Lecture Notes in Computer Science Edited by G. Goos, J. Hartmanis and J. van Leeuwen 1218 Advisory Board: W. Brauer D. Gries J. Stoer
Gheorghe Phun Arto Salomaa (Eds.) New Trends in Formal Languages Control, Cooperation, and Combinatorics ~ Springer
Series Editors Gerhard Goos, Karlsruhe University, Germany Juris Hartmanis, Cornell University, NY, USA Jan van Leeuwen, Utrecht University, The Netherlands Volume Editors Gheorghe Pfiun University of Bucharest, Institute of Mathematics Str. Academiei 14, R-70109 Bucharest, Romania E-mail: paun@roimar.imar.ro Arto Salomaa University of Turku, Department of Mathematics FIN-20014 Turku, Finland E-mail: asalomaa@sara.utu.fi Cataloging-in-Publication data applied for Die Deutsche Bibliothek - CIP-Einheilsaufnahme New trends in formal languages : control, cooperation, and combinatorics / Gheorge P~iun ; Arto Salomaa (ed.). - Berlin ; Iteidelberg ; New York ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara ; Singapore ; Tokyo : Springer, 1997 ISBN 3-540-62844-4 kart. CR Subject Classification (1991): F.4.2, F.4.3, 1.2.7 ISSN 0302-9743 ISBN 3-540-62844-4 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from SpringerVerlag. Violations are liable for prosecution under the German Copyright Law 9 Springer-Verlag Berlin Heidelberg 1997 Printed in Germany Typesetting: Camera-ready by author SPIN 10549399 06/3142-5 4 3 2 1 0 Printed on acid-free paper
Preface The present volume has emerged from a twofold intention: (1) to collect and to present to the reader results in two important and active areas of formal language theory, regulated rewriting and grammar systems (both these areas have as one of their main goals to increase the generative power of grammars by adding certain features dealing with the control of the derivation process, the cooperation of parts, the distribution of tasks among parts, and other related ideas), and (2) to mark the 50th Birthday of Jiirgen Dassow, an author who has made a significant contribution to the above mentioned areas (and who has been quite active in organizing meetings in formal language theory, as well as in theoretical computer science in general). Most of the contributions are indeed devoted to regulated rewriting and grammar systems, but, because several of Jfirgen's friends and collaborators are not working in these areas, we decided to enlarge the scope of the volume. Thus, the last two chapters were added. The first chapter (Regulated rewriting) deals both with topics which can be considered classical in formal language theory (the LBA problem reformulated in terms of programmed grammars, the index of grammars and languages, the descriptional complexity in the form of the number of nonterminals used by a grammar) and with recent (controlling the work of a grammar/automaton by means of elements of a group, or by attributes associated to strings or to symbols), or emergent topics (fuzzy grammars, array grammars, restarting automata). The next two chapters (Cooperating distributed grammar systems and Parallel communicating grammar systems) are devoted to the two main classes of grammar systems, the sequential ones (the components work in turn, one at each moment, on the same common sentential form) and the parallel ones (the components work synchronously, each on its own sentential form, and communicate on request or by command). The papers included in these chapters prove the power and the fruitfulness - both from a theoretical and a practical point of view - of the distributed architectures specific to grammar systems. There are papers investigating basic generative capacity questions, computational complexity, variants (in general suggested by computer science aspects modelled in terms of grammar systems). Special mention should be made of the two papers about colonies, a particular case of cooperating distributed grammar systems, corresponding to multi-agent systems with very simple subsystems/agents, and the papers discussing the possible use(fulness) of parallel communicating grammar systems, of grammar systems in general, in modelling constructions and phenomena occurring in natural languages. The fourth chapter (Splicing systems) deals with an exciting and hot area in computer science, which promises important developments also in automata and language theory: DNA computing. The basic ingredient here is the splicing operation modelling the DNA recombination. The first two papers investigate (parallel) grammar systems based on components using the splicing operation. (Thus, these papers can also be considered as continuations of the previous chapter.) The third paper of this
Yl chapter extends the splicing operation to arrays, opening a rich area of investigation. Chapter five (Infinite words) contains three papers whose object of study are the infinite sequences, whereas Chapter six (Algebraic approaches to languages) contains papers where the main point of view is not generative but algebraic. These areas constitute well-established branches of formal language theory, important counterparts of the %lassical" branches dealing with finite strings in a purely grammatical manner. Of course, the volume does not intend to provide an overview of formal language theory; the reader interested in such an overview can consult Handbook of Formal Languages (three volumes), published this spring by Springer-Verlag (G. Rozenberg, A. Salomaa, eds.). The contributions have been refereed in the usual way. We are very much indebted to all the people involved in the production of this volume. Most importantly, we want to thank the authors for excellent and timely cooperation, and regret that some other prospective authors who wanted to contribute were unable to do so because of time and other constraints. After fifty, other multiples of ten follow... So, Happy Birthday Jiirgen, and see you at many multiples of ten from now on! January 1997 Gh. P~un and A. Salomaa
Table of Contents Chapter 1. Regulated Rewriting... 1 H. Bordihn A Grammatical Approach to the LBA Problem... 1 H. Fernau, Mr Holzer Conditional Context-Free Languages of Finite Index... 10 A. Meduna On the Number of Nonterminals in Matrix Grammars with Leftmost Derivations... 27 V. Mitrana, R. Stiebe The Accepting Power of Finite Automata over Groups... 39 P. R. J. Asveld Controlled Fuzzy Parallel Rewriting... 49 P. BottoT~i, G. Mauri, P. Mussio On Controlling Rewriting by Properties of Strings and Symbols... 71 H. Fernau, R. Freund Accepting Array Grammars with Control Mechanisms... 95 P. Jan6ar, F. Mrdz, M. Pldtek, J. Vogel On Restarting Automata with Rewriting... 119 Chapter 2. Cooperating Distributed Grammar Systems... 137 V. Mihalache, V. Mitrana Deterministic Cooperating Distributed Grammar Systems... 137 T. B~t~nescu, H. Georgescu, M. Gheorghe Grammar Systems with Counting Derivation and Dynamical Priorities... 150 S. Dumitrescu Characterization of RE Using CD Grammar Systems with Two Registers and RL Rules... 167 D. Wiitjen On Cooperating Distributed Uniformly Limited 0L Systems... 178
VIII M. H. ter Beek Teams in Grammar Systems: Sub-Context-Free Cases... 197 M. Amin A Note on the Incomparability of the EOL Family with Certain Families of Languages Generated by Cooperating Grammar Systems... 217 J. Kelemen Colonies as Models of Reactive Systems... 220 P. Sos(k~ L. ~t~bnar Grammatical Inference of Colonies... 236 Chapter 3. Parallel Communicating Grammar Systems... 247 K. Abrahamson, L. Cai, S. Gordon A Grammar Characterization of Logarithmic-Space Computation... 247 ~. Bruda On the Computational Complexity of Context-Free Parallel Communicating Grammar Systems... 256 D. Popescu Parallel Communicating Grammar Systems with Communication by Signals... 267 A. Chitu PC Grammar Systems Versus Some Non-Context-Free Constructions from Natural and Artificial Languages... 278 M. D. Jimdnez-Ldpez, C. Martin-Vide Grammar Systems for the Description of Certain Natural Language Facts... 288 E. Csuhaj-Varj6, A. Salomaa Networks of Parallel Language Processors... 299 Chapter 4. Splicing Systems... 319 C. Zandron, C. Ferretti, G. Mauri A Reduced Distributed Splicing System for RE Languages... 319 G. Georgescu On the Generative Capacity of Splicing Grammar Systems... 330 K. Krithivasan, V. T. Chakaravarthy, R. Rama Array Splicing Systems... 346
IX Chapter 5. Infinite Words... 366 J. HromkoviS, J. Karhumiiki Two Lower Bounds on Computational Complexity of Infinite Words... 366 L. Staiger On w-power Languages... 377 A. Mateescu, G. D. Mateescu, G. Rozenberg, A. Salomaa Shuffle-Like Operations on w-words... 395 Chapter 6. Algebraic Approaches to Languages... 412 W. Kuich Generalized Lindenmayerian Algebraic Systems... 412 V. E. C~z~nescu The Structure oi" the Basic Morphisms... 422 M. KudIek, A. Mateescu On Mix Operation... 430 M. Holzer, K.-J. Lange On the Complexity of Iterated Insertions... 440 L. Ilie The Decidability of the Generalized Confluence Problem for Context-Free Languages... 454 Author Index... 465