Department of Mathematics, IST University of Lisbon

Member of CFCUL Centro de Filosofia das Ciências da Universidade de Lisboa

- BSc and a MSc in Physics, MSc in Applied Mathematics, PhD in Mathematics, and Aggregation (Habilitation) in Computer Science.
- Current research interests: Computability; Recursion-theoretical approach to formal epistemology; Philosophy of science.

- Labirintos de Literatura e Ciência, Teatro Thalia — 19 de Novembro, 2018.
- IEEE Task Force, Unconventional Computing, Emergent Technologies TC, IEEE Computational Intelligence Society.
- Matemática no Técnico: Vem conhecer as melhores profissões do mundo..., Instituto Superior Técnico — 30 de Junho, 2017.
- Invited Speaker, Unconventional Computation and Natural Computation 2017, June 5-9, 2017, University of Arkansas campus in Fayetteville, Arkansas.
- Third Lisbon International Conference on Philosophy of Science: Contemporary Issues, December 14-16, 2016, Centre for Philosophy of Science of the University of Lisbon (CFCUL).
- O Jogo da Imitação, by José Félix Costa, Jornal EXPRESSO.

- Matemática Discreta (Discrete Mathematics), by José Félix Costa and Paula Gouveia, IST Press, 727 pp, January 2018.

- Classifying the computational power of stochastic physical oracles, by Edwin Beggs, Prdro Cortez, José Félix Costa, and John V. Tucker. International Journal of Unconventional Computing, 14(1): 59--90, Old City Publishing, Inc., 2018.
- Solving Smullyan puzzles with formal systems, by José Félix Costa and Diogo Poças, Axiomathes 28(2):181-199, Springer, 2018.
- East-West Paths to Unconventional Computing, by Andrew Adamatzky, Selim Akl, Mark Burgin, Cristian S. Calude, José Félix Costa, Mohammad M. Dehshibi, Yukio-Peggio Gunji, Zoran Konkoli, Bruce MacLennan, Bruno Marchal, Maurice Margenstern, Genaro J. Martinez, Richard Mayne, Kenichi Morita, Andrew Schumann, Yaroslav D. Sergeyev, Georgios Ch. Sirakoulis, Susan Stepney, Karl Svozil, Hector Zenil, Progress in Biophysics and Molecular Biology 131(1): 469--493, 2017.
- The Power of Analogue-digital Machines, by José Félix Costa. Matthew J. Patitz and Mike Stannett (Editors), Unconventional Computation and Natural Computation 2017, 16th International Conference, UCNC 2017, Fayetteville, AR, USA, June 5-9, 2017,
*Lecture Notes in Computer Science*10240:3--7, Springer, 2017. - The unity of science as seen through the universal computer, by José Félix Costa, International Journal of Unconventional Computing, 13(1): 59--81, Old City Publishing, Inc., 2017.
- Computations with oracles that measure vanishing quantities, by Edwin Beggs, José Félix Costa, Diogo Poças, and John V. Tucker, Mathematical Structures in Computer Science, Cambridge University Press, 27(8): 1315--1363, December 2017.
- A hierarchy for BPP//log* based on counting calls to an oracle, by Edwin Beggs, Pedro Cortez, José Félix Costa, and John V. Tucker, in Andrew Adamatzky (editor): Emergent Computation (Festschrift for Selim Akl), Chapter III: 39--56. Book series: Emergence, Complexity and Computation, Vol. 21, Springer, 2017.
- An Analogue-digital Model of Computation: Turing Machines with Physical Oracles, by Tânia Ambaram, Edwin Beggs, José Félix Costa, Diogo Poças, and John V. Tucker, in Andrew Adamatzky (editor): Advances in Unconventional Computing. Chapter IV: 73--115. Book series: Emergence, Complexity and Computation, Vol. 22, Springer, 2017.
- The Physics of the Halting Problem, by José Félix Costa, Kairos, Journal of Philosophy & Science, 16(1): 14--60, De Gruyter, 2016.
- How far from P is NP, by José Félix Costa, La Nuova Critica, 61-62: 83-113, 2015 (
*Computability, Conceptual Complexity and General Semantics*). Cover. - Uncertainty in time, by José Félix Costa, Parallel Processing Letters, 25(1), 2015.
- Three forms of physical measurement and their computability, by Edwin Beggs, José Félix Costa, and John V. Tucker.
*The Review of Symbolic Logic*, 7(4): 618--646, 2014. - An Analogue-digital Church-Turing Thesis, by Edwin Beggs, José Félix Costa, Diogo Poças, and John V. Tucker.
*International Journal of Foundations of Computer Science*, 25(4): 373 -- 389, 2014. - A natural computation model of positive relativisation, by Edwin Beggs, José Félix Costa, and John V. Tucker.
*International Journal of Unconventional Computing*, 10(1-2): 111--141, Old City Publishing, Inc., 2014. - Incomputability at the Foundations of Physics (A Study in the Philosophy of Science), by José Félix Costa.
*Oxford Journal of Logic and Computation*, 23(6): 1225--1248, 2013. - Oracles that measure thresholds: The Turing machine and the broken balance, by Edwin Beggs, José Félix Costa, Diogo Poças, and John V. Tucker.
*Oxford Journal of Logic and Computation*, 23(6): 1155--1181, 2013. - The ARNN model relativizes P == NP and P =/= NP, by José Félix Costa and Raimundo Leong,
*Theoretical Computer Science*, 499(1): 2--22, Elsevier, August 12, 2013. - On the power of threshold measurements as oracles, by Edwin Beggs, José Félix Costa, Diogo Poças, and John V. Tucker. Giancarlo Mauri, Alberto Dennunzio, Luca Manzoni, and Antonio E. Porreca (Editors), Unconventional Computation and Natural Computation,
*Lecture Notes in Computer Science*7956:6--18, Springer, 2013. - Processes with Infinite Liveness Requirements, by Hélia Guerra and José Félix Costa,
*The Journal of Logic and Algebraic Programming*, 82(3-4): 137--161, Elsevier, April--May 2013. - The impact of models of a physical oracle on computational power, by Edwin Beggs, José Félix Costa, and John V. Tucker.
*Mathematical Structures in Computer Science*22(5): 853--879, Cambridge University Press, 2012. - Axiomatising physical experiments as oracles to algorithms, by Edwin Beggs, José Félix Costa, and John V. Tucker,
*Philosophical Transactions of the Royal Society, Series A (Mathematical, Physical and Engineering Sciences)*, 370(1971): 3359--3384, 2012. - Unifying science through computation: Reflections on computability and physics, by Edwin Beggs, José Félix Costa, and John V. Tucker. Olga Pombo, Juan Manuel Torres, John Symons, and S. Rahman (editors): Special Sciences and the Unity of Science, Chapter IV: 53--80. Book series:
*Logic, Epistemology, and the Unity of Science*, Vol. 24, Springer, 2012. - Limits to measurements in experiments governed by algorithms, by Edwin Beggs, José Félix Costa, and John V. Tucker.
*Mathematical Structures in Computer Science*20(06): 1019--1050, Cambridge University Press, 2010. - Physical oracles: the Turing machine and the Wheatstone bridge, by Edwin Beggs, José Félix Costa, and John V. Tucker.
*Studia Logica*, 95(1--2): 279--300, July 2010. - Computational Models of Measurement and Hempel's Axiomatization, by Edwin Beggs, José Félix Costa, and John V. Tucker.
*Book Chapter*, in Arturo Carsetti (editor):*Causality, Meaningful Complexity and Embodied Cognition*, Chapter IX: 155--184. Book series: Theory and Decision Library A, Vol. 46, Springer, 2010. - A foundation for real recursive function theory, by José Félix Costa, Bruno Loff, and Jerzy Mycka.
*Annals of Pure and Applied Logic*, 160(3): 255--288, 2009. - Computational complexity with experiments as oracles. II. Upper bounds, by Edwin Beggs, José Félix Costa, Bruno Loff, and John V. Tucker.
*Proceedings of the Royal Society, Series A (Mathematical, Physical and Engineering Sciences)*, 465(2105): 1453--1465, 2009. - Processes with local and global liveness requirements, by Hélia Guerra and José Félix Costa.
*The Journal of Logic and Algebraic Programming*, 78(3): 117--137, 2009. - Physical experiments as oracles, by Edwin Beggs, José Félix Costa, and John V. Tucker.
*Bulletin of the European Association for Theoretical Computer Science*97:137--151, February 2009. - Five views of hypercomputation, by Bruno Loff and José Félix Costa. Mike Stannett (editor): Future Trends in Hypercomputation,
*International Journal of Unconventional Computing*, 5(3--4): 193--207, Old City Publishing, Inc., 2009. - Differential equations, infinite limits and real recursive functions, by José Félix Costa, Bruno Loff, and Jerzy Mycka. M. Demiralp, W. B. Mikhael, A. A. Caballero, et al. (editors), Computational Methods and Applied Computing, Book Series: Mathematics and Computers in Science and Engineering, World Scientific and Engineering Academy and Society, 2008, 294-299. Article.
- Oracles and advice as measurements, by Edwin Beggs, José Félix Costa, Bruno Loff, and John V. Tucker. Cristian S. Calude et al. (editors), Unconventional Computation 2008, UC ' 08, Vienna, August 25--28,
*Lecture Notes in Computer Science*5204: 33--50, Springer, 2008. - Computational complexity with experiments as oracles, by Edwin Beggs, José Félix Costa, Bruno Loff, and John V. Tucker.
*Proceedings of the Royal Society, Series A (Mathematical, Physical and Engineering Sciences)*, 464: 2777--2801, October 8, 2008. - On the complexity of measurement in classical physics, by Edwin Beggs, José Félix Costa, Bruno Loff, and John V. Tucker. M. Agrawal, D. Du, Z. Duan, and A. Li (editors), Theory and Applications of Models of Computation, TAMC 2008, Xi'an, China, April 25--29, 2008,
*Lecture Notes in Computer Science*4978: 20--30, Springer, 2008. - The Euclid abstract machine, by Jerzy Mycka, José Félix Costa, and Francisco Coelho. Andrew Adamatzky and Susan Stepney (editors): Towards Theory of Unconventional Computing,
*International Journal of Unconventional Computing*, 4(3): 223--248, Old City Publishing, Inc., 2008. - The abstract immune system algorithm, by Daniel Pacheco and José Félix Costa. Selim G. Akl, Cristian S. Calude, Michael J. Dinneen, Grzegorz Rozenberg, and H. Todd Wareham (editors), Unconventional Computation 2007, UC ' 07, Kingston, August 13-17,
*Lecture Notes in Computer Science*4618: 137--149, Springer, 2007. - Computability on reals, infinite limits and differential equations, by Bruno Loff, José Félix Costa, and Jerzy Mycka.
*Applied Mathematics and Computation*, 191(2): 353--371, Elsevier, 2007. - A new conceptual framework for analog computation, by Jerzy Mycka and José Félix Costa.
*Theoretical Computer Science*, 374(1--3): 277--290, Elsevier, 2007. - The P =/= NP conjecture in the context of real and complex analysis, by Jerzy Mycka and José Félix Costa.
*Journal of Complexity*, 22(2): 287--303, Elsevier, 2006. - Undecidability over continuous-time, by Jerzy Mycka and José Félix Costa. Arnon Avron, Nachum Dershowitz, and Alexander Rabinovich (editors): Logics and Models of Computation: An International Logic and Computer Science Semester at Tel Aviv,
*Logic Journal of the IGPL*, 14(5): 649--658, Oxford University Press, 2006. - Real recursive functions and their hierarchy, by Jerzy Mycka and José Félix Costa.
*Journal of Complexity*, 20(6): 835--857, Elsevier, 2005. - The computational power of continuous dynamic systems, by Jerzy Mycka and José Félix Costa. Maurice Margenstern (editor),
*Machines, Computations, and Universality*, MCU 2004,*Lecture Notes in Computer Science*, 3354: 164--175, Springer-Verlag, 2004. - Analog computers and recursive functions over the reals, by Daniel Graça and José Félix Costa.
*Journal of Complexity*, 19(5): 644--664, 2003. - An analog characterization of the Grzegorczyk hierarchy, by Manuel Campagnolo, Cris Moore, and José Félix Costa.
*Journal of Complexity*, 18(4): 977--1000, 2002. - Canonical institutions of behaviour, by José Félix Costa and Hugo Lourenço. Maura Cerioli and Gianna Reggio (eds.),
*Lecture Notes in Computer Science*, 2267: 71--84, Springer-Verlag, 2001. - Iteration, inequalities, and differentiability in analog computers, by Manuel Campagnolo, Cris Moore, and José Félix Costa.
*Journal of Complexity*, 16(4): 642--660, 2000. - Mirror, mirror in my hand... a duality between specifications and models of process behaviour, by José Luiz Fiadeiro and José Félix Costa.
*Mathematical Structures in Computer Science*, 6(4): 353--373, 1996. - Nonsequential automata semantics for a concurrent object-based language, by Paulo B. Meneses, Amílcar Sernadas, and José Félix Costa,
*Electronic Notes in Theoretical Computer Science*, 14(1): 245--273, 1998. - Synchronization in Petri nets, by Paulo B. Meneses and José Félix Costa.
*Fudamenta Informaticae*, 26: 11--22, 1996. - Object specification logic, by Amílcar Sernadas, Cristina Sernadas, and José Félix Costa.
*Journal of Logic and Computation*, 5(5): 603--630, 1995. - Progress assumption in concurrent systems, by José Félix Costa and Amílcar Sernadas.
*Formal Aspects of Computing*, 7(1): 18--36, 1995. - Object inheritance beyond subtyping, by José Félix Costa, Amílcar Sernadas, and Cristina Sernadas.
*Acta Informatica*, 31(1): 5--26, 1994. - An institution of object behaviour, by Amílcar Sernadas, José Félix Costa, and Cristina Sernadas. H. Ehrig and F. Orejas (eds),
*Recent Trends in Data Type Specification: 9th Workshop on Specification of Abstract Data Types -- Selected Papers, Lecture Notes in Computer Science*, 785: 337--350, Springer-Verlag, 1994. - Data encapsulation and modularity: Three views of inheritance, by José Félix Costa, Amílcar Sernadas, and Cristina Sernadas. A. Borzyszkowski and S. Sokolowski (eds),
*Mathematical Foundations of Computer Science 93*,*Lecture Notes in Computer Science*, 711: 382--391. Springer-Verlag, 1993. - Process semantics of temporal logic specification, by José Luiz Fiadeiro, José Félix Costa, Amílcar Sernadas, and Tom Maibaum. M. Bidoit and C. Choppy (eds),
*Recent Trends in Data Type Specification: 8th Workshop on Specification of Abstract Data Types -- Selected Papers, Lecture Notes in Computer Science*, 655: 236--253, Springer-Verlag, 1993. - Object interaction, by José Félix Costa, Amílcar Sernadas, Cristina Sernadas, and Hans-Dieter Ehrich. I. Havel and V. Koubek (eds),
*Mathematical Foundations of Computer Science 92*,*Lecture Notes in Computer Science*, 629: 200--208, Springer-Verlag, 1992.

- Cristian S. Calude, José Félix Costa, and Hélia Guerra, (guest) editors of a Special Issue of Applied Mathematics and Computation, (219)1, September 15, 2012, Elsevier, Towards a computational interpretation of physical theories, online.
- José Félix Costa and Nachum Dershowitz, (guest) editors of a Special Issue of Natural Computing, Springer, on Unconventional Computation (UC 2009), 10(4), December 2011, online.
- Cristian S. Calude and José Félix Costa, (guest) editors of a Special Issue of International Journal of Unconventional Computing, 7(5), September/October 2011, Old City Publishing Science Journals, Special Issue on Physics and Computation (P&C 2010), online.
- Cristian S. Calude and José Félix Costa, (guest) editors of a Special Issue of Natural Computing 9(4), December 2010, Springer, Unconventional Computation (UC 2008), online.
- Cristian S. Calude, José Félix Costa, Nachum Dershowitz, Elisabete Freire, and Grzegorz Rozenberg editors of Lecture Notes in Computer Science, volume 5715, Unconventional Computation 8th International Conference, UC 2009, Ponta Delgada, Azores, Portugal, September 7--11, 2009, Proceedings, Springer, online.
- Cristian S. Calude and José Félix Costa, (guest) editors of a Special Issue of Natural Computing, 8(3), September 2009, Springer, on Physics and Computation, online.
- Cristian S. Calude and José Félix Costa, (guest) editors of a Special Issue of Applied Mathematics and Computation, 215(4), October 15, 2009, Elsevier, Physics and Computation, online.
- Cristian S. Calude, José Félix Costa, Rudolf Freund, Marion Oswald, and Grzegorz Rozenberg editors of Lecture Notes in Computer Science, volume 5204, Unconventional Computation 7th International Conference, UC 2008, Vienna, Austria, August 25--28, 2008, Proceedings, Springer, online.
- José Félix Costa and Francisco Dória, (guest) editors of a Special Issue of Applied Mathematics and Computation, 178(1), July 1, 2006, Elsevier, on Hypercomputation, online.

- Program Commitee member of the 1st International Workshop on Biological, Chemical and Physical Computations (BCPC'15), part of the 2015 Federated Conference on Computer Science and Information Systems (FedCSIS), Lodz, Poland, September 13--16, 2015.
- Program committee member of the 13th International Conference on Unconventional Computation & Natural Computation, UCNC 2014, University of Western Ontario, London, Ontario, Canada, July 14-18, 2014.
- Co-organizer (together with Valentina Harizanov) of the Session «Computability» of the Logic Colloquium 2013, Évora (Portugal), July 22--27, 2013.
- Program Commitee member of the Conference Unconventional Computation & Natural Computing 2013, Milano (Italy), July 1--5, 2013.
- Program Commitee member of the 2013 Symposium for Computing & Philosophy, University of Exeter (U.K.), April 2--5, 2013.
- Program committee member of the Conference Unconventional Computation & Natural Computing 2012, LIFO, University of Orléans (France), 3--7 September, 2012.
- Invited Speaker, Workshop Physics and Computation, Institut Henri Poincaré, 28--30 June, 2012.
- Invited Speaker, Workshop The Incomputable, Kavli Royal Society International Centre, Chicheley Hall, 12--15 June, 2012.
- Program Commitee member of the International Workshop on Theoretical Computer Science Dedicated to Professor Cristian S. Calude's 60th Birthday, Auckland, New Zealand, 21--24 Feb 2012.
- Program Commitee member of the 9th International Conference on Unconventional Computation UC 2011, FUNDIM laboratory of the Mathematics Department, University of Turku, Finland, June 6--10, 2011.
- I organized with Cristian Calude, Walid Gomaa, Hélia Guerra, and Karl Svozil the Third International Workshop on Physics and Computation 2010, Egypt, August 30 -- September 4, 2010.
- Program Commitee member of the ICALP 2010, 37th International Colloquium on Automata, Languages and Programming, July 5--12, 2010.
- Invited Speaker at the 9th International Conference on Unconventional Computation, UC 2010, Tokyo, June 21--25, 2010.
- General chair of the 8th International Conference on Unconventional Computation, UC 2009, Ponta Delgada, September 7--11, 2009.
- Invited speaker at the Workshop Complexity Resources in Physical Computation, Oxford University Computing Laboratory, Oxford, UK, August 24--26, 2009.
- Invited speaker at the Conference SPUC09, The Science and Philosophy of Unconventional Computing, Cambridge, UK, March 23--25, 2009.
- I organized with Cristian Calude the Workshop on Physics and Computation 2008, a satellitte event of the 7th International Conference on Unconventional Computation, UC 2008, Vienna, August 25--28, 2008.
- Co-chair of the program committee of the 7th International Conference on Unconventional Computation, UC 2008, Vienna, August 25--28, 2008.
- Invited speaker at the International Colloquium on Causality, Meaningful Complexity and Knowledge Construction, University of Rome "Tor Vergata", Rome, June 5--7, 2008.
- Invited speaker at the Conference TAMC 2008, 5th Annual Conference on Theory and Applications of Models of Computation, Xi ' an, China, April 25--29, 2008.
- Invited speaker at the BCTCS on Physics and computation: An essay on the unity of science through computability, April 7--10, 2008.
- Member of the program committee of the 6th International Conference on Unconventional Computation UC 2007, Queen's University, Kingston, Ontario, August 13--17, 2007.
- Invited speaker at a Special Session of the European CiE Conference Computability in Europe 2007: Computation and Logic in the Real World, University of Siena, Siena, June 18--23, 2007.
- Invited speaker at the Workshop Future Trends in Hypercomputation, Sheffield, UK, September 11--13, 2006.
- Lecturer at the International Logic and Computer Science Semester at Tel-Aviv (Tel Aviv University), March 10 -- 12, 2004.

- Invited speaker at the Escola de Inverno de Matemática, Mathematics Winter School, Instituto Superior Técnico, February 2--4, 2016.
- Porque é o céu escuro à noite?, Escola de Verão de Geometria: 100 anos de Relatividade Geral, 13--17 6--8 de julho, 2015.
- Lecturer, "Theories of Space, Time and Matter in Aristotle", Faculty of Sciences of the University of Lisbon, Centro de Filosofia das Ciências da Universidade de Lisboa, November 21, 2012.
- Invited Speaker to the special session on the Turing centennial organized by Academia das Ciências de Lisboa, November 8, 2012.
- Lecturer, "An Introduction to Neuroaesthetics", a 3 hours course, Faculty of Sciences of the University of Lisbon, Centro de Filosofia das Ciências da Universidade de Lisboa, March 21, 2012.
- Invited speaker at the Sessão Inaugural AIA Conferência "Artes, Ciências, Tecnologias", September 21, 2009.
- Invited speaker at the Workshop on Os lugares da Epistemologia e da Poética de Gaston Bachelard, December 10, 2007.
- Invited speaker in the Workshop on Ciência e Filosofia entre Rómulo de Carvalho e António Gedeão, November 24, 2006.