - STOC '07
*

We show that, assuming

doi:10.1145/1250790.1250818
dblp:conf/stoc/Austrin07
fatcat:lygw7f4q2fevzozlq3do5exeoq
*the*Unique Games Conjecture, it is NP-hard to approximate MAX 2-SAT within α − LLZ + , where 0.9401 < α − LLZ < 0.9402 is*the*believed approximation ratio*of**the*algorithm*of*Lewin ... In particular, instances in which roughly 70%*of**the*literals are unnegated variables and 30% are negated appear less amenable to approximation than instances where*the*ratio is 50%-50% ... Meanwhile,*the*study*of*inapproximability has seen a perhaps even bigger revolution, starting with*the*discovery*of**the**PCP**Theorem*[2, 1] . ...##
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Towards a More Well-Founded Cosmology
[article]

2018
*
arXiv
*
pre-print

*The*cosmic web

*of*galaxies does not expand. Potential Φ varies as -H/(cz) instead

*of*-1/r. Inertial forces arise from gravitational interaction with

*the*rest

*of*

*the*universe (not with space). ...

*The*Big-Bang pardigm and

*the*ΛCDM "concordance model" involve such beliefs:

*the*emanation

*of*

*the*universe out

*of*a non-physical stage, cosmic inflation (invented ad hoc), Λ (fictitious energy), and exotic ... Acknowledgments Thanks are due to four anonymous reviewers

*of*previous versions

*of*this paper for their detailed and/or illuminative comments. ...

##
###
Towards a More Well-Founded Cosmology

2018
*
Zeitschrift fur Naturforschung A-A Journal of Physical Sciences
*

*The*Big Bang paradigm and

*the*ΛCDM 'concordance model' involve such beliefs:

*the*emanation

*of*

*the*universe out

*of*a non-physical stage, cosmic inflation (hardly testable), Λ (fictitious energy), and 'exotic ... Potential Φ varies as −H/(cz) instead

*of*−1/r. Inertial forces reflect gradients present in comoving frames

*of*accelerated bodies (interaction with

*the*rest

*of*

*the*universe – not with space). ... Acknowledgements: Thanks are due to five anonymous reviewers for their detailed, stimulating, and/or illuminative comments on previous versions

*of*this polemical paper. ...

##
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Vanishing cycles for formal schemes

1994
*
Inventiones Mathematicae
*

l~

doi:10.1007/bf01231772
fatcat:gkkwyh4ejrds5gujkshhmj22ra
*tale*morphisms*of*formal schemes Let Y E k~ For n >_ 1, let ~,, denote*the*scheme (X, O3C/a'~Oy). ... This gives*the*required equality. [] Quasi-~*tale*topology on an analytic space Let ~ : Y --+ X be a morphism*of*k-analytic spaces. ...##
###
Illusions of Meaning in the Ipsative Assessment of Children's Ability

1992
*
The Journal of special education
*

In this study, we analyze

doi:10.1177/002246699202500407
fatcat:6nebgvjjn5dzloogbeibd3rmqy
*the*relative efficacy*of*normative and ipsative measures for*the*study*of*intra· and interindividual differences in child ability. ... in terms*of**the*evidential and consequential bases for validity. ... But*the*ipsative version*of**the*pattern tells quite another*tale*. ...##
###
Market demand by non-convex preferences

1987
*
Rendiconti del Seminario Matematico e Fisico di Milano
*

Si studiano le condizioni sotto le quali

doi:10.1007/bf02925059
fatcat:yudugh5yqnbo7drnllwbcuzz2q
*tale*domanda ~ una funzione continua dei prezzi e le condizioni che ne implicano la differenziabilit~ con continuitY. ... Although most likely this*theorem*can be simplified and generalized on*the*basis*of*a deep understanding*of**the*methods*of**the*singularity theory, it seems quite sure that merely measuretheoretical distribution ...*The*similarity to*the*ideas*of*COU~OT sketched above is apparent.w~pp(~, w, p)~ poq-l qop(~, w, p)~ q-l .*pcp*(~q, w, q-lop) This can be written as well as (*) qo~(>~,w, qop)~ ep(>~q,w,p). ...##
###
Challenging epistemology: Interactive proofs and zero knowledge

2008
*
Journal of Applied Logic
*

Possible lessons from this work for

doi:10.1016/j.jal.2008.09.002
fatcat:3j6bp43qofblpgkzku5kuo5ste
*the*epistemology*of*mathematics-our models*of*mathematical proof should incorporate interaction, our theories*of*mathematical evidence must account for probabilistic ... our theory*of*mathematical knowledge, a casual look at*the*actual practice*of*complexity theory indicates that such a distinct epistemology may not be necessary. ... Parts*of**the*essay were subsequently presented at both*the*Richard Wollheim Society and Student Logic Colloquium at*the*University*of*California, Berkeley. ...##
###
Degenerating abelian varieties via log abelian varieties
[article]

2019
*
arXiv
*
pre-print

This generalizes

arXiv:1412.5651v3
fatcat:x4k376mkvbgxxljzyqcfylspta
*the*log Tate curve*of*Kato. ... For any split totally degenerate abelian variety over a complete discrete valuation field, we construct a log abelian variety over*the*discrete valuation ring extending*the*given abelian variety. ... from*the*monoids*pCp*σq _ X Xq σPΣ .Proof. ...##
###
Analogie entre le transfert de chaleur et le transfert de masse par sublimation d'un dépôt de naphtalène

1969
*
La houille blanche
*

' tu be

doi:10.1051/lhb/1969019
fatcat:wkig3yc4t5h45flzghsul7ymmi
*the*results obtained are to within 5 pel' eent*of**the*thermal data, 'with*the*mass transfer number 6J = (h/Il) instead*of**the*lvlargouJis number and*the*Schmidt number 2> = (ll/?])) ... instead*of**the*Prandtl number, Experimental data on*the*relative variation*of*mass transfer ,coeflicienls for a hundle*of*nineteen rods in a circularsection duet are discussed and it is found that*the*...##
###
Complexity Theory, Game Theory, and Economics: The Barbados Lectures
[article]

2019
*
arXiv
*
pre-print

It consists

arXiv:1801.00734v2
fatcat:r6sz7jskqjbs7gxof52fbjikom
*of*two five-lecture sequences:*the*Solar Lectures, focusing on*the*communication and computational complexity*of*computing equilibria; and*the*Lunar Lectures, focusing on applications*of*complexity ... This document collects*the*lecture notes from my mini-course "Complexity Theory, Game Theory, and Economics," taught at*the*Bellairs Research Institute*of*McGill University, Holetown, Barbados, February ... This is*the*reason why Rubinstein [142] needs to develop customized*PCP*machinery in his proof*of**Theorem*5.1. ...##
###
Chapter 3 of Ramanujan's second notebook

1983
*
Advances in Mathematics
*

ACKNOWLEDGMENTS

doi:10.1016/0001-8708(83)90071-3
fatcat:6rctbbcy5va57kx4bhj2rdjc3i
*The*authors are very grateful to R. A. Askey, H. W. Gould, and D. Zeilberger who each provided us with several references to*the*literature. We also thank J. B. Miles and J. ... According to Gould [34] ,*the*earliest known application*of*these numbers is in an edition*of**the*Japanese*Tale**of*Genji published in*the*17th century. ... This series is (10.6) $ rp'"'(O) z2*pcp*"_,(n-l)x"-'=lY F f+"'(O) Xn-2 n. t 2 ,y2 (n -2)! ...##
###
Finite subgroups of formal groups

1997
*
Journal of Pure and Applied Algebra
*

We discuss various moduli problems involving

doi:10.1016/s0022-4049(96)00113-2
fatcat:z6wirycrm5adfkw6ustmb2ellq
*the*classification*of*finite subgroups or related structures on formal groups*of*finite height n. ... Moreover, many maps between such schemes are finite and flat, and their degrees can be predicted by thinking*of*(Q,/Z,)" as a "discrete model" for*the*formal group. @ 1997 Elsevier Science B.V. ... , [y], giving part (ii)*of**the**theorem*. ...
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