???global.info.a_carregar???
Daniel Graça. Concluiu o Título de Agregado em Matemática em 2018/06/08 pela Universidade de Lisboa - Instituto Superior Técnico, Doutoramento em Matemática em 2007/09/05 pela Universidade de Lisboa - Instituto Superior Técnico, Mestrado em Matemática Aplicada em 2002/09/06 pela Universidade de Lisboa - Instituto Superior Técnico e Licenciatura em Matemática em 2000/07/07 pela Universidade do Algarve. É Investigador no Instituto de Telecomunicações, Professor Associado na Universidade do Algarve e Investigador na Universidade de Aveiro - Centro de Investigação e Desenvolvimento em Matemática e Aplicações. Publicou 31 artigos em revistas especializadas. Possui 4 capítulos de livros. Recebeu 3 prémios e/ou homenagens. Participa e/ou participou como Investigador em 1 projeto. Atua na área de Ciências Exatas com ênfase em Matemática. No seu currículo Ciência Vitae os termos mais frequentes na contextualização da produção científica, tecnológica e artístico-cultural são: Computational models which use real numbers; Computation with dynamical systems; Computability theory; Computational complexity; .
Read full resume ↓
Identification

Personal identification

Full name
Daniel Graça

Citation names

  • Graça, Daniel
  • Daniel S. Graça

Author identifiers

Ciência ID
2D11-56DE-3F11
ORCID iD
0000-0002-0330-833X

Addresses

  • Faculdade de Ciências e Tecnologia, Universidade do Algarve, Campus de Gambelas, 8005-139, Faro, Faro, Portugal (Professional)

Websites

Knowledge fields

  • Exact Sciences - Mathematics
Education
Degree Classification
2018/06/08
Concluded
 Matemática (Título de Agregado)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2007/09/05
Concluded
 Matemática (Doutoramento)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2002/09/06
Concluded
 Matemática Aplicada (Mestrado)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2000/07/07
Concluded
 Matemática (Licenciatura)
Universidade do Algarve Faculdade de Ciências e Tecnologia, Portugal
Affiliation

Science

Category
Host institution 		Employer
2024/02/02 - Current Researcher (Research) Universidade de Aveiro Centro de Investigação e Desenvolvimento em Matemática e Aplicações, Portugal
2007/01/01 - Current Researcher (Research) Instituto de Telecomunicações, Portugal

Teaching in Higher Education

Category
Host institution 		Employer
2023 - Current Associate Professor (University Teacher) Universidade do Algarve, Portugal
2007/09/06 - 2023 Assistant Professor (University Teacher) Universidade do Algarve Faculdade de Ciências e Tecnologia, Portugal
2002/09/09 - 2007/09/05 Assistant (University Teacher) Universidade do Algarve Faculdade de Ciências e Tecnologia, Portugal
2001/05/01 - 2002/09/08 Trainee Assistant (University Teacher) Universidade do Algarve Faculdade de Ciências e Tecnologia, Portugal
1999/11/01 - 2001/04/30 Tutor (University Teacher) Universidade do Algarve Faculdade de Ciências e Tecnologia, Portugal
Projects

Contract

Designation Funders
2017/04/01 - 2023/03/31 Computing with Infinite Data
grant.731143
Researcher
Universidade do Algarve, Portugal
 European Commission
Ongoing
Outputs

Publications

Book chapter
  1. Graça, Daniel; Ning Zhong. "Computability of Differential Equations". In Handbook of Computability and Complexity in Analysis, edited by Vasco Brattka; Peter Hertling. Springer, 2021.
    In press
  2. Daniel S. Graça; Ning Zhong. "Computability of Limit Sets for Two-Dimensional Flows". 494-503. Springer International Publishing, 2021.
    10.1007/978-3-030-80049-9_48
  3. Graça, Daniel. "Rigorous numerical computation of polynomial differential equations over unbounded domains". 469-473. 2015.
    10.1007/978-3-319-32859-1
  4. Graça, Daniel. "Computability and Dynamical Systems". 2011.
    10.1007/978-3-642-11456-4_11
Conference paper
  1. Graça, Daniel. "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". 2016.
    10.4230/LIPIcs.ICALP.2016.109
  2. Graça, Daniel. "Turing machines can be efficiently simulated by the General Purpose Analog Computer". 2013.
    10.1007/978-3-642-38236-9_16
Journal article
  1. Olivier Bournez; Riccardo Gozzi; Daniel S. Graça; Amaury Pouly. "A continuous characterization of PSPACE using polynomial ordinary differential equations". Journal of Complexity 77 (2023): 101755-101755. http://dx.doi.org/10.1016/j.jco.2023.101755.
    10.1016/j.jco.2023.101755
  2. Daniel Graça; Ning Zhong. "Analytic one-dimensional maps and two-dimensional ordinary differential equations can robustly simulate Turing machines". Computability (2023): 117-144. https://doi.org/10.3233/COM-210381.
    10.3233/com-210381
  3. Riccardo Gozzi; Daniel Graça. "Characterizing time computational complexity classes with polynomial differential equations". Computability 12 1 (2023): 23-57. http://dx.doi.org/10.3233/com-210384.
    10.3233/com-210384
  4. Daniel S. Graça; Ning Zhong. "Computing the exact number of periodic orbits for planar flows". Transactions of the American Mathematical Society (2022): https://doi.org/10.1090/tran/8644.
    10.1090/tran/8644
  5. Graça, Daniel; Zhong, Ning. "The set of hyperbolic equilibria and of invertible zeros on the unit ball is computable". Theoretical Computer Science 895 (2021): 48-54. http://dx.doi.org/10.1016/j.tcs.2021.09.028.
    10.1016/j.tcs.2021.09.028
  6. Daniel Graça; Cristóbal Rojas; Ning Zhong. "Computing geometric Lorenz attractors with arbitrary precision". Transactions of the American Mathematical Society 370 - (2018): 2955-2970. http://www.it.pt/Publications/PaperJournal/21388.
    10.1090/tran/7228
  7. Olivier Bournez; Daniel Graça; Amaury Pouly. "Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length". Journal of the ACM 64 6 (2017): Article no. 38-Article no. 38. http://www.it.pt/Publications/PaperJournal/21584.
    10.1145/3127496
  8. Olivier Bournez; Daniel Graça; Amaury Pouly. "On the Functions Generated by the General Purpose Analog Computer". Information and Computation To appear To appear (2017): To appear-To appear. http://www.it.pt/Publications/PaperJournal/21583.
    10.1016/j.ic.2017.09.015
  9. Olivier Bournez; Daniel Graça; Amaury Pouly. "Computing with polynomial ordinary differential equations". Journal of Complexity 36 - (2016): 106-140. http://www.it.pt/Publications/PaperJournal/20180.
    10.1016/j.jco.2016.05.002
  10. Amaury Pouly; Daniel Graça. "Computational complexity of solving polynomial differential equations over unbounded domains". Theoretical Computer Science 626 2 (2016): 67-82. http://www.it.pt/Publications/PaperJournal/20179.
    10.1016/j.tcs.2016.02.002
  11. Daniel Graça; Ning Zhong. "An analytic system with a computable hyperbolic sink whose basin of attraction is non-computable". Theory of Computing Systems 57 2 (2015): 478-520. http://www.it.pt/Publications/PaperJournal/17557.
    10.1007/s00224-015-9609-5
  12. Bournez, O.; Graça, D.S.; Pouly, A.; Zhong, N.. "Computability and computational complexity of the evolution of nonlinear dynamical systems". Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 7921 LNCS (2013): 12-21. http://www.scopus.com/inward/record.url?eid=2-s2.0-84880400407&partnerID=MN8TOARS.
    10.1007/978-3-642-39053-1_2
  13. Bournez, O.; Graça, D.S.; Hainry, E.. "Computation with perturbed dynamical systems". Journal of Computer and System Sciences 79 5 (2013): 714-724. http://www.scopus.com/inward/record.url?eid=2-s2.0-84875216204&partnerID=MN8TOARS.
    10.1016/j.jcss.2013.01.025
  14. Bournez, O.; Graça, D.S.; Pouly, A.. "On the complexity of solving initial value problems". Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC (2012): 115-121. http://www.scopus.com/inward/record.url?eid=2-s2.0-84874996606&partnerID=MN8TOARS.
    10.1145/2442829.2442849
  15. Graça, D.S.; Zhong, N.; Buescu, J.. "Computability, noncomputability, and hyperbolic systems". Applied Mathematics and Computation 219 6 (2012): 3039-3054. http://www.scopus.com/inward/record.url?eid=2-s2.0-84868546242&partnerID=MN8TOARS.
    10.1016/j.amc.2012.09.031
  16. Graa, D.S.; Zhong, N.; Dumas, H.S.. "The connection between computability of a nonlinear problem and its linearization: The HartmanGrobman theorem revisited". Theoretical Computer Science 457 (2012): 101-110. http://www.scopus.com/inward/record.url?eid=2-s2.0-84865474591&partnerID=MN8TOARS.
    10.1016/j.tcs.2012.07.013
  17. Graça, D.S.. "Noncomputability, unpredictability, and financial markets". Complexity 17 6 (2012): 24-30. http://www.scopus.com/inward/record.url?eid=2-s2.0-84863626541&partnerID=MN8TOARS.
    10.1002/cplx.21395
  18. Graça, D.; Zhong, N.. "Computability in planar dynamical systems". Natural Computing 10 4 (2011): 1295-1312. http://www.scopus.com/inward/record.url?eid=2-s2.0-84855975981&partnerID=MN8TOARS.
    10.1007/s11047-010-9230-0
  19. Bournez, O.; Graça, D.S.; Pouly, A.. "Solving analytic differential equations in polynomial time over unbounded domains". Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 6907 LNCS (2011): 170-181. http://www.scopus.com/inward/record.url?eid=2-s2.0-80052111907&partnerID=MN8TOARS.
    10.1007/978-3-642-22993-0_18
  20. Bournez, O.; Graça, D.S.; Hainry, E.. "Robust computations with dynamical systems". Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 6281 LNCS (2010): 198-208. http://www.scopus.com/inward/record.url?eid=2-s2.0-78349277634&partnerID=MN8TOARS.
    10.1007/978-3-642-15155-2_19
  21. Graça, D.S.; Zhong, N.. "Computing domains of attraction for planar dynamics". Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 5715 LNCS (2009): 179-190. http://www.scopus.com/inward/record.url?eid=2-s2.0-70350495810&partnerID=MN8TOARS.
    10.1007/978-3-642-03745-0_22
  22. Graa, D.S.; Buescu, J.; Campagnolo, M.L.. "Computational bounds on polynomial differential equations". Applied Mathematics and Computation 215 4 (2009): 1375-1385. http://www.scopus.com/inward/record.url?eid=2-s2.0-77955309868&partnerID=MN8TOARS.
    10.1016/j.amc.2009.04.055
  23. Collins, P.; Graça, D.S.. "Effective computability of solutions of differential inclusions the ten thousand monkeys approach". Journal of Universal Computer Science 15 6 (2009): 1162-1185. http://www.scopus.com/inward/record.url?eid=2-s2.0-67650731821&partnerID=MN8TOARS.
  24. Graça, D.S.; Zhong, N.; Buescu, J.. "Computability, noncomputability and undecidability of maximal intervals of IVPS". Transactions of the American Mathematical Society 361 6 (2009): 2913-2927. http://www.scopus.com/inward/record.url?eid=2-s2.0-67249122962&partnerID=MN8TOARS.
    10.1090/S0002-9947-09-04929-0
  25. Collins, P.; Graça, D.S.. "Effective Computability of Solutions of Ordinary Differential Equations The Thousand Monkeys Approach". Electronic Notes in Theoretical Computer Science 221 C (2008): 103-114. http://www.scopus.com/inward/record.url?eid=2-s2.0-57749122078&partnerID=MN8TOARS.
    10.1016/j.entcs.2008.12.010
  26. Graça, D.S.; Buescu, J.; Campagnolo, M.L.. "Boundedness of the Domain of Definition is Undecidable for Polynomial ODEs". Electronic Notes in Theoretical Computer Science 202 C (2008): 49-57. http://www.scopus.com/inward/record.url?eid=2-s2.0-40849100355&partnerID=MN8TOARS.
    10.1016/j.entcs.2008.03.007
  27. Graça, D.S.; Campagnolo, M.L.; Buescu, J.. "Computability with polynomial differential equations". Advances in Applied Mathematics 40 3 (2008): 330-349. http://www.scopus.com/inward/record.url?eid=2-s2.0-40749124093&partnerID=MN8TOARS.
    10.1016/j.aam.2007.02.003
  28. Bournez, O.; Campagnolo, M.L.; Graça, D.S.; Hainry, E.. "Polynomial differential equations compute all real computable functions on computable compact intervals". Journal of Complexity 23 3 (2007): 317-335. http://www.scopus.com/inward/record.url?eid=2-s2.0-34249708417&partnerID=MN8TOARS.
    10.1016/j.jco.2006.12.005
  29. Bournez, O.; Campagnolo, M.L.; Graça, D.S.; Hainry, E.. "The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation". Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 3959 LNCS (2006): 631-643. http://www.scopus.com/inward/record.url?eid=2-s2.0-33745845202&partnerID=MN8TOARS.
    10.1007/11750321_60
  30. Graça, D.S.; Campagnolo, M.L.; Buescu, J.. "Robust simulations of Turing machines with analytic maps and flows". Lecture Notes in Computer Science 3526 (2005): 169-179. http://www.scopus.com/inward/record.url?eid=2-s2.0-26444476497&partnerID=MN8TOARS.
  31. Graça, D.S.. "Some recent developments on Shannon's General Purpose Analog Computer". Mathematical Logic Quarterly 50 4-5 (2004): 473-485. http://www.scopus.com/inward/record.url?eid=2-s2.0-10844222952&partnerID=MN8TOARS.
    10.1002/malq.200310113

Other

Other output
  1. Computability of Ordinary Differential Equations. 2018. Daniel S. Graça; Ning Zhong. https://doi.org/10.1007%2F978-3-319-94418-0_21.
    10.1007/978-3-319-94418-0_21
Activities

Association member

Society Organization name Role
2017 - 2025 Association Computability in Europe Member of the Council
Distinctions

Award

2016 Best paper award (track B)
43rd International Colloquium on Automata, Languages and Programming (ICALP 2016), Italy
2010 Prémio Jovens Investigadores UTL/ CGD
Universidade de Lisboa, Portugal

Other distinction

2004 Programa Gulbenkian de Estímulo à Investigação
Fundação Calouste Gulbenkian, Portugal