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: The main tools for this investigation are a characterization of the ω-languages accepted by X -automata in terms of inverse X -transductions of finite-state ω -languages and the existence of topological upper bounds on some of the families of accepted υ-l languages (independent of the storage type X).
81 citations
TL;DR: An algorithm is given which, given a finite number of invertible matrices, computes the Zariski closure of the group generated by these matrices.
80 citations
01 Apr 1997
TL;DR: One of the main directions of research has been the problem of the isomorphism of shifts of finite type, which is not yet completely solved although the latest results of Kim and Roush indicate a counterexample to a long-standing conjecture formulated by F. Williams.
Abstract: Symbolic dynamics is a field which was born with the work in topology of Marston Morse at the beginning of the 1920s [44]. It is, according to Morse, an “algebra and geometry of recurrence”. The idea is the following. Divide a surface into regions named by certain symbols. We then study the sequences of symbols obtained by scanning the successive regions while following a trajectory starting from a given point. A further paper by Morse and Hedlund [45] gave the basic results of this theory. Later, the theory was developed by many authors as a branch of ergodic theory (see for example the collected works in [59] or [12]). One of the main directions of research has been the problem of the isomorphism of shifts of finite type (see below the definition of these terms). This problem is not yet completely solved although the latest results of Kim and Roush [35] indicate a counterexample to a long-standing conjecture formulated by F. Williams [61].
79 citations
01 Jan 1993
TL;DR: This paper presents a taxonomy of nite automata minimization algorithms and shows that the equivalence relation is the greatest xed point of an equation providing a useful characterization of the required computation.
Abstract: This paper presents a taxonomy of finite automata minimization algorithms. Brzozowski's elegant minimization algorithm differs from all other known minimization algorithms, and is derived separately. All of the remaining algorithms depend upon computing an equivalence relation on states. We define the equivalence relation, the partition that it induces, and its complement. Additionally, some useful properties are derived. It is shown that the equivalence relation is the greatest fixed point of an equation, providing a useful characterization of the required computation. We derive an upperbound on the number of approximation steps required to compute the fixed point. Algorithms computing the equivalence relation (or the partition, or its complement) are derived systematically in the same framework. The algorithms include Hopcroft's, several algorithms from text-books (including Hopcroft and Ullman's [HU79], Wood's [Wood87], and Aha, Sethi, and Ullman's [ASU86]), and several new algorithms or variants of existing algorithms.
79 citations
19 Apr 1994
TL;DR: It is argued that the way finite-state automata theory is taught in schools needs to change to accommodate for the growing number of new applications.
Abstract: Finite automata have two traditional applications in computer science: modeling of finite-state systems and description of regular set of finite words. In the last few years, several new applications for finite-state automata have emerged, e.g., optimization of logic programs and specification and verification of protocols. These applications use finite-state automata to describe regular sets of infinite words and trees. I will describe such applications and will argue that we need change the way we teach automata theory.
79 citations