Much has been written about theory and practice in the law, and the tension between practitioners and theorists. Judges do not cite theoretical articles often; they rarely "apply" theories to particular cases. These arguments are not revisited. Instead the Essay explores the working and interaction of theory and practice, practitioners and theorists. The Essay starts with a story about solving a legal issue using our intellectual tools - theory, practice, and their progenies: experience and "gut." Next the Essay elaborates on the nature of theory, practice, experience and "gut." The third part of the Essay discusses theories that are helpful to practitioners and those that are less helpful. The Essay concludes that practitioners theorize, and theorists practice. They use these intellectual tools differently because the goals and orientations of theorists and practitioners, and the constraints under which they act, differ. Theory, practice, experience and "gut" help us think, remember, decide and create. They complement each other like the two sides of the same coin: distinct but inseparable.

Of Theory and Practice

CONTENTS 7 Acknowledgments Many people gave substantial suggestions to improve the contents of this book. These are, in alphabetic order, Introduction During the past few years, several of us have been asked many times about references on finite tree automata. On one hand, this is the witness of the liveness of this field. On the other hand, it was difficult to answer. Besides several excellent survey chapters on more specific topics, there is only one monograph devoted to tree automata by Gécseg and Steinby. Unfortunately, it is now impossible to find a copy of it and a lot of work has been done on tree automata since the publication of this book. Actually using tree automata has proved to be a powerful approach to simplify and extend previously known results, and also to find new results. For instance recent works use tree automata for application in abstract interpretation using set constraints, rewriting, automated theorem proving and program verification, databases and XML schema languages. Tree automata have been designed a long time ago in the context of circuit verification. Many famous researchers contributed to this school which was headed by A. Church in the late 50's and the early 60's: B. Trakhtenbrot, Many new ideas came out of this program. For instance the connections between automata and logic. Tree automata also appeared first in this framework, following the work of Doner, Thatcher and Wright. In the 70's many new results were established concerning tree automata, which lose a bit their connections with the applications and were studied for their own. In particular, a problem was the very high complexity of decision procedures for the monadic second order logic. Applications of tree automata to program verification revived in the 80's, after the relative failure of automated deduction in this field. It is possible to verify temporal logic formulas (which are particular Monadic Second Order Formulas) on simpler (small) programs. Automata, and in particular tree automata, also appeared as an approximation of programs on which fully automated tools can be used. New results were obtained connecting properties of programs or type systems or rewrite systems with automata. Our goal is to fill in the existing gap and to provide a textbook which presents the basics of tree automata and several variants of tree automata which have been devised for applications in the aforementioned domains. We shall discuss only finite tree automata, and the …

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Tree Automata Techniques and Applications

This is a reissue of the book Tree Automata by F G\'ecseg and M Steinby originally published in 1984 by Akad\'emiai Kiad\'o, Budapest Some mistakes have been corrected and a few obscure passages have been clarified Moreover, some more recent contributions and current lines of research are reviewed in an appendix that also contains several new references

Tree automata

In this chapter we will present the basic concepts of term rewriting that are needed in this book. More details on term rewriting, its applications, and related subjects can be found in the textbook of Baader and Nipkow [BN98]. Readers versed in German are also referred to the textbooks of Avenhaus [Ave95], Bundgen [Bun98], and Drosten [Dro89]. Moreover, there are several survey articles [HO80, DJ90, Klo92, Pla93] that can also be consulted.

Term Rewriting Systems

The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The author not only provides a thorough description of the theory, but also details its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.

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Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach

Weighted finite automata are classical nondeterministic finite automata in which the transitions carry weights These weights may model, for example, the cost involved when executing a transition, the resources or time needed for this, or the probability or reliability of its successful execution Weights can also be added to classical automata with infinite state sets like pushdown automata, and this extension constitutes the general concept of weighted automata Since their introduction in the 1960s they have stimulated research in related areas of theoretical computer science, including formal language theory, algebra, logic, and discrete structures Moreover, weighted automata and weighted context-free grammars have found application in natural-language processing, speech recognition, and digital image compression This book covers all the main aspects of weighted automata and formal power series methods, ranging from theory to applications The contributors are the leading experts in their respective areas, and each chapter presents a detailed survey of the state of the art and pointers to future research The chapters in Part I cover the foundations of the theory of weighted automata, specifically addressing semirings, power series, and fixed point theory Part II investigates different concepts of weighted recognizability Part III examines alternative types of weighted automata and various discrete structures other than words Finally, Part IV deals with applications of weighted automata, including digital image compression, fuzzy languages, model checking, and natural-language processing Computer scientists and mathematicians will find this book an excellent survey and reference volume, and it will also be a valuable resource for students exploring this exciting research area

Handbook of Weighted Automata

https://ris.utwente.nl/ws/files/6562639/Engelfriet85macro.pdf

Macro Tree Transducers

From the Publisher:
This is a motivated presentation of recent results on tree transducers, applied to studying the general properties of formal models and for providing semantics to context-free languages.

Syntax-Directed Semantics: Formal Models Based on Tree Transducers

We survey some important results for weighted tree automata and weighted tree transducers over finite ranked trees and semirings as weight structure. In particular, we address closure properties of the class of recognizable tree series, results on the support of such tree series, the determinization of weighted tree automata, pumping lemmata and decidability results, and finite algebraic characterizations of recognizable tree series. We discuss the equivalence between recognizable tree series and equational, rational, and MSO-definable tree series, and we present a comparison of several other models of recognizability. For weighted tree transducers we show composition and decomposition results, an inclusion diagram of some fundamental classes of tree series transformations, and hierarchies obtained by composing weighted tree transducers. We also discuss other models of weighted tree transducers.

Weighted Tree Automata and Tree Transducers

In this chapter we introduce the third formal model of syntax-directed semantics: the attributed tree transducer. It is created by abstraction from attribute grammars. It can also handle context information like a macro tree transducer, and in this sense it too is more powerful than a top-down tree transducer. However, attributed tree transducers treat context information in an explicit way rather than implicitly as macro tree transducers do.

Heiko Vogler

Papers

Handbook of Weighted Automata

Macro Tree Transducers

Syntax-Directed Semantics: Formal Models Based on Tree Transducers

Weighted Tree Automata and Tree Transducers

Attributed Tree Transducers