From the Publisher:
Although it originated as a method to study general dynamical systems, symbolic dynamics is useful in coding for data storage and transmission as well as in linear algebra. Requiring only a undergraduate knowledge of linear algebra, this first general textbook includes over 500 exercises.

An Introduction to Symbolic Dynamics and Coding

The theory of formal languages is the oldest and most fundamental area of theoretical computer science. It has served as a basis of formal modeling from the early stages of programming languages to the recent beginnings of DNA computing. This first handbook of formal languages gives a comprehensive up-to-date coverage of all important aspects and subareas of the field. Best specialists of various subareas, altogether 50 in number, are among the authors. The maturity of the field makes it possible to include a historical perspective in many presentations. The individual chapters can be studied independently, both as a text and as a source of reference. The Handbook is an invaluable aid for advanced students and specialists in theoretical computer science and related areas in mathematics, linguistics, and biology.

Handbook of Formal Languages

The subject of this chapter is the study of formal languages (mostly languages recognizable by finite automata) in the framework of mathematical logic.

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Languages, automata, and logic

Preface 1. Stringology 2. Number theory and algebra 3. Numeration systems 4. Finite automata and other models of computation 5. Automatic sequences 6. Uniform morphisms and automatic sequences 7. Morphic sequences 8. Frequency of letters 9. Characteristic words 10. Subwords 11. Cobham's theorem 12. Formal power series 13. Automatic real numbers 14. Multidimensional automatic sequences 15. Automaticity 16. k-regular sequences 17. Physics Appendix. Hints, references and solutions for selected exercises Bibliography Index.

Automatic Sequences: Theory, Applications, Generalizations

Theory of codes

The aim of this chapter is to generalize concepts and techniques of formal language theory to two dimensions. Informally, a two-dimensional string is called a picture and is defined as a rectangular array of symbols taken from a finite alphabet. A two-dimensional language (or picture language) is a set of pictures.

Two-dimensional languages

The purpose of this paper is to propose a new notion of recognizability for picture (two-dimensional) languages extending the characterization of one-dimensional recognizable languages in terms of local languages and alphabetic mappings. We first introduce the family of local picture languages (denoted by LOC) and, in particular, prove the undecidability of the emptiness problem. Then we define the new family of recognizable picture languages (denoted by REC). We study some combinatorial and language theoretic properties of REC such as ambiguity, closure properties or undecidability results. Finally we compare the family REC with the classical families of languages recognized by four-way automata.

Recognizable picture languages

https://hal-upec-upem.archives-ouvertes.fr/hal-00619578/document

Automata and forbidden words

An extension of the Burrows–Wheeler Transform

It is shown that a set of pictures (rectangular arrays of symbols) is recognized by a finite tiling system iff it is definable in existential monadic second-order logic. As a consequence, finite tiling systems constitute a notion of recognizability over two-dimensional inputs which at the same time generalizes finite-state recognizability over strings and also matches a natural logic. The proof is based on the Ehrenfeucht–Fraisse technique for first-order logic and an implementation of “threshold counting” within tiling systems.

Antonio Restivo

Papers

Two-dimensional languages

Recognizable picture languages

Automata and forbidden words

An extension of the Burrows–Wheeler Transform

Monadic second-order logic over rectangular pictures and recognizability by tiling systems