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線形マルチボトムアップ木変換器の関数性の決定可能性

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(1)情報処理学会論文誌. プログラミング. Vol.11 No.3 30 (Sep. 2018). 発表概要. 線形マルチボトムアップ木変換器の関数性の決定可能性 田端 浩明1,a). 橋本 健二2. 2018年3月1日発表. マルチボトムアップ木変換器(MBOT)はボトムアップ木変換器(BOT)の拡張クラスの 1 つである. BOT では各状態での出力がちょうど 1 本の木であるのに対して,MBOT では最終的な出力は 1 本の木で はあるが変換途中に現れる状態での出力は木の組が許される.木変換器が関数性を持つとは,各入力木に 対してその木変換器による出力木がたかだか 1 本しか存在しないことをいう.BOT やその拡張の 1 つで ある拡張ボトムアップ木変換器(XBOT)の関数性の判定問題は決定可能であることが示されているが, MBOT について関数性判定問題が決定可能であるかはこれまでに示されていない.BOT の関数性判定問 題が決定可能であることは,木変換器が関数性を持たないならば,ある上限以下の高さを持つ入力木が存 在しそれに対する出力木が複数存在することを示すことで証明できる.そのような高さの上限が存在する ことは,Engelfriet の木の代入に関する性質を用いて示すことができる.本発表では,その性質を制限さ れた木の組の代入に関する性質に拡張することで,線形 MBOT においても同様な高さの上限があること を証明し,それを用いて線形 MBOT の関数性判定が決定可能であることを示す.. Presentation Abstract. Decidability of Functionality of Linear Multi Bottom-up Tree Transducers Hiroaki Tabata1,a). Kenji Hashimoto2. Presented: March 1, 2018. Multi bottom-up tree transducers are an extension of bottom-up tree transducers. While bottom-up tree transducers translate an input tree to a single output tree at any state, multi bottom-up tree transducers can translate a subtree of an input tree to an intermediate output forest during the translation. A tree transducer is functional if every input tree is translated to at most one output tree by the transducer. The functionality problem for bottom-up tree transducers and its another extension, extended bottom-up tree transducers, was shown to be decidable, but not yet for multi bottom-up tree transducers. The decidability of the functionality problem of bottom-up tree transducers can be shown by proving that if a tree transducer is not functional, then there exists an input tree of height smaller than an upper bound such that the transducer has two or more output trees for the input tree. The existence of such an upper bound can be proved by using Engelfriet’s property on tree substitutions. We extend the property for restricted forest substitutions, and then we show that there exists the upper bound of height even for linear multi bottom-up tree transducers. This implies the decidability of functionality for the class of transducers.. 1. 2. a). 名古屋大学工学部 School of Engineering, Nagoya University, Nagoya, Aichi 464–8603, Japan 名古屋大学大学院情報学研究科 Graduate School of Informatics, Nagoya University, Nagoya, Aichi 464–8603, Japan [email protected]. c 2018 Information Processing Society of Japan . 30.

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