메뉴 건너뛰기




Volumn 44, Issue 1, 2010, Pages 1-34

A revision of the proof of the Kepler conjecture

Author keywords

Formal proof; Higher order logic; Hypermap; Interval analysis; Linear programming; Sphere packings

Indexed keywords


EID: 77952010929     PISSN: 01795376     EISSN: 14320444     Source Type: Journal    
DOI: 10.1007/s00454-009-9148-4     Document Type: Article
Times cited : (78)

References (49)
  • 1
    • 0004524866 scopus 로고
    • The four color proof suffices
    • Appel, K., Haken, W.: The four color proof suffices. Math. Intell. 8(1), 10-20 (1986).
    • (1986) Math. Intell. , vol.8 , Issue.1 , pp. 10-20
    • Appel, K.1    Haken, W.2
  • 2
    • 77952009827 scopus 로고    scopus 로고
    • Flyspeck I: Tame graphs
    • Klein, G., Nipkow, T., Paulson, L. (eds.), May
    • Bauer, G., Nipkow, T.: Flyspeck I: Tame graphs. In: Klein, G., Nipkow, T., Paulson, L. (eds.) The Archive of Formal Proofs. http://afp. sf. net/entries/Flyspeck-Tame. shtml, May 2006.
    • (2006) The Archive of Formal Proofs
    • Bauer, G.1    Nipkow, T.2
  • 3
    • 85029837057 scopus 로고
    • Quantifier elimination for real closed fields by cylindrical algebraic decomposition
    • Second GI Conf., Kaiserslautern1975Lecture Notes in Comput. Sci, Berlin: Springer
    • Collins, G. E.: Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In: Automata Theory and Formal Languages, Second GI Conf., Kaiserslautern, 1975. Lecture Notes in Comput. Sci., vol. 33, pp. 134-183. Springer, Berlin (1975).
    • (1975) Automata Theory and Formal Languages , vol.33 , pp. 134-183
    • Collins, G.E.1
  • 6
    • 33744725175 scopus 로고    scopus 로고
    • Sphere packings V. Pentahedral prisms
    • Ferguson, S. P.: Sphere packings V. Pentahedral prisms. Discrete Comput. Geom. 36(1), 167-204 (2006).
    • (2006) Discrete Comput. Geom. , vol.36 , Issue.1 , pp. 167-204
    • Ferguson, S.P.1
  • 8
    • 67349170978 scopus 로고    scopus 로고
    • Formal proof-the four-colour theorem
    • Gonthier, G.: Formal proof-the four-colour theorem. Not. Am. Math. Soc. 55(11), 1382-1393 (2008).
    • (2008) Not. Am. Math. Soc. , vol.55 , Issue.11 , pp. 1382-1393
    • Gonthier, G.1
  • 12
    • 22044441063 scopus 로고    scopus 로고
    • A proof of the Kepler conjecture
    • Hales, T. C.: A proof of the Kepler conjecture. Ann. Math. 162, 1065-1185 (2005).
    • (2005) Ann. Math. , vol.162 , pp. 1065-1185
    • Hales, T.C.1
  • 13
    • 77952011253 scopus 로고    scopus 로고
    • Coquand, T., Lombardi, H., Roy, M.-F. (eds.) Mathematics, Algorithms, Proofs, number 05021 in Dagstuhl Seminar Proceedings, Dagstuhl, Germany, Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany
    • Hales, T. C.: Introduction to the Flyspeck project. In: Coquand, T., Lombardi, H., Roy, M.-F. (eds.) Mathematics, Algorithms, Proofs, number 05021 in Dagstuhl Seminar Proceedings, Dagstuhl, Germany, 2006. Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany. http://drops. dagstuhl. de/opus/volltexte/2006/432.
    • (2006) Introduction to the Flyspeck Project
    • Hales, T.C.1
  • 14
    • 33744751776 scopus 로고    scopus 로고
    • Sphere packings. III. Extremal cases
    • Hales, T. C.: Sphere packings. III. Extremal cases. Discrete Comput. Geom. 36(1), 71-110 (2006).
    • (2006) Discrete Comput. Geom. , vol.36 , Issue.1 , pp. 71-110
    • Hales, T.C.1
  • 15
    • 33744739113 scopus 로고    scopus 로고
    • Sphere packings. IV. Detailed bounds
    • Hales, T. C.: Sphere packings. IV. Detailed bounds. Discrete Comput. Geom. 36(1), 111-166 (2006).
    • (2006) Discrete Comput. Geom. , vol.36 , Issue.1 , pp. 111-166
    • Hales, T.C.1
  • 16
    • 33744723740 scopus 로고    scopus 로고
    • Sphere packings. VI. Tame graphs and linear programs
    • Hales, T. C.: Sphere packings. VI. Tame graphs and linear programs. Discrete Comput. Geom. 36(1), 205-265 (2006).
    • (2006) Discrete Comput. Geom. , vol.36 , Issue.1 , pp. 205-265
    • Hales, T.C.1
  • 19
    • 37849041322 scopus 로고    scopus 로고
    • The Jordan curve theorem, formally and informally
    • Hales, T. C.: The Jordan curve theorem, formally and informally. Am. Math. Mon. 114(10), 882-894 (2007).
    • (2007) Am. Math. Mon. , vol.114 , Issue.10 , pp. 882-894
    • Hales, T.C.1
  • 22
    • 67650049989 scopus 로고    scopus 로고
    • Formal proof
    • Hales, T. C.: Formal proof. Not. Am. Math. Soc. 55(11), 1370-1380 (2008).
    • (2008) Not. Am. Math. Soc. , vol.55 , Issue.11 , pp. 1370-1380
    • Hales, T.C.1
  • 24
    • 77952008771 scopus 로고    scopus 로고
    • A proof of the Dodecahedral conjecture
    • to appear, math/9811079
    • Hales, T. C., McLaughlin, S.: A proof of the Dodecahedral conjecture. J. Am. Math. Soc. (2009, to appear). math/9811079.
    • (2009) J. Am. Math. Soc.
    • Hales, T.C.1    McLaughlin, S.2
  • 26
    • 26844560473 scopus 로고    scopus 로고
    • A HOL theory of Euclidean space
    • Lecture Notes in Comput. Sci, Berlin: Springer
    • Harrison, J.: A HOL theory of Euclidean space. In: Theorem Proving in Higher Order Logics. Lecture Notes in Comput. Sci., vol. 3603, pp. 114-129. Springer, Berlin (2005).
    • (2005) Theorem Proving in Higher Order Logics , vol.3603 , pp. 114-129
    • Harrison, J.1
  • 27
    • 38049043841 scopus 로고    scopus 로고
    • Verifying nonlinear real formulas via sums of squares
    • Lecture Notes in Computer Science, K. Schneider and J. Brandt (Eds.), Kaiserslautern: Springer
    • Harrison, J.: Verifying nonlinear real formulas via sums of squares. In: Schneider, K., Brandt, J. (eds.) Proceedings of the 20th International Conference on Theorem Proving in Higher Order Logics, TPHOLs 2007. Lecture Notes in Computer Science, vol. 4732, pp. 102-118. Springer, Kaiserslautern (2007).
    • (2007) Proceedings of the 20th International Conference on Theorem Proving in Higher Order Logics, TPHOLs 2007 , vol.4732 , pp. 102-118
    • Harrison, J.1
  • 28
    • 69049117898 scopus 로고    scopus 로고
    • Formal proof-theory and practice
    • Harrison, J.: Formal proof-theory and practice. Not. AMS 55(11), 1395-1406 (2008).
    • (2008) Not. AMS , vol.55 , Issue.11 , pp. 1395-1406
    • Harrison, J.1
  • 29
    • 0003668851 scopus 로고    scopus 로고
    • Classics in MathematicsDifferential Operators with Constant Coefficients; reprint of the 1983 original, Berlin: Springer
    • Hörmander, L.: The Analysis of Linear Partial Differential Operators. II. Classics in Mathematics. Springer, Berlin (2005). Differential Operators with Constant Coefficients; reprint of the 1983 original.
    • (2005) The Analysis of Linear Partial Differential Operators. II
    • Hörmander, L.1
  • 30
    • 0003589321 scopus 로고
    • IEEE Standard for binary floating-point arithmetic
    • IEEE Standards Committee 754, Institute of Electrical and Electronics Engineers, New York
    • IEEE Standards Committee 754. IEEE Standard for binary floating-point arithmetic, ANSI/IEEE Standard 754-1985. Institute of Electrical and Electronics Engineers, New York (1985).
    • (1985) ANSI/IEEE Standard 754-1985
  • 31
    • 33847696509 scopus 로고    scopus 로고
    • Elimination des quantificateurs sur les réels en Coq
    • Available on the Web from
    • Mahboubi, A., Pottier, L.: Elimination des quantificateurs sur les réels en Coq. In: Journées Francophones des Langages Applicatifs (JFLA) (2002). Available on the Web from http://www. lix. polytechnique. fr/~assia/Publi/jfla02. ps.
    • (2002) Journées Francophones des Langages Applicatifs (JFLA)
    • Mahboubi, A.1    Pottier, L.2
  • 33
    • 33749570568 scopus 로고    scopus 로고
    • An interpretation of Isabelle/HOL in HOL Light
    • Lecture Notes in Computer Science, U. Furbach and N. Shankar (Eds.), Berlin: Springer
    • McLaughlin, S.: An interpretation of Isabelle/HOL in HOL Light. In: Furbach, U., Shankar, N. (eds.) IJCAR. Lecture Notes in Computer Science, vol. 4130, pp. 192-204. Springer, Berlin (2006).
    • (2006) Ijcar , vol.4130 , pp. 192-204
    • McLaughlin, S.1
  • 34
    • 26944493043 scopus 로고    scopus 로고
    • A proof-producing decision procedure for real arithmetic
    • Lecture Notes in Comput. Sci, Berlin: Springer
    • McLaughlin, S., Harrison, J.: A proof-producing decision procedure for real arithmetic. In: Automated deduction-CADE-20. Lecture Notes in Comput. Sci., vol. 3632, pp. 295-314. Springer, Berlin (2005).
    • (2005) Automated Deduction-CADE-20 , vol.3632 , pp. 295-314
    • McLaughlin, S.1    Harrison, J.2
  • 36
    • 44249093716 scopus 로고    scopus 로고
    • The pitfalls of verifying floating-point computations
    • Monniaux, D.: The pitfalls of verifying floating-point computations. TOPLAS 30(3), 12 (2008).
    • (2008) Toplas , vol.30 , Issue.3 , pp. 12
    • Monniaux, D.1
  • 37
    • 0348126394 scopus 로고    scopus 로고
    • Isabelle/HOL: A Proof Assistant for Higher-Order Logic
    • Berlin: Springer
    • Nipkow, T., Paulson, L., Wenzel, M.: In: Isabelle/HOL: A Proof Assistant for Higher-Order Logic. Lect. Notes in Comp. Sci., vol. 2283. Springer, Berlin (2002). http://www. in. tum. de/~nipkow/LNCS2283/.
    • (2002) Lect. Notes in Comp. Sci. , vol.2283
    • Nipkow, T.1    Paulson, L.2    Wenzel, M.3
  • 38
    • 33749579435 scopus 로고    scopus 로고
    • Flyspeck I: Tame graphs
    • Lect. Notes in Comp. Sci, U. Furbach and N. Shankar (Eds.), Berlin: Springer
    • Nipkow, T., Bauer, G., Schultz, P.: Flyspeck I: Tame graphs. In: Furbach, U., Shankar, N. (eds.) Automated Reasoning (IJCAR 2006). Lect. Notes in Comp. Sci., vol. 4130, pp. 21-35. Springer, Berlin (2006).
    • (2006) Automated Reasoning (IJCAR 2006) , vol.4130 , pp. 21-35
    • Nipkow, T.1    Bauer, G.2    Schultz, P.3
  • 40
    • 33749579674 scopus 로고    scopus 로고
    • Importing HOL into Isabelle/HOL
    • Lecture Notes in Computer Science, Berlin: Springer
    • Obua, S., Skalberg, S.: Importing HOL into Isabelle/HOL. In: Automated Reasoning. Lecture Notes in Computer Science, vol. 4130, pp. 298-302. Springer, Berlin (2006).
    • (2006) Automated Reasoning , vol.4130 , pp. 298-302
    • Obua, S.1    Skalberg, S.2
  • 41
    • 1542266056 scopus 로고    scopus 로고
    • Semidefinite programming relaxations for semialgebraic problems
    • Algebraic and geometric methods in discrete optimization
    • Parrilo, P. A.: Semidefinite programming relaxations for semialgebraic problems. Math. Program., Ser. B 96(2), 293-320 (2003). Algebraic and geometric methods in discrete optimization.
    • (2003) Math. Program., Ser. B , vol.96 , Issue.2 , pp. 293-320
    • Parrilo, P.A.1
  • 42
    • 22344435283 scopus 로고    scopus 로고
    • Motivations for an arbitrary precision interval arithmetic and the MPFI library
    • Revol, N., Rouillier, F.: Motivations for an arbitrary precision interval arithmetic and the MPFI library. Reliab. Comput. 11(4), 275-290 (2005).
    • (2005) Reliab. Comput. , vol.11 , Issue.4 , pp. 275-290
    • Revol, N.1    Rouillier, F.2
  • 44
    • 77952010626 scopus 로고    scopus 로고
    • Some new results on decidability for elementary algebra and geometry
    • submitted
    • Solovay, R. M., Arthan, R. D., Harrison, J.: Some new results on decidability for elementary algebra and geometry. APAL (2009, submitted).
    • (2009) APAL
    • Solovay, R.M.1    Arthan, R.D.2    Harrison, J.3
  • 48
    • 37049007542 scopus 로고    scopus 로고
    • Lecture Notes in Computer ScienceForeword by Dana S. Scott, Lecture Notes in Artificial Intelligence, F. Wiedijk (Ed.), Berlin: Springer
    • Wiedijk, F. (eds.): The Seventeen Provers of the World. Lecture Notes in Computer Science, vol. 3600. Springer, Berlin (2006). Foreword by Dana S. Scott, Lecture Notes in Artificial Intelligence.
    • (2006) The Seventeen Provers of the World , vol.3600


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.