Discrete Mathematics and Theoretical Computer Science. Springer London Berlin Heidelberg New York Barcelona Hong Kong Milan Paris Singapore Tokyo

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1 Discrete Mathematics and Theoretical Computer Science Springer London Berlin Heidelberg New York Barcelona Hong Kong Milan Paris Singapore Tokyo

2 Series Editors Douglas S. Bridges, Canterbury University, NZ Cristian S. Calude, University of Auckland, NZ Advisory Editorial Board J. Casti, Sante Fe Institute, USA G. J. Chaitin, IBM Research Center, USA E. W. Dijkstra, University of Texas at Austin, USA J. Goguen, University of California at San Diego, USA R. L. Graham, University of California at San Diego, USA J. Hartmanis, Cornell University, USA H. Jiirgensen, University of Western Ontario, Canada A. Nerode, Cornell University, USA G. Rozenberg, Leiden University, The Netherlands A. Salomaa, Turku University, Finland

3 C.S. Calude, M.J. Dinneen and S. Sburlan (Eds) Combinatorics, Computability and Logic Proceedings of the Third International Conference on Combinatorics, Computability and Logic, (DMTCS'Ol) Springer

4 C.S. Calude M.J. Dinneen Department of Computer Science, University of Auckland, Auckland, New Zealand S. Sburlan Faculty of Mathematics and Computer Science, "Ovidius" University, Constanta, Romania British Library Cataloguing in Publication Data Combinatorics, Computability and logic: proceedings ofthe Third International Conference on Combinatorics, Computability and Logic, (DMTCS'Ol). - (Discrete mathematics and theoretical computer science) 1.Combinaotial analysis - Congresses 2.Computational complexity - Congresses 3.Logic, Symbolic and mathematical Congresses LCalude, Cristian, II.Dinneen, M.J. IILSburlan, S. IV.International Conference on Combinatorics, Computability and Logic, (DMTCS'Ol) (3rd: 2001 : Constanta, Romania) ISBN-13: e-isbn -13: DOl: / Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of repro graphic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. ISBN -13: a member of BertelsmannSpringer Science+Business Media GmbH Springer-Verlag London Limited 2001 The use of registered names, trademarks etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Typesetting: Camera ready by editors 34/ Printed on acid-free paper SPIN

5 Preface The third Discrete Mathematics and Theoretical Computer Science conference (DMTCS'OI) of the Centre for Discrete Mathematics and Theoretical Computer Science of the University of Auckland has been organised at the Faculty of Mathematics and Computer Science, "Ovidius" University, C o n s t Romania, a n ~ a, with the co-operation of the Maritime Academy "Mircea eel Batran", C o n s t It a n ~ a. was held held in the beautiful Romanian city of C o n s ton a the n ~ Black a Sea. The conference was dedicated to Professor Frank Harary on the occasion of his 80th Birthday. The four invited speakers of the conference were: F. Harary (New Mexico State University, USA), H. Ishihara (Jaist, Japan), P. Odifreddi (Thrin University, Italy), 1. Tomescu (Bucharest University, Romania). The Programme Committee consisting of C.S. Calude (Chair, Auckland), C. Ding (Hong Kong), M.J. Dinneen (Secretary, Auckland), M.R. Fellows (Victoria, Canada), M. Hallett (Zurich), M. Ito (Kyoto), S. Istrail (Rockville, USA), K-W. Lih (Taipei), S. Marcus (Bucharest), Y. Matiyasevich (St. Petersburg), Gh. Paun (Bucharest), S. Rudeanu (Bucharest), J. Rutten (Amsterdam), K. Salomaa (Kingston, Canada), S. Sburlan (Constanta), 1. Streinu (Northampton, USA), M.C. Wilson (Montana, USA), D. Wotschke (Frankfurt), M. Zimand (Baltimore) had selected 16 papers to be presented as regular contributions and 10 other poster abstracts. The additional abstracts have appeared as the CDMTCS Research Report 152, The paper reviewers for the conference were: C.P. Bonnington G. Georgescu Y. Matiyasevich K. Salomaa D.S. Bridges H. Guesgen Gh. Paun C.S. Calude P. Hertling G. Pritchard C. Ding H. Ishihara S. Rudeanu M.J. Dinneen M. Ito F. Ruskey M. Dumitrescu K-W. Lih J. Rutten L. Staiger M.C. Wilson D. Wotschke M. Zimand Finally, we want to acknowledge the dedication of the DMTCS'OI Conference Committee, which consisted of C. Bogdan, C.S. Calude, E. Calude, 1. CoJtescu, U. Guenther, (Registration) G. Marin, C. Popa, S. Sburlan (Chair), C. 'faranu, R. Vernic. We also thank our Springer-Verlag, London publishers Bevereley Ford and Rebecca Mowat for producing another beautiful volume. May 2001 C.S. Calude M.J. Dinneen S. Sburlan

6 Frank Harary Frank holds the PhD from the University of California at Berkeley, Prior to his doctorate he worked as a meteorologist, an aeronautical engineer, and an instructor of physics at Princeton University, Brooklyn College, City College of New York and New York University. During his doctoral studies in Berkeley, he was a ballroom dance instructor. He spent two years at the Institute for Advanced Study in Princeton, was a research mathematician at Bell Telephone Laboratories, a visiting assistant professor of mathematics at Princeton University, and had fellowships at Cambridge University (Churchill College) and Oxford University (Wolfson College). He had multiple visiting positions at universities on all continents. In 1955, at the University of Michigan, he created the first courses on combinatorial theory and on graph theory in the world. He founded both the Journal of Combinatorial Theory (1966) and the Journal of Graph Theory (1977). He is a member of the editorial board of 16 scholarly journals. Frank has published over 700 papers, mainly on graph theory and its applications, not only in mathematics and computer science, but also in anthropology, art, biology, linguistics, physics, chemistry, electrical engineering, geography, psychology. Frank has written 8 books and edited 10 others. His 1969 book, Graph Theory, became the fifth most cited work in the mathematical research literature during His latest, Graph Theory and Geography will be published by Wiley as an electronic book in May 200l. Frank has delivered over one thousand invited lectures at conferences and universities in 77 countries, the two most recent being Uruguay (Montevideo, August 2000) and Zimbabwe (Harare, November 2000). Frank has Erdos number 1, having written two papers with the most prolific mathematician of our times. Not an academic honor, but a rather unusual form of recognition, occurred when the successful film "Good Will Hunting" displayed formulas and graphs he had published in a paper on the enumeration of trees. In the film, these formulas were supposed to show a fiendishly difficult unsolved mathematical problem which the star, Matt Damons, solved effortlessly!

7 Table of Contents Invited papers Frank Harary Early Computer Science Adventures of a Mathematician 1 Hajime Ishihara Sequentially Continuity in Constructive Mathematics 5 Piergiorgio Odifreddi Recursive Functions: An Archeological Look loan Tomescu The Number of Graphs and Digraphs with a Fixed Diameter and Connectivity Contributed papers Hatem M. Bahig, Mohamed H. EI-Zahar and Ken Nakamula Some Results for Some Conjectures in Addition Chains Veronica Becher, Sergio Daicz and Gregory Chaitin A Highly Random Number Douglas S. Bridges Dini's Theorem: A Constructive Case Study Henning Fernau Even Linear Simple Matrix Languages: Formal Language Aspects George Georgescu and Afrodita lorgulescu Pseudo-BCK Algebras: An Extension of BCK Algebras Lane A. Hemaspaandra and Harald Hempel P-Immune Sets with Holes Lack Self-Reducibility Properties Daniel Hort and Jifi Rachunek Lex Ideals of Generalized MV-Algebras Jouni Jarvinen Armstrong Systems on Ordered Sets Vadim E. Levit and Eugen Mandrescu Unicycle Bipartite Graphs with Only Uniquely Restricted Maximum Matchings

8 x Table of Contents Martin PIatek, Tomas Holan and Vladislav K uboii On Relax-ability of Word-Order by D-grammars Adriana Popovici and Dan Popovici On the Structure of Linear Cellular Automata Robert Rettinger, Xizhong Zheng,Romain Gengler, and Burchard von Braunmiihl Monotonically Computable Real Numbers Peter Schuster, Luminita Vita and Douglas S. Bridges Apartness as a Relation Between Subsets Ludwig Staiger How Large is the Set of Disjunctive Sequences? Vincent Vajnovszki A Loopless Generation of Bitstrings without p Consecutive Ones Vitaly Voloshin Greedy Algorithms for the Lower and Upper Chromatic Numbers

Fractals and Chaos. A.J. Crilly R.A. Earnshaw H. Jones Editors. With 146 Figures in 173 Parts, 57 in Color

Fractals and Chaos. A.J. Crilly R.A. Earnshaw H. Jones Editors. With 146 Figures in 173 Parts, 57 in Color Fractals and Chaos A.J. Crilly R.A. Earnshaw H. Jones Editors Fractals and Chaos With 146 Figures in 173 Parts, 57 in Color Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona