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IT Member Profile

... Daniel da Silva Graça

Researcher

Daniel Graça

Academic position: Assistant Professor
Joining date: 31-12-2006
Roles in IT: Researcher
Thematic Line: Basic Sciences and Enabling Technologies
Group: Security and Quantum Information - Lx

Email: Send Email
Address: IT – Lisboa
Instituto Superior Técnico - Torre Norte - Piso 10
Av. Rovisco Pais, 1
1049 - 001 Lisboa
Tel: +351 21 841 84 54

Alternative Personal Web Page

ORCID iD
https://www.orcid.org/0000-0002-0330-833X

Collaboration Network
 

Scientific Achievements

  • Agregação, Instituto Superior Técnico, 08-06-2018
  • PhD, Instituto Superior Técnico, 05-09-2007
  • MSc, Instituto Superior Técnico, 09-09-2002
  • Universidade do Algarve, 01-01-2001, Assistant Professor
3Supervision of PhD theses
As Supervisor
As Co-supervisor
7Books Chapters
  • D. Graça, Computation with Real Numbers and Continuous-Time Dynamical Systems, Chapter in, Crossroads of Computability and Logic: Insights, Inspirations, and Innovations (CiE 2025), Springer, Cham, 2025
  • D. Graça, N. Zhong, Computability of Differential Equations, Chapter in, Handbook of Computability and Complexity in Analysis, Vasco Brattka and Peter Hertling, Springer International Publishing, Switzerland, 2020
  • J. Buescu, D. Graça, N. Zhong, Computability and Dynamical Systems, Chapter in, Dynamics and Games in Science I, M. Peixoto, A. Pinto, and D. Rand, Springer, 2011
  • O. Bournez, D. Graça, E. Hainry, Robust computations with dynamical systems, Chapter in, Proceedings of the 35th International Symposium on Mathematical Foundations of Computer Science (MFCS 2010), volume 6281 of Lecture Notes in Computer Science ARCoSS, pages 198-208, P. Hlinený and A. Kucera, Springer, 2010
  • D. Graça, Computing domains of attraction for planar dynamics, Chapter in, Proceedings of the 8th International Conference on Unconventional Computation (UC 2009), volume 5715 of Lecture Notes in Computer Science, C. S. Calude, J. F. Costa, N. Dershowitz, E. Freire, and G. Rozenberg, Springer, Ponta Delgada, Açores, 2009
  • O. Bournez, M.L. Campagnolo, D. Graça, E. Hainry, The General Purpose Analog Computer and Computable Analysis are two equivalent paradigms of analog computation, Chapter in, Theory and Applications of Models of Computation TAMC'06, volume 3959 of Lecture Notes in Computer Science, pages 631-643, J.-Y. Cai, S. B. Cooper, and A. Li, Springer, 2006
  • D. Graça, M.L. Campagnolo, J. Buescu, Robust simulations of Turing machines with analytic maps and flows, Chapter in, Proceedings of CiE'05, New Computational Paradigms, volume 3526 of Lecture Notes in Computer Science, pages 169-179, B. Cooper, B. Löwe, and L. Torenvliet, Springer, 2005
24Papers in Journals
  • D. Graça, N. Zhong, Robust non-computability of dynamical systems and computability of robust dynamical systems, Logical Methods in Computer Science, Vol. Volume 20, Issue 2, No., pp. -, June, 2024 | BibTex
  • O. Bournez, R. Gozzi, D. Graça, A. P. Pouly, A continuous characterization of PSPACE using polynomial ordinary differential equations, Journal of Complexity, Vol. 77, No. 1, pp. 101755 - 101755, August, 2023 | Full text (PDF 527 KBs) | BibTex
  • D. Graça, N. Zhong, Analytic one-dimensional maps and two-dimensional ordinary differential equations can robustly simulate Turing machines, Computability, Vol. 12, No. 2, pp. 117 - 144, June, 2023 | BibTex
  • D. Graça, R. Gozzi, Characterizing time computational complexity classes with polynomial differential equations, Computability, Vol. 12, No. 1, pp. 23 - 57, January, 2023 | BibTex
  • D. Graça, N. Zhong, Computing the exact number of periodic orbits for planar flows, Transactions of the American Mathematical Society, Vol. 375, No. 08, pp. 5491 - 5538, May, 2022 | BibTex
  • D. Graça, N. Zhong, The set of hyperbolic equilibria and of invertible zeros on the unit ball is computable, Theoretical Computer Science, Vol. 895, No. -, pp. 48 - 54, December, 2021 | BibTex
  • D. Graça, C. Rojas, N. Zhong, Computing geometric Lorenz attractors with arbitrary precision, Transactions of the American Mathematical Society, Vol. 370, No. -, pp. 2955 - 2970, January, 2018 | BibTex
  • O. Bournez, D. Graça, A. P. Pouly, Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length, Journal of the ACM, Vol. 64, No. 6, pp. Article no. 38 - Article no. 38, October, 2017 | BibTex
  • O. Bournez, D. Graça, A. P. Pouly, On the Functions Generated by the General Purpose Analog Computer, Information and Computation, Vol. To appear, No. To appear, pp. To appear - To appear, September, 2017 | BibTex
  • O. Bournez, D. Graça, A. P. Pouly, Computing with polynomial ordinary differential equations, Journal of Complexity, Vol. 36, No. -, pp. 106 - 140, October, 2016 | BibTex
  • A. P. Pouly, D. Graça, Computational complexity of solving polynomial differential equations over unbounded domains, Theoretical Computer Science, Vol. 626, No. 2, pp. 67 - 82, May, 2016 | BibTex
  • D. Graça, N. Zhong, An analytic system with a computable hyperbolic sink whose basin of attraction is non-computable, Theory of Computing Systems, Vol. 57, No. 2, pp. 478 - 520, February, 2015 | BibTex
  • O. Bournez, D. Graça, E. Hainry, Computation with perturbed dynamical systems, Journal of Computer and System Sciences, Vol. 79, No. 5, pp. 714 - 724, August, 2013,
    | Abstract     | Full text (PDF 325 KBs) | BibTex
  • D. Graça, N. Zhong, J. Buescu, Computability, noncomputability, and hyperbolic systems, Applied Mathematics and Computation, Vol. 219, No. 6, pp. 3039 - 3054, November, 2012 | BibTex
  • D. Graça, N. Zhong, H. S. D. Dumas, The connection between computability of a nonlinear problem and its linearization: the Hartman-Grobman theorem revisited, Theoretical Computer Science, Vol. 457, No. 26, pp. 101 - 110, October, 2012 | BibTex
  • D. Graça, Non-computability, unpredictability, and financial markets, Journal of Complexity, Vol. 17, No. 6, pp. 24 - 30, July, 2012 | BibTex
  • D. Graça, N. Zhong, Computability in planar dynamical systems, Natural Computing, Vol. 10, No. 4, pp. 1295 - 1312, December, 2011 | BibTex
  • D. Graça, N. Zhong, J. Buescu, Computability, noncomputability and undecidability of maximal intervals of IVPs, Transactions of the American Mathematical Society, Vol. 361, No. 6, pp. 2913 - 2927, January, 2009 | BibTex
  • P. Collin, D. Graça, Effective Computability of Solutions of Differential Inclusions - The Ten Thousand Monkeys Approach, JUCS - Journal of Universal Computer Science, Vol. 15, No. 6, pp. 1162 - 1185, January, 2009 | BibTex
  • D. Graça, J. Buescu, M.L. Campagnolo, Computational bounds on polynomial differential equations, Applied Mathematics and Computation, Vol. 215, No. 4, pp. 1375 - 1385, January, 2009 | BibTex
  • D. Graça, M.L. Campagnolo, J. Buescu, Computability with Polynomial Differential Equations, Advances in Applied Mathematics, Vol. 40, No. 3, pp. 330 - 349, January, 2008 | BibTex
  • O. Bournez, M.L. Campagnolo, D. Graça, E. Hainry, Polynomial differential equations compute all real computable functions on computable compact intervals, Journal of Complexity, Vol. 23, No. 3, pp. 317 - 335, June, 2007,
    | Abstract     | BibTex
  • D. Graça, Some recent developments on Shannon's General Purpose Analog Computer, Mathematical Logic Quarterly, Vol. 50, No. 4-5, pp. 473 - 485, January, 2004 | BibTex
  • D. Graça, J. F. Costa, Analog computers and recursive functions over the reals, Journal of Complexity, Vol. 19, No. 5, pp. 644 - 664, January, 2003 | BibTex
11Papers in Conferences
  • D. Graça, N. Zhong, Computability of Ordinary Differential Equations, Computability in Europe - CIE, Kiel, Germany, Vol. 10936, pp. 204 - 213, August, 2018 | BibTex
  • O. Bournez, D. Graça, A. P. Pouly, Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length - The General Purpose Analog Computer and Computable Analysis are two efficiently equivalent models of computations, International Colloquium on Automata, Languages and Programming - ICALP, Rome, Italy, Vol. Leibniz International Proceedings in Informatics (LIPIcs), volume 55, pp. 109:1 - 109:15, July, 2016 | BibTex
  • D. Graça, A. P. Pouly, Computational complexity of adaptive methods for solving polynomial differential equations over unbounded domains, Computability and Complexity in Analysis - CCA, Nancy, France, Vol. 1, pp. 1 - 12, July, 2013 | BibTex
  • O. Bournez, D. Graça, A. P. Pouly, On the complexity of solving polynomial initial value problems, International Symp. on Symbolic and Algebraic Computation - ISSAC, Grenoble, France, Vol. -, pp. 1 - 16, July, 2012 | BibTex
  • O. Bournez, D. Graça, A. P. Pouly, Solving analytic differential equations in polynomial time over unbounded domains, International Symp. on Mathematical Foundations of Computer Science, Warsaw, Poland, Vol. 6907, pp. 170 - 181, August, 2011 | BibTex
  • D. Graça, J. Buescu, M.L. Campagnolo, Computational bounds on polynomial differential equations, Workshop on Physics and Computation, Vienna, Austria, Vol. 1, pp. 1 - 20, August, 2008,
    | Abstract     | BibTex
  • P. Colins, D. Graça, Effective computability of solutions of ordinary differential equations — the thousand monkeys approach, Computability and Complexity in Analysis - CCA, Hagen, Germany, Vol. 221, pp. 104 - 113, August, 2008,
    | Abstract     | BibTex
  • D. Graça, Computability and dynamical systems: A perspective, Weak Arithmetics Days, Sevilla, Spain, Vol. -, pp. 95 - 107, June, 2008 | BibTex
  • D. Graça, J. Buescu, M.L. Campagnolo, Boundedness of the domain of definition is undecidable for polynomial odes, Computability and Complexity in Analysis - CCA, Siena, Italy, Vol. 202, pp. 49 - 57, June, 2007 | BibTex
  • D. Graça, N. Zhong, J. Buescu, The ordinary differential equation defined by a computable function whose maximal interval of existence is non-computable, Conf. on Real Numbers and Computers - RNC, Nancy, France, Vol. none, pp. 33 - 40, July, 2006 | BibTex
  • D. Graça, Computability via analog circuits, Computability and Complexity in Analysis - CCA, Cincinnati, United States, Vol. none, pp. 229 - 240, August, 2003 | BibTex

Closed Projects1

Acronym Name Funding Agency Start date Ending date
COMPUTR COMPUTR : Calcul en temps continu sur les réels INRIA 01-01-2010 01-01-2011
3Awards
  • O. Bournez, D. Graça, A. P. Pouly, Best ICALP Paper (2016), Best ICALP Paper award (track B) for the 2016 edition of the ICALP conference. The awarded paper was: * Olivier Bournez, Daniel Graça and Amaury Pouly: "Polynomial Time corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length". More information can be found on the following link: https://www.eatcs.org/index.php/best-icalp-paper, 01-07-2016
  • D. Graça, Prémio Jovens Investigadores UTL/Deloitte e UTL/Caixa Geral de Depósito 2010 (matemática), Vencedor do "Prémio Jovens Investigadores UTL/Deloitte e UTL/Caixa Geral de Depósitos 2010", na categoria de "matemática", 01-06-2010
  • D. Graça, Programa Gulbenkian de Estímulo à Investigação, Was one of the selected to get a grant from the ''Programa Gulbenkian de Estímulo à Investigação'' awarded by the Calouste Gulbenkian Foundation for the topic of ''Dynamical Systems'', with the project ''Computabilidade e Complexidade em Sistemas Dinâmicos Contínuos'', 01-02-2004
3Miscellaneous
  • O. Bournez, D. Graça, A. P. Pouly, Rigorous numerical computation of polynomial differential equations over unbounded domains, Editor of Conference Proceedings, DOI: 10.1007/978-3-319-32859-1, 01-11-2015
  • O. Bournez, D. Graça, A. P. Pouly, N. Zhong, Computability and computational complexity of the evolution of nonlinear dynamical systems, Invited Talks, DOI: https://doi.org/10.1007/978-3-642-39053-1_2, 01-07-2013
  • O. Bournez, D. Graça, A. P. Pouly, Turing machines can be efficiently simulated by the General Purpose Analog Computer, Editor of Conference Proceedings, DOI: https://doi.org/10.1007/978-3-642-38236-9_16, 01-05-2013
30Short Courses and Seminars
  • D. Graça, Computability of geometric Lorenz attractors, Germany, 11-2017
  • D. Graça, Computability of the Lorenz attractor, Portugal, Lisbon, 04-2016
  • D. Graça, A brief introduction to Computable Analysis, Portugal, Lisbon, 01-2016
  • D. Graça, Computability and complexity in continuous dynamical systems, Germany, Kochel, 09-2015
  • D. Graça, N. Zhong, Computation of the asymptotic behavior of dynamical systems, Japan, Tokyo, 07-2015
  • D. Graça, Non-computability and financial markets, Portugal, Lisboa, 07-2012
  • D. Graça, N. Zhong, Computability in Planar Dynamical Systems, Portugal, Porto, 01-2010
  • D. Graça, Boundedness of the domain of definition is undecidable for polynomial ODEs, Italy, Siena, 06-2007
  • D. Graça, Computability problems for differential equations, Spain, Seville, 06-2007
  • D. Graça, Problemas de computabilidade em equações diferenciais, Portugal, Coimbra, 05-2007
  • D. Graça, An ordinary differential equation defined by a computable function whose maximal interval of existence is non-computable, France, Nancy, 07-2006
  • D. Graça, Algumas limitações fundamentais na resolução numérica de equações diferenciais ordinárias, Portugal, Lisbon, 06-2006
  • D. Graça, The General Purpose Analog Computer and Computable Analysis are two equivalent paradigms of analog computation, China, Beijing, 05-2006
  • D. Graça, The ordinary differential equation defined by a computable function whose maximal interval of existence is non-computable, United States, Cincinnati, 02-2006
  • D. Graça, On the evolution of systems defined by computable Initial Value Problems, Portugal, Coimbra, 01-2006
  • D. Graça, On the equivalence of some models of analog computation, Portugal, Lisbon, 09-2005
  • D. Graça, Computability in the General Purpose Analog Computer, Portugal, Lisbon, 06-2005
  • D. Graça, Discrete-time and continuous-time analog computation, Italy, Bologna, 06-2005
  • D. Graça, Robust simulations of Turing machines with analytic maps and flows, Netherlands, Amsterdam, 06-2005
  • D. Graça, Computing with continuous-time analog circuits, France, Fontainebleau, 05-2005
  • D. Graça, Robust simulations of Turing machines with analytic maps and flows, France, Lyon, 03-2005
  • D. Graça, A digression over the General Purpose Analog Computer, France, Nancy, 02-2005
  • D. Graça, On robust analog simulations of Turing machines, Portugal, Lisbon, 11-2004
  • D. Graça, Formalizing computational models based on circuits, Portugal, 01-2004
  • D. Graça, Computability via analog circuits, United States, Cincinnati, 08-2003
  • D. Graça, Turing universality for the GPAC model, Portugal, Lisbon, 03-2003
  • D. Graça, Caracterização computacional de algumas classes de sistemas dinâmicos contínuos, Portugal, Faro, 01-2003
  • D. Graça, Introdução à teoria da computabilidade, Portugal, Faro, 01-2003
  • D. Graça, Recursion theory over the reals, Portugal, 05-2002
  • D. Graça, Some considerations about the GPAC model, Portugal, Lisbon, 04-2002
13Conference Committees
  • 17th International Conference on Reachability Problems (RP'23), Scientific Committee, 2023
  • Continuity, Computability, Constructivity (CCC 2023), Scientific Committee, 2023
  • 20th International Conference on Computability and Complexity in Analysis, Scientific Committee, 2023
  • Computability and Complexity in Analysis - CCA, Scientific Committee, 2020
  • Continuity, Computability, Constructivity, Conference co-chair, 2020
  • Continuity, Computability, Constructivity, Scientific Committee, 2019
  • Continuity, Computability, Constructivity, Conference co-chair, 2018
  • Computability and Complexity in Analysis - CCA, Scientific Committee, 2017
  • Computability and Complexity in Analysis - CCA, Organizing Committee, 2016
  • CIM International Conf. and Advanced Schools Mathematics of Planet Earth - MPE, Scientific Committee, 2013
  • Logic Colloquium, Organizing Committee, 2013
  • Encontro Nacional da Sociedade Portuguesa de Matemática - ENSPM, Organizing Committee, 2012
  • Computability and Complexity in Analysis - CCA, Scientific Committee, 2010
2Editorial Committees
  • Guest Editor, Logical Methods in Computer Science, 30-11-2020 - 30-05-2023
  • Guest Editor, Logical Methods in Computer Science, 31-10-2018 - 19-11-2021
1Refereeing Journals
  • Physics Letters, Section A: General, Atomic and Solid State Physics
    2007, 1 review(s);
3Refereeing Conferences
  • Appl. Semantics - APPSEM
    2004, 1 review(s);
  • Machines, Computations and Universality - MCU
    2007, 1 review(s); 2004, 1 review(s);
  • Computability and Complexity in Analysis - CCA
    2010, 1 review(s);

Activities from this researcher fall under the following United Nations Strategic Development Goals (SDGs):

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