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Table of Contents Table of Contents Preface : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : V S. Barry Cooper, Benedikt LÄowe, Leen Torenvliet Query learning of Horn formulas revisited : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 Jose L. Balc¶azar The internal logic of Bell's states : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 18 Giulia Battilotti, Paola Zizzi Logical Characterizations of PK and NPK over an Arbitrary Structure : 30 Olivier Bournez, Felipe Cucker, Paulin Jacob¶e de Naurois, Jean-Yves K Marion Fuzzy Interval-valued Processes Algebra : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 44 Yixiang Chen, Jie Zhou Computable Analysis in Systems and Control : : : : : : : : : : : : : : : : : : : : : : : : 58 Pieter Collins Polynomial complexity for analog computation : : : : : : : : : : : : : : : : : : : : : : : 59 Jose Felix Costa, Jerzy Mycka Constructive set theory with operations : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 60 Laura Crosilla, Andrea Cantini On Learning Conjunctions of Horn Clauses : : : : : : : : : : : : : : : : : : : : : : : : : 61 Joxe Gaintzarain, Montserrat Hermo, Marisa Navarro Defying Dimensions Modulo 6 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 71 Vince Grolmusz Solving SAT with membrane creation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 82 Miguel Angel¶ Guti¶errez-Naranjo, Mario J. P¶erez-Jim¶enez, Francisco Jos¶e Romero-Campero Polynomial Time Enumeration Reducibility : : : : : : : : : : : : : : : : : : : : : : : : : : 92 Charles Harris On the Prediction of Recursive Real-Valued Functions : : : : : : : : : : : : : : : : : 93 Eiju Hirowatari, Kouichi Hirata, Tetsuhiro Miyahara, Setsuo Arikawa Alan Turing: Logical and Physical : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 104 Andrew Hodges Skolemization in Intuitionistic Logic. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 105 Rosalie Iemho®, Matthias Baaz II Labeled ¯nite trees as ordinal diagrams : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 106 Herman Ruge Jervell Entanglement and its Role in Shor's Algorithm : : : : : : : : : : : : : : : : : : : : : : : 107 Vivien M. Kendon, William J. Munro Hypercomputability in Quantum Mechanics : : : : : : : : : : : : : : : : : : : : : : : : : : 117 Tien D. Kieu Almost everywhere domination and K-triviality : : : : : : : : : : : : : : : : : : : : : : : 121 Bj¿rn Kjos-Hanssen Universality of Walking Automata on a Class of Geometric Environments 122 Oleksiy Kurganskyy, Igor Potapov On an embedding of N5 lattice into the Turing degrees : : : : : : : : : : : : : : : : 132 Igor Kuznetsov Complexity in a Type-1 Framework for Computable Analysis : : : : : : : : : : : 133 Branimir Lambov RealLib: an e±cient implementation of exact real numbers : : : : : : : : : : : : 146 Branimir Lambov A Programming Language for Automated Average-Case Time Analysis : 147 Joseph Manning, Michel Schellekens Proof-Theoretical Methods in Combinatory Logic and ¸-Calculus : : : : : : : 148 Pierluigi Minari Potential In¯nity and the Church Thesis : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 158 Marcin Mostowski An Interval-valued Computing Device : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 166 Benedek Nagy On the notion of -de¯nedness of non-deterministic programs : : : : : : : : : : : 178 8 Stela K. Nikolova Computable Principles in Admissible Structures : : : : : : : : : : : : : : : : : : : : : : 188 Vadim Puzarenko A computability notion for locally ¯nite lattices : : : : : : : : : : : : : : : : : : : : : : : 198 Dimiter Skordev Non-total Enumeration Degrees : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 208 Boris Solon A lambda calculus for real analysis : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 214 Paul Taylor III Computability in Speci¯cation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 215 Raymond Turner Kleene-Kreisel Functionals and Computational Complexity : : : : : : : : : : : : 225 Paul J. Voda, Lars Kristiansen A Very Slow Growing Hierarchy for the Howard Bachmann Ordinal : : : : : 227 Andreas Weiermann Phase transition results for subrecursive hierarchies and rapidly growing Ramsey functions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 237 Andreas Weiermann Computability at the Planck Scale : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 238 Paola Zizzi Preface CiE 2005: New Computational Paradigms http://www.illc.uva.nl/CiE/ The cooperation Computability in Europe (CiE) is an informal European network covering computability in theoretical computer science and mathemat- ical logic, ranging from application of novel approaches to computation to set- theoretic analyses of in¯nitary computing models. The cooperation consists of fourteen main nodes and includes over 400 researchers; it is coordinated from Leeds (UK). More information about CiE can be found in Barry Cooper's intro- ductory paper to the LNCS proceedings volume and at http://www.amsta.leeds.ac.uk/pure/staff/cooper/cie.html. CiE 2005 is a conference on the special topic \New Computational Paradigms" held in Amsterdam in June 2005. It was initiated by and will serve as a fo- cus point for the informal cooperation CiE. The topic of \New Computational Paradigms" covers connections between computation and physical systems (e.g., quantum computation, neural nets, molecular computation) but also higher mathematical models of computation (e.g., in¯nitary computation or real com- putation). We understand CiE 2005 as an interdisciplinary venue for researchers from computer science and mathematics to exchange ideas, approaches and techniques in their respective work, thereby generating a wider community for work on new computational paradigms that allows uniform approaches to diverse ar- eas, the transformation of theoretical ideas into applicable projects, and general cross-fertilization transcending disciplinary borders. The goal to reach out to both computer scientists and mathematicians resulted in many surprises to both communities: after many years and decades of experience in academia, we were astoundingly surprised about the di®erences in general practice between two re- search communities that seem to be so close in content. For mathematicians, the proceedings distributed at a conference are just an abstract collection { having an abstract printed there doesn't count as a publication; for computer scientists, acceptance of papers at conferences to be printed in the proceedings is a key indicator of research success. These two very di®erent approaches to the submission, acceptance and pre- publication of abstracts in the two communities makes it very hard to organize a conference that appeals to both mathematicians and computer scientists. This phenomenon is known to many conference organizers in logic, but there are few known solutions. Some mathematics conferences have been inviting computer scientists as plenary speakers or special session speaker, but have been unsuc- cessful in attracting larger numbers of submissions from the CS community, VI other conferences have adopted the computer science organization and depend on the mathematicians playing according to computer science rules. We believe that in an area like computability theory which genuinely belongs to both communities, these asymmetric solutions don't work. We need confer- ences that accommodate the style of work of both mathematicians and computer scientists and consequently, we have been catering for both of them: we have a formal proceedings volume in the LNCS series and an informal abstract booklet in the ILLC Publication series that covers extended abstracts, but also informal abstracts in the style of a mathematics conference. We believe that we successfully managed to walk on the ridge between math- ematics and computer science. In the style of mathematics conferences, there will be a postproceedings vol- ume that will be reviewed according to journal standards. In addition to this, there will be special issues of the journals Theoretical Computer Science, Math- ematical Structures in Computer Science and Theory of Computing Systems covering special aspects of the conference. All speakers will be eligible for being invited to submit a paper to one of those postconference publications. The Programme Committee for CiE 2005 that ensured the scienti¯c quality of our conference consisted of K. Ambos-Spies (Heidelberg), A. Atserias (Bar- celona), J. van Benthem (Amsterdam), B. Cooper (Leeds, Chair), P. van Emde Boas (Amsterdam), S. Goncharov (Novosibirsk), B. LÄowe (Amsterdam, Chair), D. Normann (Oslo), H. Schwichtenberg (MuncÄ hen), A. Sorbi (Siena), I. Soskov (So¯a), L. Torenvliet (Amsterdam), J. Tucker (Swansea), and J. Wiedermann (Prague). The conference is sponsored by the Koninklijke Nederlandse Akademie van Wetenschappen (KNAW), Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), the Institute for Logic, Language and Computation (ILLC), the European Association for Theoretical Computer Science (EATCS) and the Association for Symbolic Logic (ASL). Last, but de¯nitely not least, we would like to take the opportunity to thank the numerous helpers for their support with the conference. Marjan Veldhuisen was responsible for catering, room reservations, the social event, registration
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