Languages, Automata, and Logic

  title={Languages, Automata, and Logic},
  author={Wolfgang Thomas},
  booktitle={Handbook of Formal Languages},
  • W. Thomas
  • Published in Handbook of Formal Languages 1 April 1997
  • Computer Science
The subject of this chapter is the study of formal languages (mostly languages recognizable by finite automata) in the framework of mathematical logic. 

Automata and Logics for Concurrent Systems: Five Models in Five Pages

This work surveys various automata models of concurrent systems and their connection with monadic second-order logic: finite automata, class memory automata%, nested-word automata!, and message-passing automata.

Model Checking Using Automata Theory

This chapter describes the theory of LTL model checking using w- automata theory, which allows applying various known results about automata to the automatic verification of programs.

An Introduction to Finite Automata and their Connection to Logic

An introduction to the syntactic monoid, and as an application give a proof of the equivalence of first-order definability and aperiodicity of finite automata and monadic second-order logic.

Boolean Algebras of Regular Languages

Some of the Boolean algebras of regular languages of finite and infinite words are characterized up to isomorphism. It is shown that classes of regular languages related to such characterizations are

Automata, Logic, and XML

We survey some recent developments in the broad area of automata and logic which are motivated by the advent of XML. In particular, we consider unranked tree automata, tree-walking automata, and

Monitor Logics for Quantitative Monitor Automata

A new logic called Monitor Logic is introduced and it is shown that it is expressively equivalent to Quantitative Monitor Automata.

Some connections between universal algebra and logics for trees

The goal of this paper is to present this problem and similar ones using the language of universal algebra, highlighting potential connections to the structural theory of finite algebras, including Tame Congruence Theory.

Nominal Monoids

It is proved that, under certain conditions, a language of data words is definable in first-order logic if and only if its syntactic monoid is aperiodic.

On the Relationship between-automata and Temporal Logic Normal Forms

This normal form for temporal logic formulae developed for use with execution and clausal resolution in temporal logics is shown how it can represent, syntactically, -automata in a high-level way.

Automata and semigroups recognizing infinite words

The various acceptance modes of automata, and two algebraic proofs of McNaughton's theorem on the equivalence between Buchi and Muller automata are given.



Weak Second‐Order Arithmetic and Finite Automata

The formalism of regular expressions was introduced by S. C. Kleene [6] to obtain the following basic theorems.

Automata on Infinite Objects and Church's Problem

Basic definitions and results Closure properties of difusable sets The sequential calculus Automaton transformations and Church's problem> Regular trees The emptiness problem The solvability problem.

On Logics, Tilings, and Automata

  • W. Thomas
  • Computer Science, Mathematics
  • 1991
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.

The theory of hybrid automata

  • T. Henzinger
  • Computer Science
    Proceedings 11th Annual IEEE Symposium on Logic in Computer Science
  • 1996
The goal is to demonstrate that concepts from the theory of discrete concurrent systems can give insights into partly continuous systems, and that methods for the verification of finite-state systems can be used to analyze certain systems with uncountable state spaces.

Chain Automata

Infinitary Languages: Basic Theory an Applications to Concurrent Systems

The aim of this paper is to provide an outlook at this part of the theory of infinitary languages that seems to be essential for understanding the modern theory of concurrent systems. In the first

Partial Commutation and Traces

Parallelism and concurrency are fundamental concepts in computer science and concerns the authors' daily life whether software written for distributed systems behaves correctly.

Quantifier Hierarchies over Word Relations

We consider analogues of the arithmetical hierarchy over word relations, obtained by replacing the class of recursive relations with some other classes which are defined by various types of finite