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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17 citations
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TL;DR: It is proved that deterministic array automata which can travel across the unmarked portions of the input array, but not write on these portions, are no more powerful than deterministic arrays which are restricted to the marked portion of their input arrays.
Abstract: In this communication, it is proved that deterministic array automata which can travel across the unmarked portions of the input array, but not write on these portions, are no more powerful than deterministic array automata which are restricted to the marked portion of their input arrays. The similar question for nondeterministic automata is still open. The one-dimensional case is also examined.
17 citations
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07 Jul 2009
TL;DR: An O (n logn ) algorithm that computes for a given finite deterministic automaton (dfa) an almost equivalent dfa that is as small as possible--such an automaton is called hyper-minimal.
Abstract: We improve a recent result [ A. Badr : Hyper-Minimization in O (n 2). In Proc. CIAA , LNCS 5148, 2008] for hyper-minimized finite automata. Namely, we present an O (n logn ) algorithm that computes for a given finite deterministic automaton (dfa) an almost equivalent dfa that is as small as possible--such an automaton is called hyper-minimal. Here two finite automata are almost equivalent if and only if the symmetric difference of their languages is finite. In other words, two almost-equivalent automata disagree on acceptance on finitely many inputs. In this way, we solve an open problem stated in [ A. Badr , V. Geffert , I. Shipman : Hyper-minimizing minimized deterministic finite state automata. RAIRO Theor. Inf. Appl. 43(1), 2009] and by Badr . Moreover, we show that minimization linearly reduces to hyper-minimization, which shows that the time-bound O (n logn ) is optimal for hyper-minimization.
17 citations
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27 Mar 2009TL;DR: It is shown that the nondeterministic automata have a decidable nonemptiness problem and it is left as an open question whether this is true for the alternating version.
Abstract: We introduce a new kind of tree automaton, a dependency tree automaton, that is suitable for deciding properties of classes of terms with binding. Two kinds of such automaton are defined, nondeterministic and alternating. We show that the nondeterministic automata have a decidable nonemptiness problem and leave as an open question whether this is true for the alternating version. The families of trees that both kinds recognise are closed under intersection and union. To illustrate the utility of the automata, we apply them to terms of simply typed lambda calculus and provide an automata-theoretic characterisation of solutions to the higher-order matching problem.
17 citations
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TL;DR: Improve the best-case running time, present an extension of this algo- rithm to non-deterministic finite automaton, and establish a relationship between this algorithm and the one proposed in Almeida et al.
Abstract: The minimal deterministic finite automaton is generally used to determine regular languages equality. Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved variant. Hopcroft and Karp proposed an almost linear algorithm for testing the equivalence of two deterministic finite automata that avoids minimisation. In this paper we improve the best-case running time, present an extension of this algorithm to non-deterministic finite automata, and establish a relationship between this algorithm and the one proposed in Almeida et al. We also present some experimental comparative results. All these algorithms are closely related with the recent coalgebraic approach to automata proposed by Rutten.
17 citations