| 研究課題/領域番号 |
23K10976
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| 研究種目 |
基盤研究(C)
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| 配分区分 | 基金 |
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| 応募区分 | 一般 |
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| 審査区分 |
小区分60010:情報学基礎論関連
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| 研究機関 | 秋田大学 |
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研究代表者 |
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| 研究期間 (年度) |
2023-04-01 – 2026-03-31
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| 研究課題ステータス |
交付 (2023年度)
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| 配分額 *注記 |
4,550千円 (直接経費: 3,500千円、間接経費: 1,050千円)
2025年度: 1,560千円 (直接経費: 1,200千円、間接経費: 360千円)
2024年度: 1,560千円 (直接経費: 1,200千円、間接経費: 360千円)
2023年度: 1,430千円 (直接経費: 1,100千円、間接経費: 330千円)
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| キーワード | automata / complexity / regularity / rewriting |
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| 研究開始時の研究の概要 |
Complexity of non-classical automata can be expressed quantitatively by the number of non-regular transitions they perform while processing inputs. I aim to generalize the concept of non-regular steps to Turing machine computations, which allows treating several stronger-than-regular models in the same framework. The key question is how much of the non-regular resources allows qualitative changes, i.e., larger classes of accepted languages. The goal is a non-regular complexity theory, where languages are classified based on the number of non-regular transitions made by their minimal machines.
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| 研究実績の概要 |
In the first year the project advanced on two fronts:
1. We defined a machine model called freezing 1-tag systems with states. Each symbol may be rewritten to another before the head moves one position to the right and each position may be rewritten only to a symbol that is smaller than the current one in a previously fixed ordering of the alphabet (freezing property). Such models are strictly stronger than finite automata, but the languages accepted are all in DTIME(n^2), so the model is at the low end of computational power. We proved separation results with respect to the classes of the Chomsky-hierarchy and showed that the model is capable of checking some surprising properties that generally require nondeterministic computations in other models.
2. We continued the study of sweep complexity of OWJFA by proving and disproving several conjectures from [Fazekas, Mercas, Wu, 2022, JALC]. We showed that there is no upper bound on machines accepting regular languages in terms of sweep complexity, as there are logarithmic and even linear complexity OWJFA accepting regular languages. We also exhibited OWJFA with logarithmic complexity accepting a non-regular language. Proving non-regularity was achieved by showing that such machines can check logarithmic/exponential relationships between the lengths of certain factors in the input, a very surprising development given that OWJFA do not have access to additional storage.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
As originally planned, in the first year we focused on establishing complexity results in some existing models and introduced new ones, with the longer term goal of obtaining an intuition for possible generalizations.
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| 今後の研究の推進方策 |
The plan for the upcoming year is to investigate related complexity measures in other automata models, as well as some algorithmic properties of these models accepting non-regular languages.
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