Open AccessJournal Article
Descriptional complexity of finite automata: concepts and open problems
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TLDR
It is argued that if one wishes a renaissance of automata theory, then one should prefer to return to the investigation of the fundamental, classical problems of Automata theory rather then searching for new applications and defining numerous questionable modifications of basic models.Abstract:
"Automata theory is not over" is the message of this paper. But if one wishes a renaissance of automata theory, then one should prefer to return to the investigation of the fundamental, classical problems of automata theory rather then searching for new applications and defining numerous questionable modifications of basic models. We argue for this opinion here and try co outline a way that could lead to a renaissance of automata theory.read more
Citations
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Journal ArticleDOI
State complexity of some operations on binary regular languages
TL;DR: It is proved that the upper bounds on the state complexity of these operations, which were known to be tight for larger alphabets, are tight also for binary alphABets.
Journal ArticleDOI
State complexity of concatenation and complementation
TL;DR: The upper bounds on the state complexity of concatenation are also tight in the case that the first automaton has more than one accepting state, and the entire range of complexities, up to the known upper bound can be produced.
Journal ArticleDOI
State complexity of cyclic shift
TL;DR: For 2- and 3-letter alphabets, it is proved 2 ⊖(n2) state complexity, and a tight 2n 2 + 1 lower bound is established for the nondeterministic state complexity of this operation using a binary alphabet.
Book ChapterDOI
Finding lower bounds for nondeterministic state complexity is hard
Hermann Gruber,Markus Holzer +1 more
TL;DR: In this article, the maximal attainable lower bound for each of the above mentioned techniques can be deduced from a canonical finite graph, the so called dependency graph of a regular language, which is very helpful when comparing the techniques with each other and with nondeterministic state complexity.
Book ChapterDOI
State complexity of concatenation and complementation of regular languages
TL;DR: The upper bounds on the state complexity of concatenation are also tight in the case that the first automaton has more than one accepting state, and the entire range of complexities, up to the known upper bound can be produced.
References
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Book
Introduction to Automata Theory, Languages, and Computation
TL;DR: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
Journal ArticleDOI
Finite automata and their decision problems
Michael O. Rabin,Dana Scott +1 more
TL;DR: Finite automata are considered as instruments for classifying finite tapes as well as generalizations of the notion of an automaton are introduced and their relation to the classical automata is determined.
Journal ArticleDOI
A method for synthesizing sequential circuits
TL;DR: A new method of synthesis is developed which emphasizes formal procedures rather than the more familiar intuitive ones, and familiarity is assumed with the use of switching algebra in the synthesis of combinational circuits.
Book ChapterDOI
An n log n algorithm for minimizing states in a finite automaton
TL;DR: An algorithm is given for minimizing the number of states in a finite automaton or for determining if two finite automata are equivalent and the running time is bounded by k n log n.