From the Publisher:
With an analytical and rigorous approach to problem solving and programming techniques,this book is oriented toward engineering. Structure and Interpretation of Computer Programs emphasizes the central role played by different approaches to dealing with time in computational models. Its unique approach makes it appropriate for an introduction to computer science courses,as well as programming languages and program design.

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Structure and Interpretation of Computer Programs

The notion of a recognizable set of finite graphs is introduced. Every set of finite graphs, that is definable in monadic second-order logic is recognizable, but not vice versa. The monadic second-order theory of a context-free set of graphs is decidable.

The monadic second-order logic of graphs. I. recognizable sets of finite graphs

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

Publisher Summary This chapter focuses on finite automata on infinite sequences and infinite trees. The chapter discusses the complexity of the complementation process and the equivalence test. Deterministic Muller automata and nondeterministic Buchi automata are equivalent in recognition power. Any nonempty Rabin recognizable set contains a regular tree and shows that the emptiness problem for Rabin tree automata is decidable. The chapter discusses the formulation of two interesting generalizations of Rabin's Tree Theorem and presents some remarks on the undecidable extensions of the monadic theory of the binary tree. A short overview of the work that studies the fine structure of the class of Rabin recognizable sets of trees is also presented in the chapter. Depending on the formalism in which tree properties are classified, the results fall in three categories: monadic second-order logic, tree automata, and fixed-point calculi.

Automata on infinite objects

Conditional rewriting logic as a unified model of concurrency

Many apparently divergent approaches to specifying formal semantics of programming languages are applications of initial algebra semantics. In this paper an overview of initial algebra semantics is provided. The major technical feature is an initial continuous algebra which permits unified algebraic treatment of iterative and recursive semantic features in the same framework as more basic operations.

Initial Algebra Semantics and Continuous Algebras

Many of the important concepts and results of conventional finite automata theory are developed for a generalization in which finite algebras take the place of finite automata The standard closure theorems are proved for the class of sets “recognizable” by finite algebras, and a generalization of Kleene's regularity theory is presented The theorems of the generalized theory are then applied to obtain a positive solution to a decision problem of second-order logic

Generalized finite automata theory with an application to a decision problem of second-order logic

The concepts of “equational≓ and “recognizable≓ are defined for sets of elements of an arbitrary abstract algebra. Context-free languages and finite-state languages become realizations of the same general concept (of equational sets) when the proper algebra is specified. A principal objective of the paper is to establish in the context of abstract algebra, relationships between such concepts as equational and recognizable sets.

Algebraic automata and context-free sets

This paper extends our earlier work on abstract data types by providing an algebraic treatment of parametrized data types (eg, sets-of-(), stacks-of-(), etc), as well as answering a number of questions on the power and limitations of algebraic specification techniques In brief: we investigate the “hidden function” problem (the need to include operations in specifications which we want to be hidden from the user); we prove that conditional specifications are inherently more powerful than equational specifications; we show that parameterized specifications must contain “side conditions” (eg, that finite-sets-of-d requires an equality predicate on d), and we compare the power of the algebraic approach taken here with the more categorical approach of Lehman and Smyth

Jesse B. Wright

Papers

Initial Algebra Semantics and Continuous Algebras

Generalized finite automata theory with an application to a decision problem of second-order logic

Algebraic automata and context-free sets

Data Type Specification: Parameterization and the Power of Specification Techniques

Data type specification: Parameterization and the power of specification techniques