Daniel Graça's publications

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• D. S. Graça. Non-computability, unpredictability, and financial markets. To appear in Complexity.

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• O. Bournez, D. S. Graça, and A. Pouly. Solving analytic differential equations in polynomial time over unbounded domains. Proceedings of the 36th International Symposium on Mathematical Foundations of Computer Science (MFCS 2011). In F. Murlak and P. Sankowski, editors, volume 6907 of Lecture Notes in Computer Science ARCoSS (Advanced Research in Computing and Software Science), pages 170-181, Springer, 2011.

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• D. S. Graça and N. Zhong. Computability in planar dynamical systems. Natural Computing, 10(4):1295-1312, 2011.

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• J. Buescu, D. S. Graça, and N. Zhong. Computability and Dynamical Systems. In M. Peixoto, A. Pinto, and D. Rand, editors, "Dynamics and Games in Science I", Springer, pages 169-181, 2011.

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• O. Bournez, D. S. Graça, and E. Hainry. Robust computations with dynamical systems. Proceedings of the 35th International Symposium on Mathematical Foundations of Computer Science (MFCS 2010). In P. Hlinený and A. Kucera, editors, volume 6281 of Lecture Notes in Computer Science ARCoSS (Advanced Research in Computing and Software Science), pages 198-208, Springer, 2010.

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• D. S. Graça, J. Buescu, and M. L. Campagnolo. Computational bounds on polynomial differential equations. Applied Mathematics and Computation, 215(4):1375-1385, 2009.

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• D. S. Graça and N. Zhong. Computing Domains of Attraction for Planar Dynamics. In C. S. Calude, J. F. Costa, N. Dershowitz, E. Freire, and G. Rozenberg, editors, Proceedings of the 8th International Conference on Unconventional Computation (UC 2009), volume 5715 of Lecture Notes in Computer Science, pages 179-190. Springer, 2009.

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• P. Collins and D. S. Graça. Effective computability of solutions of differential inclusions - the ten thousand monkeys approach. Journal of Universal Computer Science, 15(6):1162-1185, 2009.

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• D. S. Graça, N. Zhong, and J. Buescu. Computability, noncomputability and undecidability of maximal intervals of IVPs. Transactions of the American Mathematical Society, 361(6):2913-2927, 2009.

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• P. Collins and D. S. Graça. Effective computability of solutions of ordinary differential equations - the thousand monkeys approach. Electronic Notes in Theoretical Computer Science, 221:103-114, 2008. Presented at the Fifth International Conference on Computability and Complexity in Analysis (CCA 2008).

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• D. S. Graça, J. Buescu, and M. L. Campagnolo. Boundedness of the domain of definition is undecidable for polynomial odes. Electronic Notes in Theoretical Computer Science, 202:49-57, 2008. Proceedings of the 4th International Conference of Computability and Complexity in Analysis (CCA 2007).

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• D. S. Graça, M. L. Campagnolo, and J. Buescu. Computability with polynomial differential equations. Advances in Applied Mathematics, 40(3):330-349, 2008.

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• D. S. Graça. Computability and dynamical systems: A perspective. In Proceedings of the 26th Weak Arithmetics Days, pages 95-107. Universidad de Sevilla, 2008.

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• O. Bournez, M. L. Campagnolo, D. S. Graça, and E. Hainry. Polynomial differential equations compute all real computable functions on computable compact intervals. Journal of Complexity, 23:317-335, 2007.

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• D. S. Graça. Computability with Polynomial Differential Equations. PhD thesis, IST, Universidade Técnica de Lisboa, 2007. Supervised by J. Buescu and M. L. Campagnolo.

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• O. Bournez, M. L. Campagnolo, D. S. Graça, and E. Hainry. The General Purpose Analog Computer and Computable Analysis are two equivalent paradigms of analog computation. In J.-Y. Cai, S. B. Cooper, and A. Li, editors, Theory and Applications of Models of Computation TAMC'06, volume 3959 of Lecture Notes in Computer Science, pages 631-643. Springer, 2006.

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• D. S. Graça, N. Zhong, and J. Buescu. The ordinary differential equation defined by a computable function whose maximal interval of existence is non-computable. In G.Hanrot and P.Zimmermann, editors, Proceedings of the 7th Conference on Real Numbers and Computers (RNC 7), pages 33-40. LORIA/INRIA, 2006.

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• D. S. Graça, M. L. Campagnolo, and J. Buescu. Robust simulations of Turing machines with analytic maps and flows. In B. Cooper, B. Löwe, and L. Torenvliet, editors, Proceedings of CiE'05, New Computational Paradigms, volume 3526 of Lecture Notes in Computer Science, pages 169-179. Springer, 2005.

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• D. S. Graça. Some recent developments on Shannon's General Purpose Analog Computer. Mathematical Logic Quarterly, 50(4-5):473-485, 2004.

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• D. S. Graça. Computability via analog circuits. In V. Brattka, M. Schröder, K. Weihrauch, and N. Zhong, editors, Procs. International Conference on Computability and Complexity in Analysis, pages 229-240. FernUniversität in Hagen, 2003.

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• D. S. Graça and J. F. Costa. Analog computers and recursive functions over the reals. Journal of Complexity, 19(5):644-664, 2003.

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• D. S. Graça. The general purpose analog computer and recursive functions over the reals Master's thesis, IST, Universidade Técnica de Lisboa, 2002. Supervised by J. F. Costa.

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