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
••
25 Oct 1972
TL;DR: The proof reduces the emptiness problem for automata on infinite trees to that for Automata on finite trees, by showing that any automata definable set of infinite trees must contain a finitely-generable tree.
Abstract: The purpose of this paper is to give an alternative proof to the decidability of the emptiness problem for tree automata, as shown in Rabin4. The proof reduces the emptiness problem for automata on infinite trees to that for automata on finite trees, by showing that any automata definable set of infinite trees must contain a finitely-generable tree.
46 citations
••
TL;DR: It is proved that the addition of any abelian group to a finite automaton is less powerful than the added of the multiplicative group of rational numbers, thus, each language accepted by a finite Automaton over an abelians group is actually a unordered vector language.
46 citations
••
45 citations
••
01 May 1982
TL;DR: This paper describes some experiments in applying hill-climbing to modify finite automata to accept a desired regular language, and shows that many problems can be solved by this simple method.
Abstract: : The problem addressed in this paper is heuristically-guided learning of finite automata from examples. Given positive sample strings and negative sample strings, a finite automaton is generated and incrementally refined to accept all positive samples but do no negative samples. This paper describes some experiments in applying hill-climbing to modify finite automata to accept a desired regular language. We show that many problems can be solved by this simple method. We then describe the method how to 're-construct' a finite automaton if the positive and/or negative samples are slightly altered, without starting from the beginning. Finally, we have an actual system. RR: Regular set Recognizer, that learns to recognize a regular set from the samples that are given by a human teacher one by one.
45 citations
••
TL;DR: It is shown that the linearly bounded automaton can accept the set of primes, and it is conjectured that no automaton whose memory grows less rapidly can recognize the setof primes.
Abstract: A study of the problem of recognizing the set of primes by automata is presented. A simple algebraic condition is derived which shows that neither the set of primes nor any infinite subset of the set of primes can be accepted by a pushdown or finite automaton.In view of this result an interesting open problem is to determine the “weakest” automaton which can accept the set of primes. It is shown that the linearly bounded automaton can accept the set of primes, and it is conjectured that no automaton whose memory grows less rapidly can recognize the set of primes. One of the results shows that if this conjecture is true, it cannot be proved by the use of arguments about the distribution of primes, as described by the Prime Number Theorem. Some relations are established between two classical conjectures in number theory and the minimal rate of memory growth of automata which can recognize the set of primes.
45 citations