Languages, Automata, and Logic

@inproceedings{Thomas1997LanguagesAA,
  title={Languages, Automata, and Logic},
  author={Wolfgang Thomas},
  booktitle={Handbook of Formal Languages},
  year={1997}
}
  • 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. 
View via Publisher
cs.cornell.edu
1,035 Citations
Highly Influential Citations
60
Background Citations
369
Methods Citations
112
Results Citations
21

1,035 Citations

Automata and Logics for Concurrent Systems: Five Models in Five Pages
TLDR
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.
An Introduction to Finite Automata and their Connection to Logic
TLDR
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…
Some connections between universal algebra and logics for trees
TLDR
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
TLDR
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
TLDR
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
TLDR
The various acceptance modes of automata, and two algebraic proofs of McNaughton's theorem on the equivalence between Buchi and Muller automata are given.
Automata for Branching and Layered Structures
TLDR
Thesis Automata for Branching and Layered Structures, a Ph.D. dissertation for branching and layered structures, aims to describe the process of automating the construction of layered structures.
Experiments with Deterministic ω-Automata for Formulas of Linear Temporal Logic
TLDR
Safra’s determinization algorithm is studied in detail, several heuristics that attempt to decrease the size of the resulting automata are presented and experimental results are reported on.
...
...

References

SHOWING 1-10 OF 200 REFERENCES
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.
Synchronized Rational Relations of Finite and Infinite Words
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…
Application of Model Theoretic Games to Discrete Linear Orders and Finite Automata
Simulating Alternating Tree Automata by Nondeterministic Automata: New Results and New Proofs of the Theorems of Rabin, McNaughton and Safra
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…
Hierarchies of Weak Automata and Weak Monadic Formulas
Reasoning About Infinite Computations
TLDR
This work investigates extensions of temporal logic by connectives defined by finite automata on infinite words and shows that they do not increase the expressive power of the logic or the complexity of the decision problem.
...
...