CONTEMPORARY MATHEMATICS I 135 ' Symbolic Dynamics and its Applications Peter Walters Editor http://dx.doi.org/10.1090/conm/135 Symbolic Dynamics and its Applications Recent Titles in This Series 135 Peter Walters, Editor, Symbolic dynamics and its applications, 1992 134 Murray Gerstenhaber and Jim Stashefl', Editors, Deformation theory and quantum groups with applications to mathematical physics, 1992 133 Alan Adolphson, Steven Sperber, and Marvin Tretkofl', Editors, p-Adic methods in number theory and algebraic geometry, 1992 132 Mark Gotay, Jerrold Marsden, and Vincent Moncrief, Mathematical aspects of classical field theory, 1992 131 L. A. Bokut', Yu. L. Ershov, and A. I. Kostrikin, Editors, Proceedings of the International Conference on Algebra Dedicated to the Memory of A. I. Mal'cev, Part l, 2, and 3, 1992 130 L. Fuchs, K. R. Goodearl, J. T. Stafford, and C. Vinsonhaler, Editors, Abelian groups and noncommutative rings, 1992 129 John R. Graef and Jack K. Hale, Oscillation and dynamics in delay equations, 1992 128 Ridgley Lange and Shengwang Wang, New approaches in spectral decomposition, 1992 127 Vladimir Oliker and Andrejs Treibergs, Editors, Geometry and nonlinear partial differential equations, 1992 126 R. Keith Dennis, Claudio Pedrini, and Michael R. Stein, Editors, Algebraic K-theory, commutative algebra, and algebraic geometry, 1992 125 F. Thomas Bruss, Thomas S. Ferguson, and Stephen M. Samuels, Editors, Strategies for sequential search and selection in real time, 1992 124 Darrell Haile and James Osterburg, Editors, Azumaya algebras, actions, and modules, 1992 123 Steven L. Kleiman and Anders Thorup, Editors, Enumerative algebraic geometry, 1991 122 D. H. Sattinger, C. A. Tracy, and S. Venakides, Editors, Inverse scattering and applications, 1991 121 Alex J. Feingold, Igor B. Frenkel, and John F. X. Ries, Spinor construction of vertex operator algebras, triality, and E~ 1 l, 1991 120 RobertS. Doran, Editor, Selfadjoint and nonselfadjoint operator algebras and operator theory, 1991 ll9 Robert A. Metter, Azriel Rosenfeld, and Prabir Bhattacharya, Editors, Vision geometry, 1991 118 Yan Shi-Jian, Wang Jiagang, and Yang Chung-chun, Editors, Probability theory and its applications in China, 1991 117 Morton Brown, Editor, Continuum theory and dynamical systems, 1991 ll6 Brian Harbourne and Robert Speiser, Editors, Algebraic geometry: Sundance 1988, 1991 115 Nancy Flournoy and Robert K. Tsutakawa, Editors, Statistical multiple integration, 1991 114 Jeffrey C. Lagarias and Michael J. Todd, Editors, Mathematical developments arising from linear programming, 1990 113 Eric Grinberg and Eric Todd Quinto, Editors, Integral geometry and tomography, 1990 112 Philip J. Brown and Wayne A. Fuller, Editors, Statistical analysis of measurement error models and applications, 1990 Ill Earl S. Kramer and Spyros S. Magliveras, Editors, Finite geometries and combinatorial designs, 1990 ll 0 Georgia Benkart and J. Marshall Osborn, Editors, Lie algebras and related topics, 1990 109 Benjamin Fine, Anthony Gaglione, and Francis C. Y. Tang, Editors, Combinatorial group theory, 1990 l 08 Melvyn S. Berger, Editor, Mathematics of nonlinear science, 1990 107 Mario Milman and Tomas Schonbek, Editors, Harmonic analysis and partial differential equations, 1990 l 06 Wilfried Sieg, Editor, Logic and computation, 1990 (Continued in the back of this publication) CoNTEMPORARY MATHEMATICS 135 Symbolic Dynamics and its Applications Peter Walters Editor American Mathematical Society Providence, Rhode Island EDITORIAL BOARD Richard W. Beals, managing editor Craig Huneke Linda Preiss Rothschild Clark Robinson Peter Winkler The AMS Conference on Symbolic Dynamics and its Applications, held in honor of Roy Adler, was held at Yale University, New Haven, Connecticut, July 28-August 2, 1991. 1991 Mathematics Subject Classification. Primary 28099, 54H20; Secondary 60J1 0, 58F99. Library of Congress Cataloging-in-Publication Data Symbolic dynamics and its applications: proceedings of a conference in honor of Roy L. Adler held July 28 to August 2, 1991 /Peter Walters, editor. p. cm.-(Contemporary mathematics; v. 135) Proceedings of a conference held at Yale University. ISBN 0-8218-5146-2 1. Topological dynamics-Congresses. I. Adler, Roy L., 1931-11. Walters, Peter, 1943-. Ill. Series: Contemporary mathematics (American Mathematical Society); v. 135. QA611.5.S96 1992 92-20203 514174-dc20 CIP Copying and reprinting. 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The appearance of the code on the first page of an article in this book indicates the copyright owner's consent for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright law, provided that the fee of $1.00 plus $.25 per page for each copy be paid directly to the Copyright Clearance Center, Inc., 27 Congress Street, Salem, Massachusetts 01970. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. Copyright @1992 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. § Portions of this volume were printed directly from author-prepared copy. Portions of this volume were typeset by the authors using A~-T(:X, the American Mathematical Society's T(:X macro system. 10 9 8 7 6 5 4 3 2 1 97 96 95 94 93 92 Contents Introduction IX Program of the conference XI List of participants xiii The torus and the disk R. 1. ADLER 1 On the work of Roy Adler in ergodic theory and dynamical systems B. WEISS 19 The impact of Roy Adler's work on symbolic dynamics and applications to data storage B. MARCUS 33 LR conjugacies of shifts of finite type are uniquely so J. ASHLEY 57 A polynomial-time algorithm for deciding the forcing relation on cyclic permutations C. BERNHARDT AND E. M. COVEN 85 Fully positive topological entropy and topological mixing F. BLANCHARD 95 The stochastic shift equivalence conjecture is false M. BOYLE 107 Predictions with automata A. BROGLIO AND P. LIARDET 111 Common closing extensions and finitary regular isomorphism for synchro- nized systems D. FIEBIG 125 Covers for coded systems D. FIEBIG AND U.-R. FIEBIG 139 v vi CONTENTS Z-numbers and ;3-transformations 1. FLATTO 181 Quasisymmetric conjugacies for some one-dimensional maps inducing ex- pansion M. JAKOBSON 203 A monotonicity property in one dimensional dynamics J. M. GAMBAUDO AND C. TRESSER 213 Finiteness of conjugacy classes of restricted block upper triangular matrices D. HANDELMAN 223 Polynomials with a positive power D. HANDELMAN 229 Spectral radii of primitive integral companion matrices and log concave polynomials D. HANDELMAN 231 Self-replicating tilings R. KENYON 239 Markov subgroups of (Z/2Z}'l1} B. KITCHENS AND K. SCHMIDT 265 On the dimension of some graphs F. LEDRAPPIER 285 Synchronizing prefix codes and automata and the road coloring problem D. PERRIN AND M.-P. SCHUTZENBERGER 295 A zero entropy, mixing of all orders tiling system S. MOZES 319 A cocycle equation for shifts W.PAA~ ~7 In general a degree 2 map is an automorphism W. PARRY 335 zn versus z actions for systems of finite type C. RADIN 339 Principal vectors of commuting block maps F. RHODES 343 On the recurrence of countable topological Markov chains I. A. SALAMA 349 CONTENTS vii Substitutions, adic transformations, and beta-expansions B. SoLOMYAK 361 Finitary isomorphism of m-dependent processes M. SMORODINSKY 373 Constant-to-one factor maps and dimension groups P. TROW 377 Faces of Markov chains and matrices of polynomials S. TUNCEL 391 Classification of subshifts of finite type revisited J. B. WAGONER 423 Strong shift equivalence of matrices in G£(2, Z) R. F. WILLIAMS 445 This volume is dedicated to Roy L.Adler on the occasion of his 60th birthday with the affection and respect of his colleagues and friends. Roy and Audrey Adler Introduction This volume contains the proceedings of the conference Symbolic Dynamics and Its Applications held at Yale University in New Haven, Connecticut, from July 28 to August 2, 1991. The conference was held in honor of Roy L. Adler. It was organized by Ethan Coven, Shizuo Kakutani (Roy's advisor), Bruce Kitchens, Brian Marcus, Don Ornstein, and Benjamin Weiss. The conference focused on symbolic dynamics and its applications to other fields. These include ergodic theory, smooth dynamical systems, information the- ory, automata theory, and statistical mechanics. There were eighteen one-hour talks, including two on Roy Adler's work, and eighteen thirty-minute talks. There were one hundred and thirty-nine participants from thirteen countries, representing mathematics, applied mathematics, electrical engineering, and physics departments at universities as well as industry. The conference was supported by grants from the NSF and IBM. Roy is honored for both his mathematical and personal contributions to the scientific community. Among his scientific achievements are the invention of topo- logical entropy, the use of Markov partitions for invertible maps, and the application of symbolic dynamics to practical coding problems in information theory. His ideas were crucial in the formation of the subject we call symbolic dynamics. The simple but elegant way he approached difficult problems led many of us into dynamics. Roy had a wonderful partner.