ゲーデル賞(Gödel Prize)論文及びGödel 論文を英語で読む（邪道）

Gödel Prize
https://sigact.org/prizes/gödel.html

20年以上前、Gödel の論文を読もうという身内の企画があった。計算機の仕事で時間が取れずに参加できなかった。
企画そのものが空中分解したのかもしれない。

読んでないという負い目をおいながら仕事をしてきた。
Gödel Prizeがあることを知った。

何一つ読んでいない。これらをすべて読みながら、Gödel の論文も読もうと思った。

Gödel, Kurt (1931), “Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I.”, Monatshefte für Mathematik und Physik 38: 173–198, doi:10.1007/BF01700692.

英語じゃない。

Gödel, Kurt (1986), Feferman, Solomon, ed., Kurt Gödel: Collected Works: Volume I: Publications 1929-1936, Oxford University Press, pp. 144-195, ISBN 978-0-19-503964-1
Gödel, Kurt Meltzer, B.訳 (1992), On Formally 

Undecidable Propositions of Principia Mathematica and Related Systems, Dover Books on Mathematics, Dover Publications, ISBN 978-0-486-66980-9

Gödel, Kurt; Hirzel, Martin (2000-11-27), “On formally undecidable propositions of Principia Mathematica and related systems I” (PDF), Boulder: 173-196
http://hirzels.com/martin/papers/canon00-goedel.pdf

Gödel, Kurt (2002), “Some metamathematical results on completeness and consistency, On formally undecidable propositions of Principia mathematica and related systems I, and On completeness and consistency”, in van Heijenoort, Jean, From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931, Source Books in the History of the Sciences (Fourth Printing ed.), Harvard University Press, pp. 592-617, ISBN 978-0-674-32449-7

Gödel, Kurt (2004), “On Formally Undecidable Propositions of the Principia Mathematica and Related Systems. I.”, in Davis, Martin, The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions, Dover Books on Mathematics, Courier Corporation, pp. 4-38, ISBN 978-0-486-43228-1
https://books.google.co.jp/books?id=qW8x7sQ4JXgC&pg=PA4&redir_esc=y#v=onepage&q&f=false

英訳をまず確認中。

ゲーデル賞の方は、2013, 2014, 2015年の詳細記事がリンク切れになっていた。人名等を元に、論文を探して記録する。

http://citeseerx.ist.psu.edu/
https://arxiv.org
http://researchgate.net
で検索。

- Requested としたのはhttp://researchgate.net で関係者に著作物送達依頼した文献。

論文が揃ったら単語帳を作る予定。Wikipediaの記述も直接PDF等のURLを記載していないものもある。
該当する論文がWEBで無償では見当たらず、原型がArxivに掲載のあるものもある。論文URLの後ろに年号を記載した。
https://en.wikipedia.org/wiki/Gödel_Prize#cite_note-36
原文と同一のものはWikipediaに加筆する予定。

#人名一覧
2020: Robin A. Moser and Gábor Tardos
2019: Irit Dinur
2018: Oded Regev
2017: Cynthia Dwork, Frank McSherry, Kobbi Nissim, and Adam Smith
2016: Stephen Brookes and Peter W. O’Hearn
2015: Daniel A. Spielman and Shang-Hua Teng
2014: Ronald Fagin, Amnon Lotem, and Moni Naor
2013: Antoine Joux, Dan Boneh, and Matthew K. Franklin
2012: Elias Koutsoupias, Christos H. Papadimitriou, Tim Roughgarden, Éva Tardos, Noam Nisan, and Amir Ronen
2011: Johan T. Håstad
2010: Sanjeev Arora and Joseph S. B. Mitchell
2009: Omer Reingold, Salil Vadhan, and Avi Wigderson
2008: Dan Spielman and Shang-Hua Teng
2007: Alexander A. Razborov and Steven Rudich
2006: Manindra Agrawal, Neeraj Kayal, and Nitin Saxena
2005: Noga Alon, Yossi Matias and Mario Szegedy
2004: Maurice Herlihy and Nir Shavit / Michael Saks and Fotios Zaharoglou
2003: Yoav Freund and Robert Schapire
2002: Géraud Sénizergues
2001: Sanjeev Arora, Uriel Feige, Shafi Goldwasser, Carsten Lund, László Lovász, Rajeev Motwani, Shmuel Safra, Madhu Sudan, and Mario Szegedy
2000: Moshe Vardi and Pierre Wolper
1999: Peter W. Shor
1998: Seinosuke Toda
1997: Joseph Halpern and Yoram Moses
1996: Mark Jerrum and Alistair Sinclair
1995: Neil Immerman and Róbert Szelepcsényi
1994: Johan Håstad
1993: László Babai, Shafi Goldwasser, Silvio Micali, Shlomo Moran, and Charles Rackoff




# 論文一覧
#### 2020: Robin A. Moser and Gábor Tardos
https://sigact.org/prizes/gödel/citation2020.html
>The 2020 Gödel Prize is awarded to Robin A. Moser and Gábor Tardos for their algorithmic version of the Lovász Local Lemma in the paper:
“A constructive proof of the general Lovász Local Lemma,” Journal of the ACM 57(2): 11:1-11:15 (2010).
https://arxiv.org/pdf/0903.0544.pdf, 2009

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[ES91] Paul Erdo ̋s and Joel Spencer. Lopsided Lova ́sz Local Lemma and Latin Transversals. Discrete Applied Mathematics, 30:151-154, 1991.
[Bec91] J ́oszef Beck. An Algorithmic Approach to the Lova ́sz Local Lemma. Random Structures and Algorithms, 2(4):343–365, 1991.
[Alo91] Noga Alon. A parallel algorithmic version of the local lemma. Random Structures and Algorithms, 2(4):367–378, 1991.
[KST93] JanKratochv ́ılandPetrSavicky ́andZsoltTuza.Onemoreoccurrenceofvariablesmakessatisfiability jump from trivial to NP-complete. SIAM J. Comput., Vol. 22, No. 1, pp. 203–210, 1993.
[MR98] Michael Molloy and Bruce Reed. Further Algorithmic Aspects of the Local Lemma. In Proceedings of the 30th Annual ACM Symposium on the Theory of Computing, pages 524–529, 1998.
[CS00] Artur Czumaj and Christian Scheideler. Coloring non-uniform hypergraphs: a new algorithmic approach to the general Lova ́sz local lemma. Symposium on Discrete Algorithms, 30–39, 2000.
[BKS03] Piotr Berman, Marek Karpinski, and Alexander D. Scott. Approximation hardness and satisfiability of bounded occurrence instances of SAT. Electronic Colloquium on Computational Complexity (ECCC), 10(022), 2003.
[Mos06] Robin A. Moser. On the Search for Solutions to Bounded Occurrence Instances of SAT. Not published. Semester Thesis, ETH Zu ̈rich. 2006.
[PT09] J ́anos Pach and G ́abor Tardos. Conflict-free colorings of graphs and hypergraphs. Manuscript, 2009.
[Sri08] Aravind Srinivasan. Improved algorithmic versions of the Lova ́sz Local Lemma. Proceedings of the nine- teenth annual ACM-SIAM symposium on Discrete algorithms (SODA), San Francisco, California, pp. 611–620, 2008.
[Wel08] Emo Welzl. Boolean Satisfiability - Combinatorics and Algorithms. Lecture notes, Version Fall 2008.
[Mos08] Robin A. Moser. Derandomizing the Lova ́sz Local Lemma more Effectively. Eprint, arXiv:0807.2120v2,
2008.
[Mos09] Robin A. Moser. A constructive proof of the Lova ́sz Local Lemma. Proceedings of the 41st annual ACM Symposium on Theory of Computing (STOC 2009), to appear. Available at arXiv:0810.4812v2, 2008.


####2019: Irit Dinur
https://sigact.org/prizes/gödel/citation2019.pdf
>The 2019 Gödel Prize is awarded to Irit Dinur for her proof of the PCP Theorem in the paper:
The PCP theorem by gap amplification,
Journal of the ACM, Vol 54 (3), Article 12, 2007.
(preliminary version in the proceedings of the 38th Symposium on Theory of Computing, STOC 2006).
http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=CC1C896ABF24E8D7EA957CD543AAACBB?doi=10.1.1.103.2644&rep=rep1&type=pdf


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#### 2018: Oded Regev
https://eatcs.org/index.php/component/content/article/1-news/2670-2018-godel-prize
>The 2018 Gödel Prize is awarded to Professor Oded Regev for his paper:
On lattices, learning with errors, random linear codes, and cryptography Journal of the ACM, volume 56, issue 6, 2009 (preliminary version in the 37th annual Symposium on Theory of Computing, STOC 2005.)
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.215.3543&rep=rep1&type=pdf

#### 2017: Cynthia Dwork, Frank McSherry, Kobbi Nissim, and Adam Smith
https://sigact.org/prizes/gödel/citation2017.pdf
>The 2017 Gödel Prize is awarded to Cynthia Dwork, Frank McSherry, Kobbi Nissim and Adam Smith for their work on Differential Privacy in the paper:
Calibrating Noise to Sensitivity in Private Data Analysis, Journal of Privacy and Confidentiality, Volume 7, Issue 3, 2016 (preliminary version in Theory of Cryptography, TCC 2006).
http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=CC1C896ABF24E8D7EA957CD543AAACBB?doi=10.1.1.131.9267&rep=rep1&type=pdf
(Calibrating Data to Sensitivity in Private Data Analysis https://arxiv.org/pdf/1203.3453.pdf, 2014)

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####2016: Stephen Brookes and Peter W. O’Hearn
https://eatcs.org/index.php/component/content/article/1-news/2280-2016-godel-prize
>The 2016 Gödel Prize is awarded to Stephen Brookes and Peter W. O'Hearn for their invention of Concurrent Separation Logic, as described in the following two papers:
S. Brookes, A Semantics for Concurrent Separation Logic. Theoretical Computer Science 375(1-3): 227-270 (2007)
https://www.cs.cmu.edu/~brookes/papers/seplogicrevisedfinal.pdf


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>P. W. O’Hearn, Resources, Concurrency, and Local Reasoning. Theoretical Computer Science 375(1-3): 271-307 (2007)
http://www0.cs.ucl.ac.uk/staff/p.ohearn/papers/concurrency.pdf

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#### 2015: Daniel A. Spielman and Shang-Hua Teng
https://sigact.org/prizes/gödel/citation2015.pdf
>The 2015 Gödel Prize is awarded to Daniel A. Spielman and Shang-Hua Teng for their series of papers on nearly-linear-time Laplacian solvers:
Spectral sparsification of graphs. SIAM J. Computing 40:981-1025, 2011.
https://arxiv.org/pdf/0808.4134.pdf

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>A local clustering algorithm for massive graphs and its application to nearly linear time
graph partitioning. SIAM J. Computing 42:1-26, 2013.
https://arxiv.org/pdf/0809.3232.pdf


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>Nearly linear time algorithms for preconditioning and solving symmetric, diagonally dominant linear systems. SIAM J. Matrix Anal. Appl. 35:835-885, 2014.
https://arxiv.org/pdf/cs/0607105.pdf

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Pravin M. Vaidya. Solving linear equations with symmetric diagonally dominant matrices by constructing good preconditioners. Unpublished manuscript UIUC 1990. A talk based on the manuscript was presented at the IMA Workshop on Graph Theory and Sparse Matrix Computation, October 1991, Minneapolis., 1990.
V. Vassilevska Williams. Multiplying matrices faster than coppersmith-winograd. In Proceedings of the 44th Annual ACM Symposium on the Theory of Computing (STOC ’12), pages 887–898, 2012.
Dengyong Zhou, Olivier Bousquet, Thomas Navin Lal, Jason Weston, and Bernhard Scho ̈lkopf. Learning with local and global consistency. In Adv. in Neural Inf. Proc. Sys. 16, pages 321–328, 2003.
Xiaojin Zhu, Zoubin Ghahramani, and John D. Lafferty. Semi-supervised learning using Gaussian fields and harmonic functions. In Proc. 20th Int. Conf. on Mach. Learn., 2003.
Fuzhen Zhang, editor. The Schur Complement and its Applications, volume 4 of Numerical Methods and Algorithms. Springer, 2005.

####2014: Ronald Fagin, Amnon Lotem, and Moni Naor
Optimal Aggregation Algorithms for Middleware
https://arxiv.org/pdf/cs/0204046.pdf

####2013: Antoine Joux, Dan Boneh, and Matthew K. Franklin
A One Round Protocol for Tripartite Diffie–Hellman
Antoine Joux, Journal of Cryptology volume 17, pages263–276(2004)
https://link.springer.com/content/pdf/10.1007/s00145-004-0312-y.pdf


>Identity-Based Encryption from the Weil Pairing
Dan Boneh∗ Matthew Franklin
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.66.1131&rep=rep1&type=pdf

>Nisan, Noam; Ronen, Amir (2001). "Algorithmic Mechanism Design". Games and Economic Behavior. 35 (1–2): 166–196.
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.21.1731&rep=rep1&type=pdf

####2012: Elias Koutsoupias, Christos H.Papadimitriou, Tim Roughgarden, Éva Tardos, Noam Nisan, and Amir Ronen

 Koutsoupias, Elias; Papadimitriou, Christos (2009). "Worst-case equilibria". Computer Science Review. 3 (2): 65–69. doi:10.1016/j.cosrev.2009.04.003.
http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=08343A18C75A6F5A0E57B25562499E5C?doi=10.1.1.102.6991&rep=rep1&type=pdf

Roughgarden, Tim; Tardos, Éva (2002). "How bad is selfish routing?". Journal of the ACM. 49 (2): 236–259. CiteSeerX 10.1.1.147.1081. doi:10.1145/506147.506153.
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.147.1081&rep=rep1&type=pdf

 Nisan, Noam; Ronen, Amir (2001). "Algorithmic Mechanism Design". Games and Economic Behavior. 35 (1–2): 166–196. CiteSeerX 10.1.1.21.1731. doi:10.1006/game.1999.0790.
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.21.1731&rep=rep1&type=pdf

####2011: Johan T. Håstad
https://sigact.org/prizes/gödel/2011.html
>The 2011 Gödel Prize is awarded to Johan T. Håstad for his paper:
Some optimal inapproximability results, Journal of the ACM, 48: 798--859, 2001.
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.638.2808&rep=rep1&type=pdf

####2010: Sanjeev Arora and Joseph S. B. Mitchell
https://sigact.org/prizes/gödel/2010.html
>The 2010 Gödel Prize is awarded to 
Sanjeev Arora and Joseph S.B. Mitchell for their concurrent discovery of a polynomial-time approximation scheme (PTAS) for the Euclidean Travelling Salesman Problem (ETSP):
Sanjeev Arora. (1998). Polynomial-time approximation schemes for Euclidean TSP and other geometric problems, Journal ACM 45(5), 753-782.
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.23.6765&rep=rep1&type=pdf
Joseph S.B. Mitchell (1999). Guillotine subdivisions approximate polygonal subdivisions: A simple polynomial-time approximation scheme for geometric TSP, k-MST, and related problems, SIAM J. Computing 28(4), 1298-1309.
http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=EBC1BCCD86A8ECD59B018C11236ECA89?doi=10.1.1.56.4805&rep=rep1&type=pdf

####2009: Omer Reingold, Salil Vadhan, and Avi Wigderson
https://sigact.org/prizes/gödel/2009.html
>The 2009 Gödel Prize for outstanding papers in the area of theoretical computer science is awarded to
(1) Entropy waves, the zig-zag graph product and new constant degree expanders. Omer Reingold, Salil Vadhan and Avi Wigderson, Annals of Mathematics, Vol 155, (2002), 157-187
https://arxiv.org/pdf/math/0406038.pdf
and
(2) Undirected connectivity in Log-Space. Omer Reingold, Journal of ACM, Vol 55 (4) (2007).
- Requested.

####2008: Dan Spielman and Shang-Hua Teng
https://sigact.org/prizes/gödel/2008.html
>The 2008 Gödel Prize for outstanding papers in the area of theoretical computer science is awarded to 
Daniel A. Spielman and Shang-Hua Teng for their paper: Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time by Daniel A. Spielman and Shang-Hua Teng, Journal of the ACM (JACM), 51(3), May 2004, 385-463. 
First presented at the Annual ACM Symposium on the Theory of Computing (STOC 01), 2001, 296-305.
https://arxiv.org/pdf/math/0212413.pdf

####2007: Alexander A. Razborov and Steven Rudich
https://sigact.org/prizes/gödel/2007.html
>The 2007 Gödel Prize for outstanding papers in the area of theoretical computer science is awarded to Alexander A. Razborov and Steven Rudich for their paper:
Natural Proofs, Journal of Computer and System Sciences, Vol. 55, No. 1, 1997, pp. 24-35. 
First presented at the Twenty-sixth Annual ACM Symposium on Theory of computing, Montreal, Quebec, Canada. 1994, pp. 204-213.
https://reader.elsevier.com/reader/sd/pii/S002200009791494X?token=9E8D5C0FAA5F8E450DFB32BDEDED9B07CACDC4BD40EA21B35A33BF9E74A24E840B6AF2E6FF1C20F6ED02778CA1FC109C
####2006: Manindra Agrawal, Neeraj Kayal, and Nitin Saxena
https://sigact.org/prizes/gödel/2006.html
>The 2006 Gödel Prize for outstanding papers in the area of theoretical computer science is awarded to Manindra Agrawal, Neeraj Kayal, and Nitin Saxena for their paper:
PRIMES is in P. Annals of Mathematics 160(2), 781-793, 2004.
https://web.archive.org/web/20110607101302/http://math.berkeley.edu/~coleman/Courses/Fall08/Cryptography/primality_v6.pdf

#### 2005: Noga Alon, Yossi Matias and Mario Szegedy
https://sigact.org/prizes/gödel/2005.html
>The 2005 Gödel Prize for outstanding papers in the area of theoretical computer science is awarded to 
Noga Alon, Yossi Matias and Mario Szegedy for their paper: The space complexity of approximating the frequency moments. Journal of Computer and System Sciences 58 (1999), 137-147 First presented at the 28th ACM Symposium on Theory of Computing, 1996.
http://www.math.tau.ac.il/~nogaa/PDFS/amsz4.pdf

#### 2004: Maurice Herlihy and Nir Shavit / Michael Saks and Fotios Zaharoglou
https://sigact.org/prizes/gödel/2004.html
>The 2004 Gödel Prize for outstanding journal articles in theoretical computer science is shared between the papers:
"The Topological Structure of Asynchronous Computation" by Maurice Herlihy and Nir Shavit, Journal of the ACM, Vol. 46 (1999), 858-923,
http://cs.brown.edu/~mph/HerlihyS99/p858-herlihy.pdf
and
"Wait-Free k-Set Agreement Is Impossible: The Topology of Public Knowledge" by Michael Saks and Fotios Zaharoglou, SIAM J. on Computing, Vol. 29 (2000), 1449-1483.
- Requested.

#### 2003: Yoav Freund and Robert Schapire
https://sigact.org/prizes/gödel/2003.html
>The prize was awarded to 
Yoav Freund and Robert Schapire for their paper "A Decision Theoretic Generalization of On-Line Learning and an Application to Boosting," Journal of Computer and System Sciences 55 (1997), pp. 119-139. 
https://www-ai.cs.tu-dortmund.de/LEHRE/PG/PG445/literatur/freund_schapire_97a.pdf

#### 2002: Géraud Sénizergues
https://sigact.org/prizes/gödel/2002.html
>Geraud Senizergues, for "L(A)=L(B)? Decidability results from complete formal systems", Theoretical Computer Science 251 (2001), pp.1-166. 
https://reader.elsevier.com/reader/sd/pii/S0304397500002851?token=64A2B37155D426438B12D3E16D9DA7D657C01E4E4944CA307F3319EB3724727119FF108137109C77E438B12E754C1179

#### 2001: Sanjeev Arora, Uriel Feige, Shafi Goldwasser, Carsten Lund, László Lovász, Rajeev Motwani, Shmuel Safra, Madhu Sudan, and Mario Szegedy
https://sigact.org/prizes/gödel/2001.html
>The 2001 Gödel Prize for outstanding journal article in the area of theoretical computer science is awarded to 
Sanjeev Arora, Uriel Feige, Shafi Goldwasser, Carsten Lund, Laszlo Lovász, R. Motwani, Shmuel Safra, Madhu Sudan, and Mario Szegedy for the following series of papers:
"Interactive Proofs and the Hardness of Approximating Cliques". Uriel Feige, Shafi Goldwasser, Laszlo Lovász, Shmuel Safra, and Mario Szegedy. Journal of the ACM 43 (1996), 268-292.
https://www.researchgate.net/profile/Mario_Szegedy/publication/234783217_Interactive_proofs_and_the_hardness_of_approximating_cliques/links/09e41514878e8c2f78000000/Interactive-proofs-and-the-hardness-of-approximating-cliques.pdf
"Probabilistic Checking of Proofs: A New Characterization of NP". Sanjeev Arora and Shmuel Safra. Journal of the ACM 45 (1998), 70-122.
https://web.archive.org/web/20110610101051/http://www.cs.umd.edu/~gasarch/pcp/AS.pdf
"Proof Verification and the Hardness of Approximation Problems". Sanjeev Arora, Carsten Lund, Rajeev Motwani, Madhu Sudan, and Mario Szegedy. Journal of the ACM 45 (1998), 501-555.
https://web.archive.org/web/20110610101241/https://www.cs.umd.edu/~gasarch/pcp/ALMSS.pdf

#### 2000: Moshe Vardi and Pierre Wolper
https://sigact.org/prizes/gödel/2000.html
>The 2000 Gödel Prize is awarded to 
Moshe Vardi and Pierre Wolper for their paper:
Reasoning about infinite computations. Moshe Y. Vardi, Pierre Wolper. Information and Computation 115 (1994), 1-37.
https://web.archive.org/web/20110825210914/http://reference.kfupm.edu.sa/content/r/e/reasoning_about_infinite_computations__102167.pdf

#### 1999: Peter W. Shor
https://sigact.org/prizes/gödel/1999.html
>The 1999 Gödel Prize for outstanding journal article in the area of theoretical computer science is awarded to 
Peter W. Shor for his paper "Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer", SIAM Journal on Computing 26 (1997), 1484-1509.
https://arxiv.org/pdf/quant-ph/9508027.pdf

#### 1998: Seinosuke Toda
https://sigact.org/prizes/gödel/1998.html
>The 1998 Gödel Prize for outstanding journal article in the area of theoretical computer science will be awarded to 
Seinosuke Toda for his paper "PP is as Hard as the Polynomial-Time Hierarchy," SIAM Journal on Computing 20 (1991), 865-877.
https://people.engr.tamu.edu/j-chen3/courses/637/2008/pres/korben.pdf

#### 1997: Joseph Halpern and Yoram Moses
https://sigact.org/prizes/gödel/1997.html
>The 1997 Gödel Prize for outstanding journal articles in the area of theoretical computer science will be awarded to 
Joseph Halpern and Yoram Moses for their paper "Knowledge and Common Knowledge in a Distributed Environment," J. ACM 37} (1990), 549-587.
https://www.cs.cornell.edu/home/halpern/papers/common_knowledge.pdf

#### 1996: Mark Jerrum and Alistair Sinclair
https://sigact.org/prizes/gödel/1996.html
>The 1996 Gödel Prize for outstanding journal articles in the area of theoretical computer science was awarded on May 23, 1996 jointly to 
Mark Jerrum and Alistair Sinclair for their papers "Approximate counting, unform generation and rapidly mixing Markov chains," Information and Computation 82 (1989), 93-133, by Sinclair and Jerrum, 
https://reader.elsevier.com/reader/sd/pii/0890540189900679?token=518EF4273B015187831CB0A883A601D699224964F2F448061BEE0B856FC0FE6A24FCDD1567B81553115DC281EB962793
and 
"Approximating the permanent," SIAM Journal on Computing 18 (1989), 1149-1178, by Jerrum and Sinclair.
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.431.4190&rep=rep1&type=pdf

#### 1995: Neil Immerman and Róbert Szelepcsényi
https://sigact.org/prizes/gödel/1995.html
>The Gödel prize committee has selected the co-recipients of the Gödel Prize for 1995. The prize is awarded for the following two papers: 
Neil Immerman, "Nondeterministic space is closed under complementation," SIAM Journal on Computing 17 (1988), 935-938 
https://people.cs.umass.edu/~immerman/pub/space.pdf
and 
Róbert Szelepcsényi, "The method of forced enumeration for nondeterministic automata," Acta Informatica 26 (1988), 279-284.
https://dml.cz/bitstream/handle/10338.dmlcz/120489/ActaOstrav_03-1995-1_10.pdf

#### 1994: Johan Håstad
https://sigact.org/prizes/gödel/1994.html
>Johan Håstad, "Almost optimal lower bounds for small depth circuits," Advances in Computing Research 5 (1989), 143-170.
https://web.archive.org/web/20120222163102/http://reference.kfupm.edu.sa/content/a/l/almost_optimal_lower_bounds_for_small_de_134215.pdf

#### 1993: László Babai, Shafi Goldwasser, Silvio Micali, Shlomo Moran, and Charles Rackoff
https://sigact.org/prizes/gödel/1993.html
>The 1993 Gödel Prize was shared by two papers, 
László Babai and Shlomo Moran, "Arthur-Merlin games: a randomized proof system and a hierarchy of complexity classes," Journal of Computer and System Sciences, 36 (1988), 254-276, 
http://crypto.cs.mcgill.ca/~crepeau/COMP647/2007/TOPIC01/AMgames-Babai-Moran.pdf
and 
Shafi Goldwasser, Silvio Micali, and Charles Rackoff, "The knowledge complexity of interactive proof systems," SIAM Journal on Computing 18 (1989), 186-208.
http://crypto.cs.mcgill.ca/~crepeau/COMP647/2007/TOPIC02/GMR89.pdf

#作業場(work space)

まずゲーテルの論文の単語帳。

自分のPCにあるフォルダ名が
/Users/administrator/Downloads/godel
の場合

```os:shell
$ docker run -v /Users/administrator/Downloads/godel:/tmp/godel -it kaizenjapan/godel /bin/bash
```


いつもは上位１００語を表示する。
数式が多く、１語は式でしか現れないかもしれない。
１０語以上だと上位１３６位まで。
整列は表計算ソフトに読み込んで並べ替えをした。

|work|count|
|--:|--:|
|the|413|
|x|395|
|of|255|
|a|237|
|is|211|
|n|182|
|y|159|
|and|146|
|to|120|
|that|119|
|for|112|
|v|106|
|in|102|
|r|80|
|we|77|
|by|75|
|i|73|
|z|71|
|not|69|
|are|66|
|number|63|
|this|59|
|p|58|
|formula|55|
|it|51|
|provable|49|
|q|48|
|primitive|47|
|one|46|
|as|44|
|be|43|
|if|43|
|with|43|
|forall|41|
|sign|39|
|axiom|37|
|length|37|
|class|36|
|k|36|
|free|35|
|item|35|
|or|35|
|recursive|35|
|from|34|
|subst|34|
|which|34|
|there|33|
|an|32|
|proof|32|
|relation|31|
|type|31|
|system|30|
|theorem|30|
|formulae|29|
|variable|29|
|all|28|
|numbers|28|
|where|28|
|will|28|
|can|27|
|e|27|
|you|27|
|axioms|26|
|on|26|
|s|25|
|xn|25|
|b|24|
|have|23|
|every|22|
|natural|22|
|paper|22|
|succ|22|
|other|21|
|such|21|
|but|19|
|following|19|
|sequence|19|
|go|18|
|translation|18|
|would|18|
|also|17|
|rq|17|
|u|17|
|consistency|16|
|consistent|16|
|del|16|
|then|16|
|basic|15|
|finite|15|
|text|15|
|undecidable|15|
|variables|15|
|any|14|
|defined|14|
|function|14|
|has|14|
|pm|14|
|seq|14|
|signs|14|
|argmin|13|
|because|13|
|call|13|
|concepts|13|
|does|13|
|now|13|
|only|13|
|first|12|
|formal|12|
|holds|12|
|more|12|
|no|12|
|prooffor|12|
|used|12|
|was|12|
|at|11|
|decision|11|
|define|11|
|fact|11|
|functions|11|
|its|11|
|let|11|
|schema|11|
|set|11|
|so|11|
|systems|11|
|these|11|
|c|10|
|example|10|
|hand|10|
|my|10|
|obtained|10|
|proposition|10|
|quantor|10|
|relations|10|
|some|10|
|well|10|

## 受賞論文

２論文が未入手、２論文が事前投稿論文。
式の中に２文字の記号を含むと仮定すると
676語は式中の記号の可能性がある。

ひとまず出現頻度が100までの683語を示す。

残りは、最後に記載したのDocker Hub上にファイルあり。


```docker:ubuntu/bash
./ptt.sh
cat text/* > all.txt
 awk -f wc.awk all.txt > wc.txt
```

|word|count|note|
|--:|--:|--:|
|the|29214|
|a|19144|
|of|18139|
|and|11769|
|is|11715|
|in|10220|
|y|9933|
|f|9700|
|i|9139|
|to|9012|
|x|8913|
|that|8803|
|b|8657|
|s|8465|
|n|8129|
|h|7348|
|we|7335|
|u|7322|
|for|6999|
|q|6720|
|p|5916|
|c|5906|
|g|5442|
|k|5207|
|m|4554|
|e|4407|
|v|4307|
|by|4258|
|t|4257|
|d|4090|
|be|4043|
|j|4022|
|this|3882|
|r|3542|
|l|3330|
|as|3196|
|with|3119|
|on|3094|
|an|2935|
|if|2741|
|it|2565|
|are|2553|
|let|2399|
|then|2198|
|at|2137|
|w|2051|
|proof|2000|
|from|1929|
|can|1921|
|z|1873|
|lemma|1717|
|which|1700|
|o|1692|
|not|1646|
|all|1577|
|such|1562|
|have|1509|
|each|1419|
|log|1411|
|set|1407|
|theorem|1394|
|where|1315|
|there|1278|
|algorithm|1201|
|some|1187|
|one|1186|
|random|1172|
|time|1143|
|any|1132|
|will|1130|
|our|1090|
|probability|1053|
|or|1041|
|every|1019|
|has|998|
|_|993|
|polynomial|959|
|number|957|
|case|920|
|two|895|
|given|887|
|only|883|
|bi|856|
|since|844|
|graph|825|
|so|823|
|function|821|
|most|802|
|problem|776|
|these|743|
|when|739|
|using|722|
|section|719|
|also|715|
|its|714|
|follows|710|
|de|696|
|first|683|
|now|682|
|use|677|
|following|661|
|size|649|
|least|645|
|us|639|
|computer|635|
|input|624|
|ii|616|
|than|615|
|thus|611|
|value|611|
|system|599|
|more|594|
|over|594|
|but|592|
|no|589|
|show|588|
|see|587|
|linear|575|
|hence|548|
|prove|543|
|state|543|
|other|529|
|definition|518|
|same|512|
|pp|511|
|note|509|
|xu|507|
|science|505|
|np|504|
|above|503|
|may|503|
|free|495|
|ca|477|
|do|475|
|variables|459|
|vertex|459|
|constant|457|
|result|448|
|bound|446|
|consider|442|
|new|441|
|problems|435|
|algorithms|433|
|TRUE|429|
|approximation|428|
|verifier|425|
|paper|424|
|does|421|
|protocol|421|
|assume|413|
|deterministic|411|
|was|409|
|step|407|
|vol|407|
|exists|398|
|between|397|
|degree|397|
|th|395|
|complexity|394|
|denote|391|
|point|390|
|xi|390|
|output|389|
|define|384|
|pr|384|
|si|383|
|edges|381|
|example|380|
|edge|379|
|resource|379|
|used|376|
|fact|373|
|theory|371|
|values|371|
|must|366|
|graphs|361|
|bits|357|
|oracle|357|
|both|351|
|max|351|
|length|349|
|assignment|345|
|functions|343|
|their|342|
|form|339|
|key|339|
|would|336|
|they|335|
|process|334|
|results|331|
|computing|328|
|matrix|327|
|work|327|
|defined|325|
|acm|324|
|condition|323|
|under|318|
|list|316|
|proofs|316|
|test|316|
|possible|315|
|way|314|
|min|313|
|lower|311|
|systems|311|
|suppose|307|
|mod|306|
|property|306|
|here|304|
|cost|303|
|small|303|
|order|301|
|instance|300|
|into|300|
|get|298|
|sequence|297|
|tree|296|
|how|294|
|distribution|292|
|second|291|
|well|291|
|whose|289|
|un|288|
|emp|287|
|wi|287|
|non|286|
|however|285|
|obtain|283|
|ai|281|
|implies|281|
|ui|280|
|within|280|
|been|279|
|vi|279|
|need|278|
|vertices|277|
|map|275|
|factor|273|
|quantum|273|
|based|272|
|access|271|
|complex|271|
|part|270|
|optimal|269|
|model|267|
|points|266|
|even|265|
|independent|265|
|analysis|264|
|make|261|
|nite|261|
|symposium|261|
|about|260|
|simplex|260|
|vector|260|
|al|259|
|because|259|
|bounded|256|
|path|253|
|proceedings|253|
|computation|252|
|sum|252|
|yjv|252|
|say|251|
|sets|251|
|string|251|
|variable|251|
|class|250|
|program|248|
|corresponding|246|
|large|246|
|main|245|
|while|245|
|hard|244|
|ud|244|
|udc|244|
|depth|243|
|automata|241|
|known|241|
|procedure|241|
|automaton|240|
|construction|239|
|natural|236|
|sj|236|
|accepts|235|
|bit|235|
|bounds|235|
|either|234|
|formula|234|
|ta|234|
|give|233|
|theoretical|233|
|particular|232|
|logic|231|
|object|231|
|objects|228|
|general|227|
|check|226|
|nition|225|
|last|223|
|many|221|
|chosen|220|
|space|220|
|proposition|218|
|udy|218|
|otherwise|217|
|simple|217|
|zero|216|
|et|215|
|notion|213|
|states|213|
|ratio|212|
|sorted|212|
|properties|211|
|local|210|
|product|210|
|interactive|209|
|parallel|209|
|call|208|
|approximate|207|
|equations|207|
|complete|206|
|full|206|
|claim|204|
|di|204|
|holds|203|
|integer|203|
|ti|203|
|find|202|
|finite|202|
|next|202|
|ne|201|
|satisfying|200|
|inequality|199|
|pi|199|
|similar|199|
|up|199|
|xud|199|
|ia|198|
|close|197|
|just|197|
|mechanism|197|
|poly|196|
|annual|195|
|hhv|195|
|processes|195|
|recall|195|
|circuit|193|
|gives|193|
|unsat|193|
|left|192|
|weight|192|
|choose|191|
|conditions|191|
|task|191|
|therefore|190|
|very|190|
|flow|188|
|ned|188|
|corollary|187|
|times|187|
|arbitrary|186|
|called|185|
|line|185|
|standard|185|
|subdivision|185|
|top|185|
|proc|183|
|compute|182|
|cannot|181|
|queries|181|
|uniform|181|
|contains|180|
|expected|180|
|structure|180|
|ieee|179|Institute of Electrical and Electronics Engineers| 
|probabilistic|179|
|running|179|
|chain|178|
|languages|178|
|enizergues|177|human name|
|induction|177|
|language|177|
|group|176|
|shown|176|
|reduction|175|
|type|175|
|code|174|
|distance|174|
|information|174|
|obtained|174|
|required|174|
|rule|173|
|agent|172|
|describe|172|
|without|171|
|after|170|
|construct|170|
|figure|170|
|exactly|169|
|should|169|
|assumption|168|
|cau|168|
|could|168|
|hypothesis|168|
|satis|168|
|what|168|
|almost|167|
|positive|167|
|matrices|166|
|three|166|
|uses|166|
|grade|165|
|satisfies|165|
|described|164|
|below|162|
|fixed|162|
|good|162|
|nu|162|
|out|162|
|ri|162|
|solution|162|
|version|162|
|knowledge|160|
|pair|160|
|terms|160|
|counting|159|
|different|159|
|whether|159|
|alphabet|158|
|connected|158|
|constraint|158|
|ji|158|
|siam|158|Society for Industrial and Applied Mathematics| 
|vectors|158|
|choice|157|
|clearly|157|
|efficient|157|
|sat|157|
|steps|157|
|agents|156|
|cs|156|computer science|
|inputs|156|
|pages|156|
|programs|156|
|those|156|
|public|154|
|shows|153|
|special|152|
|them|152|
|easy|151|
|fraction|151|
|less|151|
|proved|151|
|approximating|150|
|pcp|150|
|apply|149|
|decision|149|
|high|149|
|notation|149|
|right|149|
|scheme|149|
|similarly|149|
|am|147|
|before|147|
|prover|147|
|abort|146|
|cases|146|
|were|146|
|another|145|
|cut|145|
|finally|145|
|know|145|
|through|145|
|discrete|144|
|id|144|identifier|
|method|144|
|arora|143|
|au|142|
|outputs|142|
|constraints|141|
|ei|141|
|error|141|
|view|141|
|elements|140|
|makes|140|
|rst|140|
|regular|139|
|rules|139|
|subset|139|
|takes|139|
|fp|138|
|lattice|138|
|memory|138|
|optimality|138|
|prime|138|
|much|137|
|relation|137|
|requires|136|
|single|136|
|again|135|
|being|135|
|equivalent|135|
|series|135|
|hand|134|
|satisfy|134|
|nodes|133|
|partition|133|
|programming|133|
|boolean|132|
|gf|132|
|observe|132|
|st|132|
|total|132|
|vb|132|
|words|132|
|field|131|
|game|131|
|machine|131|
|self|131|
|write|131|
|answer|130|
|numbers|130|
|power|130|
|real|130|
|argument|129|
|basic|129|
|database|129|
|done|129|
|might|129|
|owned|129|
|run|129|
|take|129|
|able|128|
|accept|128|
|curve|128|
|seen|128|
|springer|128|
|start|128|
|useful|128|
|circuits|127|
|equal|127|
|moreover|127|
|present|127|
|always|126|
|pairing|126|
|entries|125|
|markov|125|
|put|125|
|accesses|124|
|comput|124|
|level|124|
|merlin|124|
|original|124|
|remark|124|
|context|123|
|combinatorial|122|
|dom|122|
|further|122|
|idea|122|
|nd|122|
|tsp|122|
|ci|121|
|cr|121|
|execution|121|
|notes|121|
|simplicial|121|
|xk|121|
|aw|120|
|exist|120|
|low|120|
|randomized|120|
|rather|120|
|aggregation|119|
|applications|119|
|formal|119|
|notice|119|
|operations|119|
|exp|118|
|family|118|
|inv|118|
|perfect|118|
|query|118|
|sense|118|
|upper|118|
|aq|117|
|bk|117|
|restriction|117|
|square|117|
|trace|117|
|transition|117|
|approach|116|
|equation|116|
|polynomials|116|
|root|116|
|heap|115|
|word|115|
|conclude|113|
|encoding|113|
|hardness|113|
|made|113|
|maximum|113|
|previous|113|
|techniques|113|
|uj|113|
|element|112|
|private|112|
|separation|112|
|simply|112|
|strategy|112|
|design|111|
|event|111|
|journal|111|
|lists|111|
|nc|111|
|writes|111|
|arthur|110|
|encryption|110|
|er|110|
|instances|110|
|ny|110|
|soundness|110|
|yj|110|
|chromatic|109|
|equivalence|109|
|generator|109|
|li|109|
|models|109|
|nonzero|109|
|respectively|109|
|completeness|108|
|dl|108|
|lecture|108|
|security|108|
|acceptance|107|
|buf|107|
|bw|107|
|open|107|
|checking|106|
|classes|106|
|iff|106|
|minimum|106|
|tb|106|
|formulas|105|
|important|105|
|initial|105|
|read|105|
|side|105|
|unique|105|
|xn|105|
|conductance|104|
|latency|104|
|paths|104|
|appear|103|
|bn|103|
|boundary|103|
|distinct|103|
|oracles|103|
|sequential|103|
|still|103|
|strings|103|
|accepting|102|
|ap|102|
|computed|102|
|long|102|
|node|102|
|question|102|
|associated|101|
|easily|101|
|im|101|
|udn|101|
|gate|100|
|like|100|
|matching|100|
|means|100|
|ownership|100|
|partial|100|
|provided|100|
|row|100|
|symmetric|100|
|weighted|100

## tools
単語出現頻度計数

```awk:wc.awk
# Print list of word frequencies
# https://researchmap.jp/jomd7nobo-45644/
# https://qiita.com/kaizen_nagoya/items/670d4d332e07fd2e5fc2
# This is for papers, not for programming.
# remove _ from gsub list 20200101 @kaizen_nagoya

{
    $0 = tolower($0)    # 
    gsub(/[^a-z \t]/, " ", $0)  #
    for (i = 1; i <= NF; i++)
        freq[$i]++
}

END {
    for (word in freq)
        printf "%s\t%d\n", word, freq[word]
}
```
一括処理

```shell:ptt.sh
#!/bin/bash
# https://news.mynavi.jp/article/bashonwindows-17/
# https://qiita.com/kaizen_nagoya/items/319672853519990cee42

 cd ../pdf
 for File in *; do
    case ${File##*.} in
        pdf|PDF )
            echo "Convert the PDF:" ${File}
            pdftotext -q ${File} ../text/${File}.txt ;;
        *) ;;
    esac
 done
```
# docker hub登録
docker 起動（最初）

```os:shell
$ docker run -v /Users/administrator/Downloads/godel:/tmp/godel -it ubuntu /bin/bash
```
dockerでの作業

```docker:ubuntu/bash
# apt update; apt -y upgrade
# apt install -y poppler-utils vim wget
# wget http://hirzels.com/martin/papers/canon00-goedel.pdf
# pdftotext -q  canon00-goedel.pdf canon00-goedel.txt
# awk -f wc.awk canon00-goedel.txt >godelwc.txt
```
docker hub 登録

```pc:bash 
$ docker commit 7aa98d94d8da kaizenjapan/godel 
$ docker push kaizenjapan/godel
```
次回起動

```os:shell
$ docker run -v /Users/administrator/Downloads/godel:/tmp/godel -it kaizenjapan/godel /bin/bash
```


# 文書履歴(document history)
ver. 0.01 初稿 20201020
ver. 0.02 ゲーデル論文URL記載 20201024午前
ver. 0.03 ゲーテル論文単語帳 20201024午後
ver. 0.04 単語帳作成、docker登録 20201024 夜
ver. 0.05 Reference 追記 20201025