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The tale of the PCP theorem

Dana Moshkovitz
2012 XRDS Crossroads The ACM Magazine for Students  
In other words, it is a 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.  ... 
doi:10.1145/2090276.2090286 fatcat:aim67yzrxrhsnjfs72dkfomzae

Relativization: a Revisionistic Retrospective [chapter]

Juris Hartmanis, Richard Chang, Suresh Chari, Desh Ranjan, Pankaj Rohatgi
1993 Current Trends in Theoretical Computer Science  
We begin with 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).  ... 
doi:10.1142/9789812794499_0040 dblp:series/wsscs/HartmanisCCRR93 fatcat:xi32jv2ukjg4lbvrk62gorwjyu

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

Per Austrin
2007 Proceedings of the thirty-ninth annual ACM symposium on Theory of computing - STOC '07  
We show that, assuming 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] .  ... 
doi:10.1145/1250790.1250818 dblp:conf/stoc/Austrin07 fatcat:lygw7f4q2fevzozlq3do5exeoq

Towards a More Well-Founded Cosmology [article]

Hartmut Traunmüller
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.  ... 
arXiv:1107.2529v3 fatcat:2ix3e2rgkrgo5g6idgjmwmxbbm

Towards a More Well-Founded Cosmology

Hartmut Traunmüller
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.  ... 
doi:10.1515/zna-2018-0217 fatcat:n3mjjjdl6ba4nhsfjohgmave3a

Vanishing cycles for formal schemes

Vladimir G. Berkovich
1994 Inventiones Mathematicae  
l~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.  ... 
doi:10.1007/bf01231772 fatcat:gkkwyh4ejrds5gujkshhmj22ra

Illusions of Meaning in the Ipsative Assessment of Children's Ability

Paul A. McDermott, John W. Fantuzzo, Joseph J. Glutting, Marley W. Watkins, Andrew R. Baggaley
1992 The Journal of special education  
In this study, we analyze 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.  ... 
doi:10.1177/002246699202500407 fatcat:6nebgvjjn5dzloogbeibd3rmqy

Market demand by non-convex preferences

Walter Trockel
1987 Rendiconti del Seminario Matematico e Fisico di Milano  
Si studiano le condizioni sotto le quali 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).  ... 
doi:10.1007/bf02925059 fatcat:yudugh5yqnbo7drnllwbcuzz2q

Challenging epistemology: Interactive proofs and zero knowledge

Justin Bledin
2008 Journal of Applied Logic  
Possible lessons from this work for 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.  ... 
doi:10.1016/j.jal.2008.09.002 fatcat:3j6bp43qofblpgkzku5kuo5ste

Degenerating abelian varieties via log abelian varieties [article]

Heer Zhao
2019 arXiv   pre-print
This generalizes 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 pCpσq _ X Xq σPΣ .Proof.  ... 
arXiv:1412.5651v3 fatcat:x4k376mkvbgxxljzyqcfylspta

Analogie entre le transfert de chaleur et le transfert de masse par sublimation d'un dépôt de naphtalène

1969 La houille blanche  
' tu be 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  ... 
doi:10.1051/lhb/1969019 fatcat:wkig3yc4t5h45flzghsul7ymmi

Complexity Theory, Game Theory, and Economics: The Barbados Lectures [article]

Tim Roughgarden
2019 arXiv   pre-print
It consists 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.  ... 
arXiv:1801.00734v2 fatcat:r6sz7jskqjbs7gxof52fbjikom

Chapter 3 of Ramanujan's second notebook

Bruce C Berndt, Ronald J Evans, B.M Wilson
1983 Advances in Mathematics  
ACKNOWLEDGMENTS 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)!  ... 
doi:10.1016/0001-8708(83)90071-3 fatcat:6rctbbcy5va57kx4bhj2rdjc3i

Finite subgroups of formal groups

Neil P. Strickland
1997 Journal of Pure and Applied Algebra  
We discuss various moduli problems involving 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.  ... 
doi:10.1016/s0022-4049(96)00113-2 fatcat:z6wirycrm5adfkw6ustmb2ellq
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