## Ninth Colloquium on Trees in Algebra and Programming: 5-7 March 1984, Bordeaux, FranceThe international Colloquium on Trees in Algebra and Programming is an annual conference on Theoretical Computer Science. Its central theme is the algebraic and combinatorial properties of trees, graphs and other combinatorial objects that appear in many different fields of computer science. These include formal languages and automata, rewriting systems, complexity and validity of algorithms and programs, program schemes, concurrent processes, databases, data structures, specification methods, models of lambda-calculus, VLSI circuits and semantics of programming languages. However, trees and graphs have such a wide range of uses in computer science that no aspect is excluded. This book contains the twenty-two communications of the ninth colloquium held in Bordeaux, France in March 1984. Of these, three invited papers survey existing work in three different fields and nineteen present new results. |

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### Contents

Invited Lectures | 1 |

K Mehlhorn On optimal VLSlciAcuiti IoA the baiic aAithmetic | 23 |

Contributions | 51 |

J P Braquelaire Giaphi and national expAeiiioni denoting | 73 |

N Dershowitz S Zaks PatteAni in tAeA | 93 |

J Françon C Puech HiitoiAeA dZ hileA de phÀ ohJLte avec | 119 |

Gogolla PaAtlally oKdeAed ioAti in algebAaic | 139 |

A Kanda NumeAation modeZi oh calculuA | 155 |

E Paul Pioohi by induction in equ cuU onal theoiei utiAh | 211 |

Puel ?loohi in the hinal algebto | 227 |

Raoult On QKouph KemÀXÀ ngh | 243 |

G Rozenberg E Welzl Boundaiy hILC Qiarrmau | 257 |

Soria J M steyaert AveAage ehhicÀency oh patteAn matching | 271 |

K Theobald A theoAy oh Aepn eiZnJja ble cpoi | 283 |

E Timmerman Vieldi oh infinitZ tAZeM | 299 |

Wegener Optimal deciiion tAeei and onetoneonty bAanckinq | 313 |

Kaufmann HeaAJLy tigkt boundi hoi the longeit edge in | 169 |

S Miyano T Hayashi KtteKnatinQ JmvLte aatomata | 195 |

### Common terms and phrases

Abstract Data Types antichain antichain definable aperiodic arbres bijection binary BNLC grammar BNLC language Boolean functions branching programs BT(M called circuits clés combinatory completion algorithm Computer Science construction countable cpo's critical pairs decision trees definition denote deterministic dom(t domain edges elementary decompositions equivalent étiquetés example exists fichier files de priorité final algebra finite automata formula given graph language histoires indexed grammars inductively complete infinite initial algebra integer labelled Lemma lower bound m-theories model of x-calculus morphism multiset natural numbers niveau nodes nombre nonterminal normal form obtained occurs operators partial ordering partition path pattern problem proof properties Proposition prove pushdown quasi-tree recursion theory recursive function reflexive set regular expression regular tree relations between constructors resp result rewrite rule root semantics sequence sommet specification star-free storage type structure subset subtree symbols term rewriting system Theorem theory tree languages variables VLSI