Tree Automata and Languages

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Overview

The theory of tree languages, founded in the late Sixties and still active in the Seventies, was much less active during the Eighties. Now there is a simultaneous revival in several countries, with a number of significant results proved in the past five years. A large proportion of them appear in the present volume.

The editors of this volume suggested that the authors should write comprehensive half-survey papers. This collection is therefore useful for everyone interested in the theory of tree languages as it covers most of the recent questions which are not treated in the very few rather old standard books on the subject. Trees appear naturally in many chapters of computer science and each new property is likely to result in improvement of some computational solution of a real problem in handling logical formulae, data structures, programming languages on systems, algorithms etc. The point of view adopted here is to put emphasis on the properties themselves and their rigorous mathematical exposition rather than on the many possible applications.

This volume is a useful source of concepts and methods which may be applied successfully in many situations: its philosophy is very close to the whole philosophy of the ESPRIT Basic Research Actions and to that of the European Association for Theoretical Computer Science.

The theory of tree languages, founded in the late Sixties and still active in the Seventies, was much less active during the Eighties. Now there is a simultaneous revival in several countries, with a number of significant results proved in the past five years. A large proportion of them appear in the present volume.

The editors of this volume suggested that the authors should write comprehensive half-survey papers. This collection is therefore useful for everyone interested in the theory of tree languages as it covers most of the recent questions which are not treated in the very few rather old standard books on the subject. Trees appear naturally in many chapters of computer science and each new property is likely to result in improvement of some computational solution of a real problem in handling logical formulae, data structures, programming languages on systems, algorithms etc. The point of view adopted here is to put emphasis on the properties themselves and their rigorous mathematical exposition rather than on the many possible applications.

This volume is a useful source of concepts and methods which may be applied successfully in many situations: its philosophy is very close to the whole philosophy of the ESPRIT Basic Research Actions and to that of the European Association for Theoretical Computer Science

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Product Details

Table of Contents

Foreword
Binary tree codes 1
Suffix, prefix and maximal tree codes 21
A monoid approach to tree automata 41
A theory of tree language varieties 57
Interpretability and tree automata: A simple way to solve algorithmic problems on graphs closely related to trees 83
Computing trees with graph rewriting systems with priorities 115
Recognizable sets of unrooted trees 141
Fixed point characterization of weak monadic logic definable sets of trees 159
Automata on infinite trees and rational control 189
Recognizing sets of labelled acyclic graphs 201
Rational and recognizable infinite tree sets 225
Algebraic specification of action trees and recursive processes 235
Trees and algebraic semantics 291
A survey of tree transductions 311
Structural complexity of classes of tree languages 327
Ambiguity and valuedness 355
Decidability of the inclusion in monoids generated by tree transformation classes 381
Tree-adjoining grammars and lexicalized grammars 409
A short proof of the factorization forest theorem 433
Unification procedures in automated deduction methods based on matings: A survey 439
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