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.
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TL;DR: This work introduces a new type of internal memory for finite automata and real-time automata that allows arbitrary group structure of the internal memory of the automata.
Abstract: We introduce a new type of internal memory for finite automata and real-time automata. Instead of using tapes with a prescribed Euclidean structure (one-dimensional or two-dimensional tapes) we allow arbitrary group structure of the internal memory of the automata.
Journal Article•
TL;DR: In this paper, it was shown that the standard methods for the random generation of finite automata are inadequate if considered over the domain of the regular languages, and a consolidated, practical method was proposed for the unary generation of automata over the domains of regular languages.
Abstract: We show that the standard methods for the random generation of finite automata are inadequate if considered over the domain of the regular languages, for finite automata with a small number of states. We then present a consolidated, practical method for the random generation of unary finite automata over the domain of the regular languages.
Dissertation•
01 Jan 2008
TL;DR: In this paper, the focus of the paper is finitely generated subgroups of the automorphism group of an infinite spherically homogeneous rooted tree (regular or irregular).
Abstract: The focus of this thesis is finitely generated subgroups of the automorphism group of an infinite spherically homogeneous rooted tree (regular or irregular). The first chapter introduces the topic and outlines the main results. The second chapter provides definitions of the terminology used, and also some preliminary results. The third chapter introduces a group that appears to be a promising candidate for a finitely generated group of infinite upper rank with finite upper $p$-rank for all primes $p$. It goes on to demonstrate that in fact this group has infinite upper $p$-rank for all primes $p$. As a by-product of this construction, we obtain a finitely generated branch group with quotients that are virtually-(free abelian of rank $n$) for arbitrarily large $n$. The fourth chapter gives a complete classification of ternary automata with $C_2$-action at the root, and a partial classification of ternary automata with $C_3$-action at the root. The concept of a `windmill automaton' is introduced in this chapter, and a complete classification of binary windmill automata is given. The fifth chapter contains a detailed study of the non-abelian ternary automata with $C_3$-action at the root. It also contains some conjectures about possible isomorphisms between these groups.
Posted Content•
TL;DR: This paper introduces a new structure, namely multi-head Watson–Crick automata, where the single tape of a multi- head finite automaton is replaced by a DNA double strand and the content of the second tape is determined using a complementarity relation similar to the Watson-Crick complementarity relationship.
Abstract: Inspired by multi-head finite automata and Watson-Crick automata in this paper, we introduce new structure namely multi-head Watson-Crick automata where we replace the single tape of multi-head finite automaton by a DNA double strand. The content of the second tape is determined using a complementarity relation similar to Watson-Crick complementarity relation. We establish the superiority of our model over multi-head finite automata and also show that both the deterministic and non-deterministic variant of the model can accept non-regular unary languages. We also compare our model with parallel communicating Watson-Crick automata systems and prove that both of them have the same computational power.
TL;DR: A bound for stability is given and under which conditions identifier experiments exist if the state set of the automaton is a (not necessarily abelian) group with multiple operators.