Automata on linear orderings
Véronique Bruyère,Olivier Carton +1 more
TLDR
It is proved that for countable scattered linear orderings, the two notions of finite automata and rational expressions are equivalent, which extends Kleene's theorem.About:
This article is published in Journal of Computer and System Sciences.The article was published on 2007-02-01 and is currently open access. It has received 66 citations till now. The article focuses on the topics: Quantum finite automata & Nested word.read more
Citations
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Book ChapterDOI
Algebraic Recognizability of Languages
TL;DR: In this article, the authors explore how this word-related notion extends to more complex models, such as those developed for modeling distributed or timed behaviors, and explore why that is.
Journal Article
Higher dimensional automata
Zoltán Ésik,Zoltán L. Németh +1 more
TL;DR: It is provided the basics of a 2-dimensional theory of automata on series-parallel biposets and relates these classes to languages of series-Parallel bipOSets definable in monadic second-order logic.
Book ChapterDOI
Regular and algebraic words and ordinals
Stephen L. Bloom,Zoltán Ésik +1 more
TL;DR: A summary of results on regular words, some of which have been obtained very recently, and include some new results for algebraic words.
Book ChapterDOI
Factorisation Forests for Infinite Words
TL;DR: The theorem of factorisation forests shows the existence of nested factorisations for finite words and has important applications in semigroup theory, and beyond.
Journal ArticleDOI
Logic and Rational Languages of Words Indexed by Linear Orderings
TL;DR: It is proved that every rational language of words indexed by linear orderings is definable in monadic second-order logic, and it is shown that the converse is true for the class of languages indexed by countable scattered linear ordering, but false in the general case.
References
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Book ChapterDOI
Representation of Events in Nerve Nets and Finite Automata
TL;DR: This memorandum is devoted to an elementary exposition of the problems and of results obtained on the McCulloch-Pitts nerve net during investigations in August 1951.
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
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.
Book ChapterDOI
CHAPTER 1 – Finite Automata
TL;DR: The field of finite automata is a branch of mathematics connected with the algebraic theory of semigroups and associative algebras as discussed by the authors, which is one of the most important areas of automata research.
Book
Finite automata
TL;DR: The chapter presents a complete proof of P. Schutzenberger's theorem, stating the equality between star-free sets and aperiodic sets, and describes the applications of finite automata, such as string matching or file indexing.