Showing papers on "ω-automaton published in 1981"
TL;DR: A precisely attainable lower bound on the succinctness of representing regular languages by boolean automata is shown; namely, it is shown that, for every n ⩾ 1, there exists a reduced automaton D n with n states such that the smallest boolean automaton accepting the same language has also n states.
154 citations
45 citations
Book•
01 Jan 1981
TL;DR: When you read more every page of this automata theory machines and languages, what you will obtain is something great.
Abstract: Read more and get great! That's what the book enPDFd automata theory machines and languages will give for every reader to read this book. This is an on-line book provided in this website. Even this book becomes a choice of someone to read, many in the world also loves it so much. As what we talk, when you read more every page of this automata theory machines and languages, what you will obtain is something great.
36 citations
TL;DR: It is shown that this class of cellular automata can accept various string languages in O(log n) time, where n is the length of the input string defining the initial states of the leaf vertices in the tree.
Abstract: This paper introduces a special class of cellular automata, called triangle cellular automata, which accept as input strings of length a power of two. In particular, we study the special case in which state information can only move upward through a complete binary tree of finite-state automata. It is shown that this class of cellular automata can accept various string languages in O(log n) time, where n is the length of the input string defining the initial states of the leaf vertices in the tree. Extensions to two dimensions, defining a pyramid cellular automaton, are also given.
21 citations
17 citations
Book•
01 Jan 1981
TL;DR: A model for predicting the behavior of stochastic automata based on representations for state automata and prediction theory for stochastics automata.
Abstract: Getting started: Basic definitions and constructions.- Asymptotic behavior of stochastic automata.- Representations for state automata.- Presentations for automata with output.- Prediction theory for stochastic automata.
17 citations
TL;DR: It is shown that the upper bound of 2 n + 1 on the number of states of the corresponding reduced automaton can be attained for all n ⩾ 2, i.e., theupper bound 2 n - 1 is optimal.
16 citations
31 Aug 1981
TL;DR: This work gives a fundamental notion of implementation of one algebraic data type by another one that gives a unifying framework for studying various recent approaches to algebraic implementation, and is consistent with the classical theory of finite automata realization developed by Hartmanis and Stearns.
Abstract: We give a fundamental notion of implementation of one algebraic data type by another one that gives a unifying framework for studying various recent approaches to algebraic implementation, and at the same time is consistent with the classical theory of finite automata realization developed by Hartmanis and Stearns Much uniformity and simplicity is achieved by discarding reduction problems from automata realization as well as specification problems from algebraic data type implementation As a result of our approach, we get new insights in the composability of algebraic implementations and the existence of normal forms for algebraic implementations
16 citations
13 Jul 1981
12 citations
TL;DR: It is shown that 3-head automata with one read-write head followed by two read-only heads are as powerful as any multihead automaton.
Abstract: Nondeterministic one-wayk-head writing finite automata are investigated. It is shown that 3-head automata with one read-write head followed by two read-only heads are as powerful as any multihead automaton. Furthermore, a new way to detect a coincidence of heads is introduced, which has as a consequence that it makes no difference, whether the heads make stationary moves ore-moves.
8 citations
TL;DR: It is shown that there exists a monomorphism from a multithreshold symmetric automata into a binary threshold symmetry automata, which implies that both automata have the same transient and cyclic behaviour.
Abstract: It is shown that there exists a monomorphism from a multithreshold symmetric automata into a binary threshold symmetric automata. This implies that both automata have the same transient and cyclic behaviour. By a theorem proved in Goles and Olivos (1981) we conclude that a multithrehold symmetric automata does not have cycles of length greater than two.
TL;DR: Algorithms for computing the least upper bound and the greatest lower bound of given two elements in each class which forms a lattice of automata are given.
Abstract: A class of Σautomata is considered as a partially ordered set by homomorphism relation. We show first that some classes of automata. e.g., quasiperfect automata, perfect automata and strongly cofinal automata, are lattices, and other classes, e.g., strongly connected automata, cyclic automata and cofinal automata, are not lattices. At the same time, we give algorithms for computing the least upper bound and the greatest lower bound of given two elements in each class which forms a lattice.
TL;DR: A new graph-acceptor model which can be considered as a canonical generalization of finite automata from strings to labelled (selector-) graphs is introduced.
Abstract: We introduce a new graph-acceptor model which can be considered as a canonical generalization of finite automata from strings to labelled (selector-) graphs.
TL;DR: An algorithm for updating the action probabilities of the automata, taking into account environmental reactions at all the levels, is proposed and it is shown that the hierarchical system of automata operating according to this algorithm is Є -optima.
31 Aug 1981
TL;DR: A new approach to accepting graph languages employs ordinary finite (string) automata traversing (directed edgelabeled) graphs to characterize the class of graph languages obtained.
Abstract: A new approach to accepting graph languages is introduced It employs ordinary finite (string) automata traversing (directed edgelabeled) graphs Several characterizations of the class of graph languages obtained in this way are provided
01 Jan 1981
TL;DR: This work shows that the usual minimisation process applied to mefas is unnecessarily weak and proposes a more natural alternative that solves a current problem and provides a unique (in a restricted sense) minimal structure.
Abstract: A multiple entry finite automaton (mefa) can be viewed as a set of finite automata acting in parallel but in a compacted form. Mefas are defined in a similar manner to finite automata except that any state can be initial. Unlike finite automata, they cannot be minimised in a unique way. We show that the usual minimisation process applied to mefas is unnecessarily weak. We propose a more natural alternative. This solves a current problem and provides a unique (in a restricted sense) minimal structure.
31 Aug 1981
TL;DR: Tolerance inductions and coinductions are used to tolerate the remaining two sets in each case and a general definition of a tolerance automaton is suggested and the morphisms of the category defined.
Abstract: Suitable ways of putting tolerance structures onto automata are sought. Inertial tolerance on the state set is discussed, but for black box automata an observed or even inertial tolerance on the output set is thought to be more appropriate. Tolerance inductions and coinductions are used to tolerate the remaining two sets in each case. A general definition of a tolerance automaton is suggested and the morphisms of the category defined. The particular case of an (M‐R) automaton is considered and required to yield a stable tolerance structure. Some illustrative examples are given.