Luis M. Pardo, Succinct obituary in memoriam of Joos Heintz. Journal of Complexity 87, April 2025, 101919.
Luis M. Pardo, Exploring implications of Trace (Inversion) Formula and Artin algebras in extremal Combinatorics. Appl. Algebra in Engineering, Comm. and Comput. 35 (2024), 71-118.
Luis M. Pardo (with J. Heintz, E.C. Segura, H. Ocar, A. Rojas-Paredes), An unfeasibility view of neural network learning. Journal of Complexity 75, April (2023), 101710.
Luis M. Pardo (with D. Sebastián), A promenade through correct test sequences I: Degree of constructible sets, Bézout's Inequality and density. Journal of Complexity 68 (2022), 101588.
Luis M. Pardo (with A. Hashemi, J. Heintz, P. Solernó), On Bézout Inequalities for non-homogeneous polynomial ideals. Journal of Symbolic Computation 106 (2021), 1-22.
Luis M. Pardo (with A. Hashemi, J. Heintz, 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.
Luis M. Pardo (with 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.
Luis M. Pardo (with B. Bank, J. Heintz, G. Matera, J. L. Montaña, A. Rojas-Paredes), Quiz Games as a model for Information Hiding. J. of Complexity 34 (2016), 1-29.
Luis M. Pardo (with C. Tirnauca, J. L Montaña, S. Ontañón, A.J. González ), Behavioral Modeling Based on Probabilistic Finite Automata: An Empirical Study. Sensors 16 (2016), 958 (16 pgs.); doi:10.3390/s16070958.
Luis M. Pardo (with C.E. Borges, J.L. Montaña), 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)
Luis M. Pardo (with M. Fernández), An Arithmetic Poisson Formula for the Multi--variate Resultant. Journal of Complexity 29 (2013), 323-350.
Luis M. Pardo (with J. Berthomieu), Spherical Radon Transform and the average of the condition number on certain Schubert varieties of a Grassmannian. Journal of Complexity 28 (2012), 382-421.
Luis M. Pardo (with B. Bank, M. Giusti, J. Heintz, L. Lehmann), Algorithms of Intrinsic Complexity for Point Searching in Compact Real Singular Hypersurfaces. Foundations of Computational Mathematics 12 (2012), 75-122.
Luis M. Pardo (with C. Beltrán), Fast Linear Homotopy to Find Approximate Zeros of Polynomial Systems. Foundations of Computational Mathematics 11 (2011), 95-129.
Luis M. Pardo (with C. Beltrán), 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.
Luis M. Pardo (with B.Bank, M. Giusti, J. Heintz), Bipolar varieties and real solving of a singular polynomial equation. Jaen Journal on Approximation 2 (2010), 65-77.
Luis M. Pardo (with C. Beltrán), Smale's 17th Problem: Average Polynomial Time to Compute Affine and Projective Solutions. Journal of the American Mathematical Society 22 (2009), 363-385.
Luis M. Pardo (with C. Beltrán), Efficient polynomial system-solving by numerical methods. Journal Fixed Point Theory and Applications 6 (2009), 65-85.
Luis M. Pardo (with J.L. Montaña), On the Vapnik-Chervonenkis dimension of computer programs which use transcendental elementary operations. Annals of Mathematics in Artificial Intelligence 56 (2009), 371-388.
Luis M. Pardo (with B. Bank, M. Giusti, J. Heintz), On the intrinsic complexity of point finding in real singular hypersurfaces, Information Processing Letters 109 (2009), 1141-1144.
Luis M. Pardo (with C. Beltrán), On Smale's 17th Problem: A probabilistic positive solution. Found. of Computational Mathematics 8 (2008), 1-43.
Luis M. Pardo (with C. E. Borges), On the probability distribution of data at points in real complete intersection varieties. Journal of Complexity 24 (2008), 492-523.
Luis M. Pardo (with M. Callau, J.L. Montaña), 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.
Luis M. Pardo (with C. Beltrán), Estimates on the distribution of the condition number of singular matrices. Foundations of Computational Mathematics 7 (2007), 87-134.
Luis M. Pardo (with C. Beltrán), 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.
Luis M. Pardo (with C. Beltrán), On the probability distribution of singular varieties of given corank. J. of Symbolic Computation 42 (2007), 4-29.
Luis M. Pardo (with C. Beltrán), 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.
Luis M. Pardo (with C. Beltrán), Upper Bounds on the distribution of the condition number of singular matrices. Comptes Rendues Mathematique 340 (2005), 915-919.
Luis M. Pardo (with C.L. Alonso, J.L. Montaña), 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.
Luis M. Pardo (with B. Bank, M. Giusti, J. Heintz), Generalized polar varieties: geometry and algorithms. J. of Complexity 21 (2005), 377-412.
Luis M. Pardo (with B. Bank, M. Giusti, J. Heintz), Generalized polar varieties and an efficient real elimination procedure. Kybernetika 40 (2004), 519-550.
Luis M. Pardo (with J. San Martín), Deformation techniques to solve Generalised Pham Systems. Theoretical Computer Science 315 (2004), 593-625.
Luis M. Pardo (with D. Castro, M. Giusti, J. Heintz, G. Matera), The Hardness of Polynomial Equation Solving. Foundations of Computational Mathematics 3 (2003), 347-420.
Luis M. Pardo (with D. Castro, J. San Martín), Systems of Rational Polynomial Equations have Polynomial Size Approximate Zeros on the Average. Journal of Complexity 19 (2003), 161--209.
Luis M. Pardo (with D. Castro, J.L. Montaña, J. San Martín), The distribution of condition numbers of rational data of bounded bit length. Foundations of Computational Mathematics 2 (2002), 1-52.
Luis M. Pardo (with T. Krick, M. Sombra), Sharp estimates for the arithmetic Nullstellensatz. Duke Mathematical Journal 109 (2001), 521-98.
Luis M. Pardo (with D. Castro, K. Hägele, J.E. Morais), Kronecker's and Newton's approaches to solving: a first comparison. Journal of Complexity 17 (2001), 212-303.
Luis M. Pardo (with M. Aldaz, G. Matera, J.L. Montaña), A new method to obtain lower bounds for polynomial evaluation. Theoretical Computer Science 259 (2001), 577-596.
Luis M. Pardo (with M. Aldaz, J. Heintz, G. Matera, J.L. Montaña), Time-Space Tradeoffs in algebraic complexity theory. Journal of Complexity 16 (2000), 2-49.
Luis M. Pardo (with K. Hägele, J.E. Morais, M. Sombra), On the intrinsic complexity of the Arithmetic Nullstellensatz. Journal of Pure and Applied Algebra 146 (2000), 103-183.
Luis M. Pardo (wih M. Aldaz, J. Heintz, G. Matera, J.L. Montaña), Time-space tradeoffs for polynomial evaluation. Comptes Rendues Acad. Sci. Paris, Sér. I 327 (1998), 907-912.
Luis M. Pardo (with M. Giusti, J. Heintz, J.E. Morais, J. Morgenstern), Straight-line programs in geometric elimination theory. Journal of Pure and Applied Algebra 124 (1998), 101-146.
Luis M. Pardo (with J.L. Montaña), On Kolmogorov complexity in the Real Turing machine setting. Information Processing Letters 67 (1998), 81-86.
Luis M. Pardo (with M. Aldaz, J. Heintz, G. Matera, J.L. Montaña), 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.
Luis M. Pardo (with J. Heintz, G. Matera, R. Wachenchauzer), The intrinsic complexity of parametric elimination methods. Electronic J. of SADIO 1 (1998), 37-51.
Luis M. Pardo (with M. Giusti, J. Heintz, J.E. Morais), Le rôle des structures des données dans les problèmes d'élimination. Comptes Rendues Acad. Sci. Paris, Sér. I 325 (1997), 1223-1228.
Luis M. Pardo (with M. Giusti, K. Hägele, J. Heintz, J.E. Morais, J.L. Montaña), Lower bounds for diophantine approximations,. Journal of Pure and Applied Algebra 117 & 118 (1997), 277-317.
Luis M. Pardo (with J.L. Montaña, J.E. Morais), Lower Bounds for Arithmetic Networks II. Sum of Betti Numbers. Applicable Algebra in Engineering Communications and Computing 7 (1996), 41-51.
Luis M. Pardo (with T. Krick), 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.
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.
Luis M. Pardo (with M. Giusti, J. Heintz, J.E. Morais), 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.
Luis M. Pardo (with F. Cucker, J.L. Montaña), 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)
Luis M. Pardo (with M. Giusti, J. Heintz, J. Sabia, P. Solerno, F. Smietansky), Sur la Complexité du Théorème des Zéros. In Approximation and Optimization 8 , J. Guddat et al. eds., Peter Lange Verlag, 1995, 274-329. (ISBN:3-631-49071-2)
Luis M. Pardo (with J.L. Montaña, T. Recio), A Note on Rabin's Width of a Complete Proof. Computational Complexity 4 (1994), 12-36.
Luis M. Pardo (with T. Krick), Une approche informatique pour l'approximation diophantienne. Comptes Rendues Acad. Sci. Paris, Sér. I 318 (1994), 407-412.
Luis M. Pardo (with J.L. Montaña), Lower Bounds for Arithmetic Networks. Applicable Algebra in Engineering Communications and Computing 4 (1993), 1-24.
Luis M. Pardo (with J.L. Montaña, R. Ramanakoraisina), An Extension of Warren's Lower Bounds for Approximations. Journal of Pure and Applied Algebra 87 (1993), 251-258.
Luis M. Pardo (with F. Cucker, J.L. Montaña), Time Bounded Computations over the Reals. International Journal of Algebra and Computation 2 (1992), 395-408.
Luis M. Pardo (with J.L. Montaña, 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.
Luis M. Pardo (with T. Recio), Rabin's Width of a Complete Proof and the Width of a Semi-Algebraic Set. In "Proc. EUROCAL'87" , J.H. Davenport ed., Lecture Notes in Computer Science 378 , Springer Verlag, 1989, 456--462.
Luis M. Pardo (with F. Cucker, 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.
Luis M. Pardo, The Polynomial Separation problem in Spec_r(A). Comptes Rendus Mathématiques // Mathematical Reports Acad. Sci. Canada 9 (1987), 17-20.
Journal of Complexity, Elsevier. (ISSN: 0885-064X) Member of the Editorial Board. Since Jan, 2004.
Applicable Algebra in Engineering, Communication and Computing, Springer-Nature. (ISSN: 0938-1279).
Member of the Managing Board. Since December, 2019
Member of the Editorial Board. Since June, 2014.
Luis M. Pardo, J. L. Montaña (eds.), Recent Advances in Real Complexity and Computation. Contemporary Mathematics 604 , RSME-AMS, Amer. Math. Soc., 2013. (ISBN: 978-0-521-68161-2)
Luis M. Pardo, A. Pinkus, E. Sulli, M. Todd (eds,), Foundations of Computational Mathematics, Santander 2005. London Mathematical Society Lecture Notes Series 331 , Cambridge University Press, 2006.(ISBN: 978-0-521-68161-2)
C. Bertone, F. Cioffi, Luis M. Pardo (eds.), Special Issue: Algebraic Geometry from an Algorithmic Point of View, ACA 2019, Montréal, Canada. Applicable Algebra in Engineering, Communications and Computing 31, issues 5-6, (2020), 323-482. (ISSN: 0938-1279 (print version), 1432-0622 (electronic version))
C. D'Andrea, M. Giusti, Luis M. Pardo, R. Piene (eds.), Effective Methods in Algebraic Geometry'2009, Barcelona. Journal of Symbolic Computation Vol. 45, No. 12, (2010), 1251-1470. (ISSN: 0747-7171)
A. Galligo, Luis M. Pardo, J. Schicho (eds.), MEGA'2007. Journal of Symbolic Computation Vol. 44, No. 9, (2009), 1087-1358. (ISSN: 0747-7171)
T. Lickteig, Luis M. Pardo (eds.), Festschrift for the 70th Birthday of Arnold Schönhage. Journal of Complexity 21, No. 4, (2005), pp. 369-650. (ISSN: 0885-064X)
M. Giusti, Luis M. Pardo (eds.), International Symposium on Symbolic and Algebraic Computation 2002. Journal of Symbolic Computation 36, No. 3-4, (2003), 287-683. (ISSN: 0747-7171)
[Sebastián, 2025] Daniel Sebastián San Martín. "Conjuntos Constructibles y Conjuntos Cuestores: Teoría de la Intersección y Primeras Interacciones con la Teoría del Aprendizaje Computacional". Universidad de Cantabria (September, 9, 2025). Advisor: Luis M. Pardo.
[Borges, 2011] Enrique Borges Hernández. "Programación Genética, Algoritmos Evolutivos y Aprendizaje Inductivo: Hacia una Solución al Problema XVII de Smale en el Caso Real". Universidad de Cantabria (March, 25th, 2011). Advisors: Luis M. Pardo, J.L. Montaña.
[Beltrán, 2006] Carlos Beltrán Álvarez. "Sobre el Problema 17 de Smale: Teoría de la Intersección y Geometría Integral". Universidad de Cantabria (September, 8th, 2006). Advisor: Luis M. Pardo.
[Castro, 2001] David Castro Esteban. "Sobre la Complejidad de la Representación de Variedades Algebraicas". Universidad de Cantabria (July, 6th, 2001). Advisor: Luis M. Pardo.
[Aldaz, 1999] Miguel Aldaz Zaragüeta. "Cotas Inferiores para problema de evaluación en la Teoría de la Complejidad Algebraica". Universidad Pública de Navarra (July, 18th, 1999). Advisors: Luis M. Pardo, J.L. Montaña.
[Hägele, 1998] Klemens Hägele. "Intrinsic Height Estimates for the Nullstellensatz". Universidad de Cantabria (July, 17th, 1998). Advisors: Luis M. Pardo, J. Heintz.
[Morais, 1997] José Enrique Morais San Miguel, "Resolución Eficaz de Sistemas de Ecuaciones Polinomiales Multivariadas". Universidad de Cantabria (December, 22th, 1997). Advisors: Luis M. Pardo, J. Heintz.
[Montaña, 1992] José Luis Montaña Arnaiz, "Cotas Inferiores para Problemas DeciSionales en la Teoría de la Complejidad Algebraica". Universidad de Cantabria (June, 3rd, 1992). Advisors: Luis M. Pardo, T. Recio.
2019. PhD Thesis: Ujué Etayo Rodríguez, "El problema de la distribución de puntos en la esfera". Advisor: Carlos Beltrán. Universidad de Cantabria , AsMember of the examining committee. March 15th, 2019.
2018. PhD Thesis: Juan González Criado del Rey, "Métricas de Condicionamiento y Puntos Bien Distribuidos en Variedades". Advisor: Carlos Beltrán. Universidad de Cantabria . As President of the examining committee). July 26th, 2018.
2015. PhD Thesis: Martijn Baartse, "The PCP Theorem in Real Number Complexity Theory". Advisor: K. Meer. Brandenburgischen Technischen Universität Cottbus–Senftenberg. As Gutachter (Reviewer). November 27th, 2015.
2013. PhD Thesis: Ariel Waissbein, "Algoritmos de deformación para la resolución de sistemas polinomiales". Advisor: G. Matera. Universidad de Buenos Aires. As Jurado (Reviewer). September 10th, 2013.
2010. PhD Thesis: Ezequiel Dratman, "Resolución eficiente de ciertos sistemas no lineales derivados de ecuaciones diferenciales". Advisor: G. Matera. Universidad de Buenos Aires. As Jurado (Reviewer). 2010 .
2008. PhD Thesis: Clemence Durvye, "Algorithmes pour la décomposition primaire des idéaux polynomiaux de dimension nulle donnés en évaluation". Advisor: G. Lecerf. Université de Versailles Sant-Quentin-en-Yvelines. As Rapporteur (Reviewer). June 9th, 2008.
2007. PhD Thesis: Carmen Martínez-Fernández, "Códigos y Grafos sobre Anillos de Enteros Complejos".Advisor: R. Beivide. Universidad de Cantabria , Spain. As Member of the examining committee.January, 2007.
2006. PhD Thesis: Clement Pernet, "Algèbre linéaire exacte efficace : le calcul du polynôme caractéristique". Advisors: D. Duval, J.G. Dumas. Université Jospeh Fourier Grenoble. As Examinateur (Member of the examining committee). September 27th, 2006.
2006. PhD Thesis: Xabier Dahan, "Sur la représentation des systémes polynomiaux: triangulation, méthodes modulaires, évaluation dynamique". Advisors: M. Giusti, E. Schost. École Polytechnique. As Examinateur (Member of the examining committee). November 24th, 2006.
2003. Habilitation à Diriger des Chercheurs : Gilles Villard, "Algorithmique en algèbre linéaire exacte". École Normale Supérieure de Lyon. As Membre du Jury (Member of the examining committee). March 21st, 2003.
2001. PhD Thesis: Cyril Brunie, "Étude et preuve de la faisabilité de l'approche combinée fractions continues/sous-résultants symétriques, implantation sur la machine de Turing TP de Schönhage et applications". Advisor: T. Lickteig. Univeristé de Limoges. As Rapporteur (Reviewer). June 29th, 2001.
2001. PhD Thesis: Marcela Almeida, "Aspectos algorítmicos para el cálculo de bases de módulos sobre anillos de polinomios". Advisor: P. Solerno. Universidad de Buenos Aires. As Jurado (Reviewer). November, 2001.
1999. PhD Thesis: Guy Mbakop, "Effiziente Lösung reeller polynomialer Gleichungssysteme". Advisor: B. Bank. Humboldt Universitäte zu Berlin. As Gutachter (Reviewer). September 24th, 1999.
[Pardo, 2014] Mario Pardo Serrano, The Height of the Discriminant Locus. Master Thesis, Mathematics & Computation , Universidad de Cantabria (February, 17th, 2014). Advisor: Luis M. Pardo.
[Fernández, 2012] Mario Fernández Pendás, Some Metric Aspects in Algebraic Geometry, on the Average. Master Thesis, Mathematics & Computation , Universidad de Cantabria (September, 2012). Advisor: Luis M. Pardo.
[Borges, 2005] Cruz Enrique Borges Hernández, Test de Primalidad, el AKS. Trabajo Académicamente Dirigido, Licenciado en Matemáticas (Plan BOE 2000) , Universidad de Cantabria (June, 2005). Advisor: Luis M. Pardo.
[Castro, 1997] David Castro Esteban, Sobre la complejidad de la Aproximación Diofántica y los Fundamentos del Análisis Numérico. Tesina de Licenciatura, Licenciado en Matemáticas (Plan BOE 1978) , Universidad de Cantabria (September, 1997). Advisor: Luis M. Pardo.
[Montaña, 1989] José Luis Montaña Arnaiz, Introducción del Modelo No-Escalar en Geometría Computacional . Tesina de Licenciatura, Licenciado en Matemáticas (Plan BOE 1978) , Universidad de Cantabria (June, 1989). Advisor: Luis M. Pardo.
Luis M. Pardo, Semblanza de Joos Heintz. Reseñas Ciencia y Teconología,Tomo 9, No. 2, (2021), 41-42. ISSN:2314-3134.
Luis M. Pardo (con T. Recio), El devenir de los ideales. In “Ejemplos Nebrija: M. José Garbayo Moreno. Catedrática de Matemáticas. Profesora Universitaria”, Fundación Antonio de Nebrija, 2018, 1-21.
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.
Luis M. Pardo, La Conjetura de Cook (P = NP?). Parte I: Lo Básico La Gaceta de la RSME 15 N. 1 (2012), 117-147.
Luis M. Pardo (with M. Giusti), Arithmetic with Polynomials, Rational Functions and Power Series. In "Computer Algebra Handbook", Springer Verlag, 2003, 13-17. (ISBN: 978-3-540-65466-7)
Luis M. Pardo (with M. Giusti, 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)
Luis M. Pardo (with T. Recio), El Profesor abellanas y la Falsa Moneda . Revista de la Sociedad Puig--Adams 58 (2001), 78-94. (ISSN: 11350261)
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)
Luis M. Pardo (with M. Aldaz, J.E. Morais, J.L. Montaña), 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)