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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.


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Book ChapterDOI
06 Jun 2011
TL;DR: This tutorial surveys computational aspects of cellular automata, a discrete dynamical model introduced by S. Ulam and J. von Neumann in the late 40s: a regular grid of finite state cells evolving synchronously according to a common local rule described by a finite automaton.
Abstract: This tutorial surveys computational aspects of cellular automata, a discrete dynamical model introduced by S. Ulam and J. von Neumann in the late 40s: a regular grid of finite state cells evolving synchronously according to a common local rule described by a finite automaton.

1 citations

Journal ArticleDOI
TL;DR: A new class of groups with solvable word problem is introduced, namely groups specified by a confluent set of short-lex-reducing Knuth–Bendix rules which form a regular language, and a computer program is described which looks for such a set of rules in an arbitrary finitely presented group.
Abstract: We introduce a new class of groups with solvable word problem, namely groups specified by a confluent set of short-lex-reducing Knuth–Bendix rules which form a regular language. This simultaneously generalizes short-lex-automatic groups and groups with a finite confluent set of short-lex-reducing rules. We describe a computer program which looks for such a set of rules in an arbitrary finitely presented group. Our main theorem is that our computer program finds the set of rules, if it exists, given enough time and space. (This is an optimistic description of our result — for the more pessimistic details, see the body of the paper.) The set of rules is embodied in a finite state automaton in two variables. A central feature of our program is an operation, which we call welding, used to combine existing rules with new rules as they are found. Welding can be defined on arbitrary finite state automata, and we investigate this operation in abstract, proving that it can be considered as a process which takes as input one regular language and outputs another regular language. In our programs we need to convert several nondeterministic finite state automata to deterministic versions accepting the same language. We show how to improve somewhat on the standard subset construction, due to special features in our case. We axiomatize these special features, in the hope that these improvements can be used in other applications. The Knuth–Bendix process normally spends most of its time in reduction, so its efficiency depends on doing reduction quickly. Standard data structures for doing this can become very large, ultimately limiting the set of presentations of groups which can be so analyzed. We are able to give a method for rapid reduction using our much smaller two variable automaton, encoding the (usually infinite) regular language of rules found so far. Time taken for reduction in a given group is a small constant times the time taken for reduction in the best schemes known (see [5]), which is not too bad since we are reducing with respect to an infinite set of rules, whereas known schemes use a finite set of rules. We hope that the method described here might lead to the computation of automatic structures in groups for which this is currently infeasible. Some proofs have been omitted from this paper in the interests of brevity. Full details are provided in [4].

1 citations


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