Book ChapterDOI
On Logics, Tilings, and Automata
Wolfgang Thomas
- pp 441-454
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A notion of “graph acceptor” is introduced which can specify monadic second-order properties and allows to treat known types of finite automata in a common framework.Abstract:
We relate the logical and the automata theoretic approach to define sets of words, trees, and graphs. For this purpose a notion of “graph acceptor” is introduced which can specify monadic second-order properties and allows to treat known types of finite automata in a common framework. In the final part of the paper, we discuss infinite graphs that have a decidable monadic second-order theory.read more
Citations
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Book ChapterDOI
Languages, automata, and logic
TL;DR: The subject of this chapter is the study of formal languages (mostly languages recognizable by finite automata) in the framework of mathematical logic.
Book ChapterDOI
Two-dimensional languages
Dora Giammarresi,Antonio Restivo +1 more
TL;DR: The aim of this chapter is to generalize concepts and techniques of formal language theory to two dimensions.
Journal ArticleDOI
Adding nesting structure to words
Rajeev Alur,P. Madhusudan +1 more
TL;DR: In this paper, the authors define nested word automata, which generalize both words and ordered trees, and allow both word and tree operations, and show that the resulting class of regular languages of nested words has all the appealing theoretical properties that the classical regular word languages enjoys: deterministic nestedword automata are as expressive as their non-deterministic counterparts; the class is closed under union, intersection, complementation, concatenation, Kleene-a, prefixes, and language homomorphisms; membership, emptiness, language equivalence are all decidable;
Journal ArticleDOI
Linear time computable problems and first-order descriptions
TL;DR: In this article, it was shown that an arbitrary FO-problem over relational structures of bounded degree can be solved in linear time, using an old technique of Hanf (Hanf 1965) and other techniques developed to prove the decidability of formal theories in mathematical logic.
Journal ArticleDOI
On a monadic NP vs monadic co-NP
TL;DR: In this paper, it was shown that connectivity of finite graphs is not in monadic co-NP, even in the presence of arbitrary built-in relations of moderate degree (that is, degree (log n)o(1)).
References
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Book
Handbook of theoretical computer science
TL;DR: The Handbook of Theoretical Computer Science provides professionals and students with a comprehensive overview of the main results and developments in this rapidly evolving field.
Book ChapterDOI
Automata on infinite objects
TL;DR: This 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.
Book ChapterDOI
On a Decision Method in Restricted Second Order Arithmetic
TL;DR: The interpreted formalism of SC as mentioned in this paper is a fraction of the restricted second order theory of natural numbers, or of the first-order theory of real numbers, and it is easy to see that SC is equivalent to the first order theory [Re, +, Pw, Nn], whereby Re, + are the sets of non-negative reals, integral powers of 2, and natural numbers.
Book ChapterDOI
Weak Second-Order Arithmetic and Finite Automata
TL;DR: The formalism of regular expressions was introduced by S. C. Kleene to obtain the following basic theorems.