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Logical Methods: In Honor of Anil Nerode’s Sixtieth Birthday PDF

828 Pages·1993·22.25 MB·English
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Progress in Computer Science and Applied Logic Volume 12 Editor John C. Cherniavsky, Georgetown University Associate Editors Robert Constable, Cornell University Jean Gallier, University of Pennsylvania Richard Platek, Cornell University Richard Statman, Carnegie-Mellon University Logical Methods In Honor of AniI Nerode's Sixtieth Birthday John N. Crossley Jeffrey B. Remmel Richard A. Shore Moss E. Sweedler Editors Springer Science+Business Media, LLC John N. Crossley Jeffrey B. Remmel Dept. of Mathematics I Comp. Science Dept. of Mathematics Monash University University of California at San Diego Clayton, Victoria La Jolla, CA 92093 Australia 3168 Richard A. Shore Moss E. Sweedler Mathematical Sciences Institute Mathematical Sciences Institute Cornell University Cornell University Ithaca, NY 14853 Ithaca, NY 14853 Library of Congress Cataloging-in-Publication Data Logical rnethods : in honor of AniI Nerode's sixtieth birthday I John N. Crossley ... [et al.], editors p. cm. --(Progress in computer science and applied logic; v. 12) Includes bibliographical references. ISBN 978-1-4612-6708-9 ISBN 978-1-4612-0325-4 (eBook) DOI 10.1007/978-1-4612-0325-4 1. Logic programming. 2. Logic, Symbolic and mathematical. 3. Nerode, AniI, 1932- 1. Nerode, AniI, 1932- II. Crossley, John N. III. Series. QA76.63.L59L641993 511--dc20 93-21451 CIP Printed on acid-free paper. © Springer Science+Business Media New York 1993. Originally published by Birkhăuser Boston in 1993 Softcover reprint of the hardcover 1s t edition 1993 Copyright is not claimed for works of U.S. Govemement employees. AII rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior permission of the copyright owner. Permission to photocopy for internal or personal use, or the internal or personal use of specific clients is granted by Birkhliuser Boston for libraries and other users registered with the Copyright Clearance Center (CCC), provided that the base fee of $6.00 per copy, plus $.20 per page is paid directly to CCC, 21 Congress Street, Salem, MA 01970, U.S.A. Special requests should be addressed directly to Springer Science+Business Media, LLC. ISBN 978-1-4612-6708-9 Camera-ready copy provided by the editors. 987654321 Anil Nerode Contents Preface ix List of Participants xii The Work of Anil Nerode: A Retrospective Jeffrey B. Remmel and John N. Crossley 1 Bibliography of Anil Nerode . . . . . . . . 86 Embedding Distributive Lattices Preserving 1 Below A Nonzero Recursively Enumerable Turing Degree Klaus Ambos-Spies, Ding Decheng, and Peter A. Fejer ... 92 Prime Isols and the Theorems of Fermat and Wilson J. Barback ............... . 130 Problem Solving Strategies for the Derivation of Programs Jaime Boh6rquez and Rodrigo Cardoso 143 Effective Real Dynamics Douglas Cenzer . . . . . . . . . . . . 162 An Integer Lattice Arising in the Model Theory of Wreath Products Gregory Cherlin and Gary Marlin 178 Undecidability and Definability for Parametrized Polynomial Time m-Reducibilities Peter Cholak and Rod Downey 194 Extracting Programs from Proofs by an Extension of the Curry-Howard Process John N. Crossley and John C. Shephenison 222 A Bird's-Eye View of Twilight Combinatorics J. C. E. Dekker ......... . 289 Effectively and Noneffectively Nowhere Simple Subspaces R. G. Downey and Jeffrey B. Remmel . . . . . . 314 Index Sets in Recursive Combinatorics William Gasarch and Georgia Martin 352 Computability in Unitary Representations of Compact Groups Xiaolin Ge and J. Ian Richards 386 Recursive Properties of Intervals of Recursive Linear Orders Geoffrey Hird ................. 422 Algorithmic Stability of Models B. M. Kho'USsainov and R. Dadajanov 438 The Combinatorics of the Friedberg-Muchnick Theorem Kyriakos Kontostathis ........... . 467 Partial Automata and Finitely Generated Congruences: An Extension of Nerode's Theorem D. Kozen 490 Minimal Pair Constructions and Iterated Trees of Strategies S. Lempp, M. Lerman, and F. Weber 512 Intuitionistic L Robert S. Lubarsky 555 n-Recursive Linear Orders Without (n + I}-Recursive Copies Michael Moses ....... . 572 Multiple Agent Autonomous Control A Hybrid Systems Architecture Anil Nerode and Wolf Kohn ......... . 593 Distributed Concurrent Programs as Strategies in Games Anil Nerode, Alexander Yakhnis, and Vladimir Yaklmis 624 Dempster-Shafer Logic Programs and Stable Semantics Raymond Ny and V. S. Subrahmanian 654 Who Put the "Back" in Back-and-Forth? J. M. Plotkin . . . . . . . . . . 705 Polynomial Time Categoricity and Linear Orderings Jeffrey B. Remmel ........... . 713 The Disjunction and Numerical Existence Properties for Intuitionistic Analysis Philip Scowcroft 747 On the Strength of Fralsse's Conjecture Richard A. Shore ...... . 782 Preface The twenty-six papers in this volume reflect the wide and still expanding range of Anil Nerode's work. A conference on Logical Methods was held in honor of Nerode's sixtieth birthday (4 June 1992) at the Mathematical Sciences Institute, Cornell University, 1-3 June 1992. Some of the conference papers are here, but others are from students, co-workers and other colleagues. The intention of the conference was to look forward, and to see the directions currently being pursued, in the development of work by, or with, Nerode. Here is a brief summary of the contents of this book. We give a retrospective view of Nerode's work. A number of specific areas are readily discerned: recursive equivalence types, recursive algebra and model theory, the theory of Turing degrees and r.e. sets, polynomial-time computability and computer science. Nerode began with automata theory and has also taken a keen interest in the history of mathematics. All these areas are represented. The one area missing is Nerode's applied mathematical work relating to the environment. Kozen's paper builds on Nerode's early work on automata. Recursive equivalence types are covered by Dekker and Barback, the latter using directly a fundamental metatheorem of Nerode. Recursive algebra is treated by Ge & Richards (group representations). Recursive model theory is the subject of papers by Hird, Moses, and Khoussainov & Dadajanov, while a combinatorial problem in recursive model theory is discussed in Cherlin & Martin's paper. Cenzer presents a paper on recursive dynamics. The theory of Turing degrees and r.e. sets is treated by Ambos-Spies, Ding & Fejer; Downey & Remmel; Lempp, Lerman & Weber; Gasarch & Martin; and Kontostathis. Shore, who has worked closely with Nerode in this general area, presents a paper in Reverse Mathematics. Polynomial-time computability is the area of papers by Remmel & Cenzer, and of one by Cholak & Downey which takes a distinctive new approach. Cantor's back-[and-forth] argument is Plotkin's historical subject. Intuitionistic mathematics IS covered by Scowcroft on analysis, and Lubarsky on set theory. Computer Science has had a profound effect on the expansion of Nerode's work during the last decade or so. The variety of papers here reflects this: Crossley & Shepherdson on the Curry-Howard process, Ng & Subrahmanian on Dempster-Shaeffer theory and stable models, and Boh6rquez & Cardoso on program design. Nerode himself has participated in two papers: one, with the Yakhnis brothers, extends the Nerode-Yakhnis-Yakhnis theory of using games to model concurrent programs to model distributed computing, and the other, with Kohn, extends the Kohn-Nerode model for simple hybrid systems to multiple agent hybrid systems. The conference was financially supported by the National Science Foundation, the Army Research Office, ACSyAM (Center for Symbolic Methods in Algorithmic Mathematics), the Mathematics Department and Computer Science Department at Cornell University, the Center for Applied Mathematics, Cornell University, the Mathematical Sciences Institute and in particular the symbolic computation group, the Office of Sponsored Programs, Cornell University, the Dean of Arts and Sciences, Cornell University, and also the Association for Symbolic Logic, which sponsored the meeting. We gratefully acknowledge all this support. All conferences depend for their success on the organizational staff. In this case we were especially well provided for by the staff of the Mathematical Sciences Institute led by John Chiment: Diana Drake and Valerie Styles. We also acknowledge assistance from the Mathematics Department, Cornell University, especially its chairman, Keith Dennis and secretary Cathy Stevens. The typesetting was all done by Anne-Marie Vandenberg of the Mathematics Department, Monash University, to whom we extend grateful thanks. Thanks also to the referees who assisted us in editing this volume. We should also like to take this opportunity to thank the participants in the conference who came from all around the world, including Nerode's co-worker Huang Wenqi from China. Anil Nerode has stimulated and contributed a great deal of work in the areas of logic, computer science and applied

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The twenty-six papers in this volume reflect the wide and still expanding range of Anil Nerode's work. A conference on Logical Methods was held in honor of Nerode's sixtieth birthday (4 June 1992) at the Mathematical Sciences Institute, Cornell University, 1-3 June 1992. Some of the conference paper
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