Journal ArticleDOI
A survey of two-dimensional automata theory
Katsushi Inoue,Itsuo Takanami +1 more
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TLDR
The main purpose of this paper is to survey several properties of alternating, nondeterministic, and deterministic two-dimensional Turing machines (including two- dimension finite automata and marker automata), and to briefly survey cellular types of two- dimensional automata.About:
This article is published in Information Sciences.The article was published on 1991-06-03. It has received 114 citations till now. The article focuses on the topics: Automata theory & Quantum finite automata.read more
Citations
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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
Monadic second-order logic over rectangular pictures and recognizability by tiling systems
TL;DR: It is shown that a set of pictures is recognized by a finite tiling system iff it is definable in existential monadic second-order logic, which generalizes finite-state recognizability over strings and also matches a natural logic.
Journal ArticleDOI
Complexity of Two-Dimensional Patterns
TL;DR: In this paper, the first few levels of a hierarchy of complexity for two-or-more-dimensional patterns are studied, and several definitions of "regular language" or "local rule" that are equivalent in d = 1 lead to distinct classes in d ≥ 2.
Journal ArticleDOI
Complexity of two-dimensional patterns
TL;DR: A complexity measure based on a mean information gain that does not require knowledge of the “maximal” entropy of the pattern, and at the same time sensitively accounts for the inherent correlations in the system.
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
Relationships between nondeterministic and deterministic tape complexities
TL;DR: The amount of storage needed to simulate a nondeterministic tape bounded Turingmachine on a deterministic Turing machine is investigated and a specific set is produced, namely the set of all codings of threadable mazes, such that, if there is any set which distinguishes nondeter microscopic complexity classes from deterministic tape complexity classes, then this is one such set.
Journal ArticleDOI
Nondeterministic space is closed under complementation
TL;DR: It immediately follows that the context-sensitive languages are closed under complementation, thus settling a question raised by Kuroda.
Journal ArticleDOI
The method of forced enumeration for nondeterministic automata
TL;DR: Every family of languages, recognized by nondeterministic L(n) tape-bounded Turing machines, where L( n)≥logn, is closed under complement, and as a special case, the family of context-sensitive languages isclosed under complement.
Proceedings ArticleDOI
Hierarchies of memory limited computations
TL;DR: The computational complexity of binary sequences as measured by the rapidity of their generation by multitape Turing machines is investigated and a "translational" method which escapes some of the limitations of earlier approaches leads to a refinement of the established hierarchy.