Preprints

Publications in WoS

  1. Luis M. Pardo, Exploring implications of Trace (Inversion) Formula and Artin algebras in extremal Combinatorics.   To appear in Appl. Algebra in Engineering, Comm. and Comput., 2024.
  2. J. Heintz, Luis M. Pardo, E.C. Segura, H. Ocar, A. Rojas-Paredes, An unfeasibility view of neural network learning.   Journal of Complexity 75 (2023), 101710.
  3. Luis M. Pardo, D. Sebastian, A promenade through correct test sequences I: Degree of constructible sets, Bézout's Inequality and density.   Journal of Complexity 68 (2022), 101588
  4. A. Hashemi, J. Heintz, Luis M. Pardo, P. Solernó, On Bézout Inequalities for non-homogeneous polynomial ideals.   Journal of Symbolic Computation 106 (2021), 1-22.
  5. A. Hashemi, J. Heintz, Luis M. Pardo, P. Solernó, Intrinsic complexity for constructing zero-dimensional Groebner bases.   In Computer Algebra and Scientific Computing , Lecture Notes in Computer Science 12291 , Springer, 2020, 245-265.
  6. Luis M. Pardo, M. Pardo, On the zeta Mahler measure function of the Jacobian determinant, condition numbers and the height of the generic Discriminant.   Applicable Algebra, Engineering Communications and Computing, 27 (2016), 303-358.
  7. B. Bank, J. Heintz, G. Matera, J. L. Montaña, Luis M. Pardo, A. Rojas-Paredes, Quiz Games as a model for Information Hiding.   J. of Complexity 34 (2016), 1-29.
  8. M. Fernández, Luis M. Pardo, An Arithmetic Poisson Formula for the Multi--variate Resultant .  Journal of Complexity 29 (2013), 323-350.
  9. J. Berthomieu, Luis M. Pardo, Spherical Radon Transform and the average of the condition number on certain Schubert varieties of a Grassmannian .  Journal of Complexity 28 (2012), 382-421.
  10. B. Bank, M. Giusti, J. Heintz, L. Lehmann, Luis M. Pardo, Algorithms of Intrinsic Complexity for Point Searching in Compact Real Singular Hypersurfaces .  Foundations of Computational Mathematics 12 (2012), 75-122.
  11. C. Beltrán, Luis M. Pardo, Fast Linear Homotopy to Find Approximate Zeros of Polynomial Systems .   Foundations of Com- putational Mathematics 11 (2011), 95-129.
  12. C. Beltrán, Luis M. Pardo, Efficient Polynomial System Solving by Numerical Methods .   In "Randomization, Relaxation, and Complexity in Polynomial Equation Solving" , L. Gurvits, P. Pébay, J.M. Rojas, D. Thompson, eds., Contemporary Mathe- matics, vol. 556, American Mathematical Society, 2011, 1-35.
  13. C. Beltrán, Luis M. Pardo, Smale's 17th Problem: Average Polynomial Time to Compute Affine and Projective Solutions .   Journal of the American Mathematical Society 22 (2009), 363-385.
  14. C. Beltrán, Luis M. Pardo, Efficient polynomial system-solving by numerical methods .   Journal Fixed Point Theory and Applications 6 (2009), 65-85.
  15. J.L. Montaña, Luis M. Pardo, On the Vapnik-Chervonenkis dimension of computer programs which use transcendental ele- mentary operations .   Annals of Mathematics in Artificial Intelligence 56 (2009), 371-388.
  16. B. Bank, M. Giusti, J. Heintz, Luis M. Pardo, On the intrinsic complexity of point finding in real singular hypersurfaces .   Information Processing Letters 109 (2009), 1141-1144.
  17. C. Beltrán, Luis M. Pardo, On Smale's 17th Problem: A probabilistic positive solution .   Foundations of Computational Mathematics 8 (2008), 1-43.
  18. C. E. Borges, Luis M. Pardo, On the probability distribution of data at points in real complete intersection varieties .   Journal of Complexity 24 (2008), 492-523.
  19. M. Callau, J.L. Montaña, Luis M. Pardo, VC Dimension Bounds for Analytic Algebraic Computations .   In "Computing and Combinatorics" , Lecture Notes in Computer Science 5092, X. Hu & J. Wang eds., Springer Verlag, 2008, 62-71.
  20. C. Beltrán, Luis M. Pardo, Estimates on the distribution of the condition number of singular matrices .   Foundations of Computational Mathematics 7 (2007), 87-134.
  21. C. Beltrán, Luis M. Pardo, On the probability distribution of condition numbers of complete intersection varieties and the average radius of convergence of Newton's method in the underdetermined case .   Mathematics of Computation 76 (2007), 1393-1424.
  22. C. Beltrán, Luis M. Pardo, On the probability distribution of singular varieties of given corank .   Journal of Symbolic Computation 42 (2007), 4-29.
  23. C. Beltrán, Luis M. Pardo, Upper Bounds on the distribution of the condition number of singular matrices .   Comptes Rendues Mathematique 340 (2005), 915-919.
  24. C.L. Alonso, J.L. Montaña, Luis M. Pardo, On the number of random digits required in MonteCarlo integration of definable functions .   In "Mathematical Foundations of Computer Science 2005" , J. Jedrzejowicz, A. Szepietowski, eds., Lecture Notes in Computer Science 3618, Springer Verlag, 2005, 83-94.
  25. B. Bank, M. Giusti, J. Heintz, Luis M. Pardo, Generalized polar varieties: geometry and algorithms .   Journal of Complexity 21 (2005), 377-412.
  26. B. Bank, M. Giusti, J. Heintz, Luis M. Pardo, Generalized polar varieties and an efficient real elimination procedure .   Kybernetika 40 (2004), 519-550.
  27. J. San Martín, Luis M. Pardo, Deformation techniques to solve Generalised Pham Systems .   Theoretical Computer Science 315 (2004), 593-625.
  28. D. Castro, M. Giusti, J. Heintz, G. Matera, Luis M. Pardo, The Hardness of Polynomial Equation Solving .   Foundations of Computational Mathematics 3 (2003), 347-420.
  29. D. Castro, J. San Martín, Luis M. Pardo, Systems of Rational Polynomial Equations have Polynomial Size Approximate Zeros on the Average .   Journal of Complexity 19 (2003), 161--209.
  30. D. Castro, J.L. Montaña, J. San Martín, Luis M. Pardo, The distribution of condition numbers of rational data of bounded bit length .   Foundations of Computational Mathematics 2 (2002), 1-52.
  31. T. Krick, Luis M. Pardo, M. Sombra, Sharp estimates for the arithmetic Nullstellensatz . Duke Mathematical Journal 109 (2001), 521-98.
  32. D. Castro, K. Hägele, J.E. Morais, Luis M. Pardo, Kronecker's and Newton's approaches to solving: a first comparison . Journal of Complexity 17 (2001), 212-303.
  33. M. Aldaz, G. Matera, J.L. Montaña, Luis M. Pardo, A new method to obtain lower bounds for polynomial evaluation . Theoretical Computer Science 259 (2001), 577-596.
  34. M. Aldaz, J. Heintz, G. Matera, J.L. Montaña, Luis M. Pardo, Time-Space Tradeoffs in algebraic complexity theory . Journal of Complexity 16 (2000), 2-49.
  35. K. Hägele, J.E. Morais, Luis M. Pardo, M. Sombra, The intrinsic complexity of the Arithmetic Nullstellensatz . Journal of Pure and Applied Algebra 146 (2000), 103-183.
  36. M. Aldaz, J. Heintz, G. Matera, J.L. Montaña, Luis M. Pardo, Time-space tradeoffs for polynomial evaluation . Comptes Rendues Acad. Sci. Paris, Sér. I 327 (1998), 907-912.
  37. M. Giusti, J. Heintz, J.E. Morais, J. Morgenstern, Luis M. Pardo, Straight-line programs in geometric elimination theory . Journal of Pure and Applied Algebra 124 (1998), 101-146.
  38. J.L. Montaña, Luis M. Pardo, On Kolmogorov complexity in the Real Turing machine setting . Information Processing Letters 67 (1998), 81-86.
  39. M. Aldaz, J. Heintz, G. Matera, J.L. Montaña, Luis M. Pardo, Combinatorial Hardness Proofs for Polynomial Evaluation . In "Mathematical Foundations of Computer Science 1998" L. Brim, J. Gruska, J. Zlatuska, eds., Lecture Notes in Computer Science 1450 , Springer Verlag, 1998, 167-175.
  40. M. Giusti, J. Heintz, J.E. Morais, Luis M. Pardo, Le rôle des structures des données dans les problèmes d'élimination . Comptes Rendues Acad. Sci. Paris, Sér. I 325 (1997), 1223-1228.
  41. M. Giusti, K. Hägele, J. Heintz, J.E. Morais, J.L. Montaña, Luis M. Pardo, Lower bounds for diophantine approximations . Journal of Pure and Applied Algebra 117 & 118 (1997), 277-317.
  42. J.L. Montaña, J.E. Morais, Luis M. Pardo, Lower Bounds for Arithmetic Networks II. Sum of Betti Numbers . Applicable Algebra in Engineering Communications and Computing 7 (1996), 41-51.
  43. T. Krick, Luis M. Pardo, A computational method for diophantine approximations . In "Algorithms in Algebraic Geometry" , L. González Vega, T. Recio, eds., Progress in Mathematics 143 , Birkhauser Verlag, 1996, 193-253.
  44. Luis M. Pardo, How lower and upper complexity bounds meet in elimination theory . In "Applied Algebra, Algebraic Algorithms and Error-Correcting Codes" , G. Cohen, M. Giusti & T. Mora, eds., Lecture Notes in Computer Science 948 , Springer Verlag, 1995, 33-69.
  45. M. Giusti, J. Heintz, J.E. Morais,Luis M. Pardo, When polynomial equation systems can be "solved" fast? . In "Applied Algebra, Algebraic Algorithms and Error-Correcting Codes" , G. Cohen, M. Giusti & T. Mora, eds., Lecture Notes in Computer Science 948 , Springer Verlag, 1995, 205-231.
  46. J.L. Montaña, Luis M. Pardo, T. Recio, A Note on Rabin's Width of a Complete Proof . Computational Complexity 4 (1994), 12-36.
  47. T. Krick, Luis M. Pardo, Une approche informatique pour l'approximation diophantienne . Comptes Rendues Acad. Sci. Paris, Sér. I 318 (1994), 407-412. (pdf version)
  48. J.L. Montaña, Luis M. Pardo, Lower Bounds for Arithmetic Networks . Applicable Algebra in Engineering Communications and Computing 4 (1993), 1-24.
  49. J.L. Montaña, Luis M. Pardo, R. Ramanakoraisina An Extension of Warren's Lower Bounds for Approximations . Journal of Pure and Applied Algebra 87 (1993), 251-258.
  50. F. Cucker, J.L. Montaña, Luis M. Pardo, Time Bounded Computations over the Reals . International Journal of Algebra and Computation 2 (1992), 395-408.
  51. J.L. Montaña, Luis M. Pardo, T. Recio, The Non-Scalar Model of Complexity in Computational Geometry . In Progress in Mathematics 94 , T. Mora & C. Traverso, eds., Birkhauser Verlag, 1991, 347--361.
  52. Luis M. Pardo, T. Recio, Rabin's Width of a Complete Proof and the Width of a Semi-Algebraic Set . In "EUROCAL'87" , J.H. Davenport ed., Lecture Notes in Computer Science 378 , Springer Verlag, 1989, 456--462.
  53. F. Cucker, Luis M. Pardo, M. Raimondo, T. Recio, M.F. Roy, On the Computation of the Local and Global Analytic Branches of a Real Algebraic Curve . In "Applied Algebra, Algebraic Algorithms and Error-Correcting Codes" , L. Huguet & A. Poli, eds., Lecture Notes in Computer Science 356 , Springer Verlag, 1989, 161--181.

Other Referred Publications

  1. C.E. Borges, J.L. Montaña, Luis M. Pardo, A Sharp Fitness Function for the Problem of Finding Roots of Polynomial Equations Systems . In "Proceedings of the International Conference on Evolutionary Computation Theory and Applications (ECTA-2014)" , A. Rosa, J.J. Merelo & J. Filipe, eds., SCITEPRESS (Science and Technology Publications, Lda.), 2014, 294-301. (ISBN: 978-989-758-052-9)
  2. B.Bank, M. Giusti, J. Heintz, Luis M. Pardo, Bipolar varieties and real solving of a singular polynomial equation . Jaen Journal on Approximation 2 (2010), 65-77.
  3. C. Beltrán, Luis M. Pardo, On the Complexity of Non Universal Polynomial Equation Solving: Old and New Results . In "Foundations of Computational Mathematics, Santander 2005" , L.M. Pardo, A. Pinkus, E. Sülli & M. Todd, eds., London Mathematical Society Lecture Notes Series 331 Cambridge University Press, 2006, 1-35.
  4. J. Heintz, G. Matera, Luis M. Pardo, R. Wachenchauzer, The intrinsic complexity of parametric elimination methods . Electronic J. of SADIO 1 (1998), 37-51.
  5. F. Cucker, J.L. Montaña Luis M. Pardo, Models for Parallel Computation with real Numbers . In "Number Theoretic and Algebraic Methods in Computer Science (Moscow, 1993)" , A.J. van der Poorten, I. Shparlinski & H.G. Zimmer, eds., World Scientific, 1995, 53-63. (ISBN: 981-0-22334-X)
  6. M. Giusti, J. Heintz, Luis M. Pardo,, J. Sabia, P. Solerno, F. Smietansky, Sur la Complexité du Théorème des Zéeros . In Approximation and Optimization 8 , J. Guddat et al. eds., Peter Lange Verlag, 1995, 274-329. (ISBN:3-631-49071-2)
  7. Luis M. Pardo, The Polynomial Separation problem in $Spec_r(A)$ . Comptes Rendus Mathématiques // Mathematical Reports Acad. Sci. Canada 9 (1987), 17-20.

Other

  1. Luis M. Pardo, La Conjetura de Cook (P = NP?). Parte II: Probabilidad, Interactividad y Comprobación Probabilística de Demostraciones . La Gaceta de la RSME 15 N. 2 (2012), 303-333.
  2. Luis M. Pardo, La Conjetura de Cook (P = NP?). Parte I: Lo Básico . La Gaceta de la RSME 15 N. 1 (2012), 117-147.
  3. M. Giusti, Luis M. Pardo, Arithmetic with Polynomials, Rational Functions and Power Series . In "Computer Algebra Handbook", Springer Verlag, 2003, 13-17. (ISBN: 978-3-540-65466-7)
  4. M. Giusti, Luis M. Pardo, V. Weispfenning, Algorithms of Commutative Algebra and Algebraic Geometry. Algorithms for Polynomial Ideals and their varieties . In "Computer Algebra Handbook", Springer Verlag, 2003, 51-54. (ISBN: 978-3-540-65466-7)
  5. Luis M. Pardo, T. Recio, El Profesor abellanas y la Falsa Moneda . Revista de la Sociedad Puig--Adams 58 (2001), 78-94. (ISSN: 11350261)
  6. Luis M. Pardo, Universal Elimination requires Exponential running Time (Extended Abstract) . In "Actas EACA'2000", A. Montes ed., Univ. Politécnica de Cataluña, 2000, 25-51. (ISBN: 8469930370)
  7. M. Aldaz, J.E. Morais, J.L. Montaña, Luis M. Pardo, Lower Bounds for the complexity of arithmetic problems with integer input . In "The Bulletin of the Workshop on Model Theory and Complexity", Kronos, 1997, 3-8. (ISBN: 84-88620-08-X)

# Sexenios = 5

These publications yield 30 years of positive evaluation ( 5 periods of 6 years each, called "sexenios" in the Spanish academic system), based on research achievements and starting in 1988. I must submit for evaluation my publications of the next "sexenio" (2018-2023) in December, 2023 (too old to rock and roll, too young to die).
Period Evaluation
1988-1993 Positive
1994-1999 Positive
2000-2005 Positive
2005-2011 Positive
2012-2017 Positive
2018-2023 Posibly retired