Topic
ω-automaton
About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.
Papers published on a yearly basis
Papers
More filters
TL;DR: The result that the matrix product corresponding to a given input tape can be decomposed into the sum of a finite number of fundamental matrices which are determined by the matrices corresponding to the input symbols is derived.
Abstract: In this paper, we discuss the algebraic treatments of probabilistic automata with two states. We derive the result that the matrix product corresponding to a given input tape can be decomposed into the sum of a finite number of fundamental matrices which are determined by the matrices corresponding to the input symbols. We introduced the new concept of probabilistic automata completely isolated by the L -th approximation . With respect to these automata, all tapes of length greater than or equal to L + 1 can be classified into 2{su L +1} sets by means of their ( L + 1)-suffixes. By using this concept, we demonstrate that a two-input symbol actual automaton with two states can realize any definite event.
5 citations
01 Feb 1989
TL;DR: It is shown that, taking for ϑ the greatest root of the characteristic polynomial of thelinear recurrence, the normal representation can be obtained from any representation by a finite automaton which is the composition of two sequential transducers derived from the linear recurrence.
Abstract: In numeration systems defined by a linear recurrence relation, as well as in the set of developments of numbers in a non integer basis ϑ, we define the notion of normal representation of a number. We show that, taking for ϑ the greatest root of the characteristic polynomial of the linear recurrence, and under certain conditions of confluence, the normal representation can be obtained from any representation by a finite automaton which is the composition of two sequential transducers derived from the linear recurrence. The addition of two numbers can be performed by a left sequential transducer.
5 citations
5 citations
Journal Article•
TL;DR: It is proved that the size of the subsequence automaton for a set of k strings of length n is Ω(n k ) for any k≥ 1, which solves an open problem posed by Crochemore and Tronicek in 1999.
Abstract: Given a set of strings, the subsequence automaton accepts all subsequences of these strings. We will derive a lower bound for the maximum number of states of this automaton. We will prove that the size of the subsequence automaton for a set of k strings of length n is Ω(n k ) for any k > 1. It solves an open problem posed by Crochemore and Tronicek [2] in 1999, in which only the case k < 2 was shown.
5 citations
TL;DR: It is shown that every random environment discussed up to the present is a special case of this machine and the system consisting of this environment and an automaton is equivalent to an autonomous stochastic automaton.
5 citations