The Incomputable Journeys Beyond the Turing Barrier

This book questions the relevance of computation to the physical universe. Our theories deliver computational descriptions, but the gaps and discontinuities in our grasp suggest a need for continued discourse between researchers from different disciplines

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The Incomputable Journeys Beyond the Turing Barrier

Theory and Applications of Computability In cooperation with the association Computability in Europe

Series editors Laurent Bienvenu Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier (LIRMM) Montpellier France [email protected] Paola Bonizzoni Università degli Studi di Milano-Bicocca Dipartimento di Informatica Sistemistica e Comunicazione (DISCo) Milano Italy [email protected] Vasco Brattka Universität der Bundeswehr München Fakultät für Informatik Neubiberg Germany University of Cape Town Department of Mathematics & Applied Mathematics Rondebosch South Africa [email protected] Elvira Mayordomo Universidad de Zaragoza Departamento de Informática e Ingeniería de Sistemas Zaragoza Spain [email protected] Prakash Panangaden McGill University School of Computer Science Montreal Canada [email protected] Founding Editors: P. Bonizzoni, V. Brattka, S.B. Cooper, E. Mayordomo

Books published in this series will be of interest to the research community and graduate students, with a unique focus on issues of computability. The perspective of the series is multidisciplinary, recapturing the spirit of Turing by linking theoretical and real-world concerns from computer science, mathematics, biology, physics, and the philosophy of science. The series includes research monographs, advanced and graduate texts, and books that offer an original and informative view of computability and computational paradigms. Series Advisory Board Samson Abramsky, University of Oxford Eric Allender, Rutgers, The State University of New Jersey Klaus Ambos-Spies, Universität Heidelberg Giorgio Ausiello, Università di Roma, “La Sapienza” Jeremy Avigad, Carnegie Mellon University Samuel R. Buss, University of California, San Diego Rodney G. Downey, Victoria University of Wellington Sergei S. Goncharov, Novosibirsk State University Peter Jeavons, University of Oxford Nataša Jonoska, University of South Florida, Tampa Ulrich Kohlenbach, Technische Universität Darmstadt Ming Li, University of Waterloo Wolfgang Maass, Technische Universität Graz Grzegorz Rozenberg, Leiden University and University of Colorado, Boulder Alan Selman, University at Buffalo, The State University of New York Wilfried Sieg, Carnegie Mellon University Jan van Leeuwen, Universiteit Utrecht Klaus Weihrauch, FernUniversität Hagen Philip Welch, University of Bristol More information about this series at http://www.springer.com/series/8819

S. Barry Cooper • Mariya I. Soskova Editors

The Incomputable Journeys Beyond the Turing Barrier

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Editors S. Barry Cooper School of Mathematics University of Leeds Leeds, United Kingdom

Mariya I. Soskova Dept. of Mathematical Logic & Applications Sofia University Sofia, Bulgaria

ISSN 2190-619X ISSN 2190-6203 (electronic) Theory and Applications of Computability ISBN 978-3-319-43667-8 ISBN 978-3-319-43669-2 (eBook) DOI 10.1007/978-3-319-43669-2 Library of Congress Control Number: 2016956098 © Springer International Publishi