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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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Journal ArticleDOI
TL;DR: Saturation of tree automata as discussed by the authors is a technique that consists of adding new transitions to an automaton while preserving its language, which can reduce the size of automata by merging states and removing superfluous transitions.
Abstract: We introduce saturation of nondeterministic tree automata, a technique that consists of adding new transitions to an automaton while preserving its language. We implemented our algorithm on minotaut - a module of the tree automata library libvata that reduces the size of automata by merging states and removing superfluous transitions - and we show how saturation can make subsequent merge and transition-removal operations more effective. Thus we obtain a Ptime algorithm that reduces the size of tree automata even more than before. Additionally, we explore how minotaut alone can play an important role when performing hard operations like complementation, allowing to both obtain smaller complement automata and lower computation times. We then show how saturation can extend this contribution even further. We tested our algorithms on a large collection of automata from applications of libvata in shape analysis, and on different classes of randomly generated automata.

1 citations

Book ChapterDOI
27 Aug 1990
TL;DR: In this article, it was shown that for a finite automaton with n states and distance 2n−2, the maximum distance of a word recognized by this automaton is at most linear in the input length.
Abstract: A distance automaton (DA) is a nondeterministic finite automaton which is equipped with a nonnegative cost function on its transitions. The distance of a word recognized by such a machine quantifies the expenses associated with the recognition of this word. The distance of a DA is the maximal distance of a word recognized by this DA or is infinite, depending on whether or not a maximum exists. We present DA's having n states and distance 2n−2. We also show: Given a finitely ambiguous DA with n states, then either its distance is at most 3n−2, or the growth of the distance in this DA is linear in the input length. As a by-product of the first result we obtain regular languages having exponential finite order.

1 citations

01 Jan 2008
TL;DR: This article shows specific type of probabilistic automata: the reactive Probabilistic finite automata with accepting states, and definitions of languages accepted by it, and defines relation of indistinguishableness of automata states, on base of which automata minimization could be effectuated.
Abstract: The problem of finite automata minimization is important for software and hardware designing. Different types of automata are used for modeling systems or machines with finite number of states. The limitation of number of states gives savings in resources and time. In this article we show specific type of probabilistic automata: the reactive probabilistic finite automata with accepting states (in brief the reactive probabilistic automata), and definitions of languages accepted by it. We present definition of bisimulation relation for automata's states and define relation of indistinguishableness of automata states, on base of which we could effectuate automata minimization. Next we present detailed algorithm reactive probabilistic automata's minimization with determination of its complexity and analyse example solved with help of this algorithm.

1 citations

Journal ArticleDOI
Zamir Bavel1
TL;DR: Bell's table comparing the efficiency of his method with that of Maurer's indicates that this extra initialization cost is justified only if checking a single entry is a relatively time consuming operation.
Abstract: searched only if we replace the \"fixed constmlt\" by a number congruent to-Q/v2. However, even if this is done, there is still the problem that when Q ~-0, only one table location is examined! To correct these problems, replace steps (3) and (4) of Bell's algorithm with: (3) Initialize A with C, where C is defined below. (4) Increment A by 2Q. For this algorithm, we have a = Q + C, b = Q. We must then choose C so that C ~-QifQ ¢ 0andC ¢-Qif Q ~-0. The algorithm will then search (p + 1)/2 locations if Q ~ 0, and will search all p locations if Q-= 0. The trouble with this algorithm is that it requires testing for Q ~ 0, which means performing an extra division. A seemingly possible way out is to observe that if (p-a)/vb-j, b ¢ 0, then the algorithm searchesj fewer locations before it starts reexamining locations. We can then try to choose C so that we get j to be small, thereby examining nearly half the table before repeating. However, this requires that we make C ~-(j + 1)Q. There does not appear to be any simple algorithm for choosing a C satisfying this congruence for a small j when Q fi 0, and choosing C ¢-Q when Q ~ 0. ~ It seems that the division is necessary. The corrected version of Bell's algorithm still contains a gross inefficiency. For Q ~ 0, it decided that the search is a failure after p tries, instead of the necessary (p q-1)/2 tries. This is easily corrected by changing the criterion for failure. In summary, Bell's algorithm requires a correction which adds an extra division to the initialization procedure. This must be considered in evaluating its efficiency. Bell's table comparing the efficiency of his method with that of Maurer's indicates that this extra initialization cost is justified only if checking a single entry is a relatively time consuming operation.

1 citations


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