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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
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Journal Article
TL;DR: This paper considers monogenic n.d. automata, and for each i = 1,2,3, it is presented sharp bounds for the maximal lengths of the shortest Di-directing words.
Abstract: A finite automaton is said to be directable if it has an input word, a directing word, which takes it from every state into the same state For nondeterministic (nd) automata, directability can be generalized in several ways, three such notions, D1-, D2-, and D3-directability, are used In this paper, we consider monogenic nd automata, and for each i = 1,2,3, we present sharp bounds for the maximal lengths of the shortest Di-directing words

2 citations

Journal ArticleDOI
TL;DR: This work defines and studies a class of random automata networks, called randomized cellular automata, which are defined on random directed graphs with constant out-degrees and evolve according to cellular automaton rules.
Abstract: We define and study a few properties of a class of random automata networks. While regular finite one-dimensional cellular automata are defined on periodic lattices, these automata networks, called randomized cellular automata, are defined on random directed graphs with constant out-degrees and evolve according to cellular automaton rules. For some families of rules, a few typical a priori unexpected results are presented.

2 citations

Book ChapterDOI
20 Jul 2015
TL;DR: This work provides a procedure computing for a game automaton an equivalent weak alternating automaton with the minimal index and a quadratic number of states and obtains that, as for deterministic automata, the weak index and the Borel rank coincide.
Abstract: Game automata are known to recognise languages arbitrarily high in both the non-deterministic and alternating Rabin–Mostowski index hierarchies. Recently it was shown that for this class both hierarchies are decidable. Here we complete the picture by showing that the weak index hierarchy is decidable as well. We also provide a procedure computing for a game automaton an equivalent weak alternating automaton with the minimal index and a quadratic number of states. As a by-product we obtain that, as for deterministic automata, the weak index and the Borel rank coincide.

2 citations

Dissertation
01 Jan 2008
TL;DR: This work examines automatic structures, mathematical objects which can be represented by automata, and applies resulting observations to computer science, and measures the complexity of automatic structures via well-established concepts from model theory, topology, and set theory.
Abstract: Finite state automata are Turing machines with fixed finite bounds on resource use. Automata lend themselves well to real-time computations and efficient algorithms. Continuing a tradition of studying computability in mathematics, we examine automatic structures, mathematical objects which can be represented by automata, and apply resulting observations to computer science. We measure the complexity of automatic structures via well-established concepts from model theory, topology, and set theory. We prove the following results. The ordinal height of any automatic well-founded partial order is bounded by ωω. The ordinal heights of automatic well-founded relations are unbounded below wCK1 , the first uncomputable ordinal. For any computable ordinal α, there is an automatic structure of Scott rank at least α. Moreover, there are automatic structures of Scott rank wCK1,w CK1+1. . For any computable ordinal α, there is an automatic successor tree of Cantor-Bendixson rank α. Next, we study infinite graphs produced from a natural unfolding operation applied to finite graphs. Graphs produced via such operations have finite degree and can be described by finite automata over a one-letter alphabet. We investigate algorithmic properties of such graphs in terms of their finite presentations. In particular, we ask how hard it is to check whether a given node belongs to an infinite component, whether two given nodes in the graph are reachable from one another, and whether the graph is connected. We give polynomial-time algorithms answering each of these questions. For a fixed input graph, the algorithm for infinite component membership works in constant time and reachability is decided uniformly by a single automaton. Hence, we improve on previous work, in which nonelementary or nonuniform algorithms were found. We turn our attention to automata techniques for deciding first-order logical theories. These techniques are useful in Integer Linear Programming and Mixed Integer Linear Programming, which in turn have applications in diverse areas of computer science and engineering. We extend known work to address the enumeration problem for linear programming solutions. Then, we apply a similar paradigm to give an automata theoretic decision procedure for the p-adic valued ring under addition and for formal Laurent series over a finite field with valuation and addition.

2 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20238
202219
20201
20191
20185
201748