| Co-Investigator(Kenkyū-buntansha) |
KATSURA Masashi Kyoto Sangyo University, Department of Mathematics , Professor, 理学部, 教授 (80065870)
DOMOSI Pal Lajoc Kossuth大学, 数学計算機学科, 教授
GECSEG Feren Jozset Attila大学, 情報科学部, 教授
IMREH Balazi Jozset Attila大学, 情報科学部, 推教授
ESIK Zoltan Jozset Attila大学, 情報科学部, 教授
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| Budget Amount *help |
¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 1999: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1998: ¥2,000,000 (Direct Cost: ¥2,000,000)
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| Research Abstract |
A deterministic automaton A =(A,X) is said to be directable if there exists a word μ∈ XィイD1*ィエD1 such that |AuィイD1AィエD1| = 1.In this case, the notion of directability can be uniquely defined. On the other hand, the directability of nondeterministic automata can be difined in several nonequivalent ways. We provide the following three notions of directability.
A word u ∈ XィイD1*ィエD1 over X is said to be :
(1) a D1 -directing word of a D1 -directable automation A if (∃c ∈ A) (∀a ∈A) (auィイD1AィエD1 ={c}),
(2) a D2 directing word of a D2 -directable automaton A if (∀a, b∈ A) (auィイD1AィエD1 = buィイD1AィエD1),
(3) a D3-directing word of a D3 -directable automaton A if (∃c ∈ A) (∀a∈A) (c∈ auィイD1AィエD1).
By DィイD2iィエD2(A) we denote the set of all Di-directing word of A. Notice that the above three notions are equivalent for deterministic automata, I.e.DィイD21ィエD2(A) = DィイD23ィエD2(A). In this case, we denote these languages as D(A), we define the following classes of languages : ∠ィイD2DィエD2 = {D(A)|A : a determin
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istic directable automation}, ∠ィイD2nd(i)ィエD2 ={Di(A) | A : a nondeterministic Di-directable automaton } ∠ィイD2cnd(i)ィエD2 ={Di(A) | A : a complete nondeterministic Di-directable automaton }(I= 1,2,3).
Then each of the above classes of languages becomes a subclass of regular languages, More exactly, these classes constitute a lower lattice under inclusion relation, Now we consider the class of all nondeterministic commutative automata. By ∠ィイD2DィエD2, ∠ィイD2nd(I)ィエD2, ∠ィイD2cnd(I)ィエD2, we denote corresponding classes of commutative languages, then these classes constitute a linear ordered set, For the class of deterministic directable automata A = (A, X) with |A| = n, the following Cerny's conjecture is well-known :
Let A = (A,X) be a deterministic directable automation with |A| = n.By P(A), we denote the number min {|u| | |AuィイD1AィエD1| = 1}. let d(n) = max{p(A) | A : a deterministic directable automaton with |A| =n}. Then d(n) = (n - 1)ィイD12ィエD1.
We have dealt with corresponding problems for the class of nondeterministic directable automata.
The above research has been done mainly with B. Irma. Moreover, during the research term, the research related so shuffle operations on posets and languages has been done with M.Katsura and Z.Esik. The research related to the set of all primitive words has been also done with M.Katsura and P.Domosi. Less
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