Fundamental Properties of Pushdown Tree Transducer (PDTT)--A Top-Down Case--

Katsunori YAMASAKI

Fundamental Properties of Pushdown Tree Transducer (PDTT)--A Top-Down Case--

Katsunori YAMASAKI

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String grammars (languages) have been extensively studied from 60's. On the other hand, the transformational grammar, proposed by Chomsky, contains the transformation from the set of derivation trees of context-free language to the surface set. And the grammar regarded a tree as an input sentence to some transducer. After that from latter half of 60's, the studies of acceptor, transducer, and so on, whose input is a tree, have been done extensively. In this paper we propose, as a model, a new type of transducer which translates trees into trees and investigate its fundamental properties. The model proposed here is the pushdown tree transducer (for shortly PDTT) that is an extension of the finite state tree transducer discussed by J. W. Thacher, W. C. Rounds, J. Engelfriet, and so on. The main subjects discussed here (we consider only top-down case (t-PDTT)), are as follows: (1) final state t-PDTT translation is equivalent to empty stack t-PDTT translation and vice versa, (2) for any t-PDTT, a single state t-PDTT which is equivalent to it always exists, (3) as a standard form the symmetric stack form t-PDTT is proposed and based on this, it is shown that any single state t-PDTT can be always converted into a linear stack t-PDTT, and so on.

Publication: IEICE TRANSACTIONS on Information Vol.E76-D No.10 pp.1234-1242

Publication Date: 1993/10/25

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Type of Manuscript: PAPER

Category: Automaton, Language and Theory of Computing

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Katsunori YAMASAKI, "Fundamental Properties of Pushdown Tree Transducer (PDTT)--A Top-Down Case--" in IEICE TRANSACTIONS on Information, vol. E76-D, no. 10, pp. 1234-1242, October 1993, doi: .
Abstract: String grammars (languages) have been extensively studied from 60's. On the other hand, the transformational grammar, proposed by Chomsky, contains the transformation from the set of derivation trees of context-free language to the surface set. And the grammar regarded a tree as an input sentence to some transducer. After that from latter half of 60's, the studies of acceptor, transducer, and so on, whose input is a tree, have been done extensively. In this paper we propose, as a model, a new type of transducer which translates trees into trees and investigate its fundamental properties. The model proposed here is the pushdown tree transducer (for shortly PDTT) that is an extension of the finite state tree transducer discussed by J. W. Thacher, W. C. Rounds, J. Engelfriet, and so on. The main subjects discussed here (we consider only top-down case (t-PDTT)), are as follows: (1) final state t-PDTT translation is equivalent to empty stack t-PDTT translation and vice versa, (2) for any t-PDTT, a single state t-PDTT which is equivalent to it always exists, (3) as a standard form the symmetric stack form t-PDTT is proposed and based on this, it is shown that any single state t-PDTT can be always converted into a linear stack t-PDTT, and so on.
URL: https://global.ieice.org/en_transactions/information/10.1587/e76-d_10_1234/_p

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@ARTICLE{e76-d_10_1234,
author={Katsunori YAMASAKI, },
journal={IEICE TRANSACTIONS on Information},
title={Fundamental Properties of Pushdown Tree Transducer (PDTT)--A Top-Down Case--},
year={1993},
volume={E76-D},
number={10},
pages={1234-1242},
abstract={String grammars (languages) have been extensively studied from 60's. On the other hand, the transformational grammar, proposed by Chomsky, contains the transformation from the set of derivation trees of context-free language to the surface set. And the grammar regarded a tree as an input sentence to some transducer. After that from latter half of 60's, the studies of acceptor, transducer, and so on, whose input is a tree, have been done extensively. In this paper we propose, as a model, a new type of transducer which translates trees into trees and investigate its fundamental properties. The model proposed here is the pushdown tree transducer (for shortly PDTT) that is an extension of the finite state tree transducer discussed by J. W. Thacher, W. C. Rounds, J. Engelfriet, and so on. The main subjects discussed here (we consider only top-down case (t-PDTT)), are as follows: (1) final state t-PDTT translation is equivalent to empty stack t-PDTT translation and vice versa, (2) for any t-PDTT, a single state t-PDTT which is equivalent to it always exists, (3) as a standard form the symmetric stack form t-PDTT is proposed and based on this, it is shown that any single state t-PDTT can be always converted into a linear stack t-PDTT, and so on.},
keywords={},
doi={},
ISSN={},
month={October},}

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TY - JOUR
TI - Fundamental Properties of Pushdown Tree Transducer (PDTT)--A Top-Down Case--
T2 - IEICE TRANSACTIONS on Information
SP - 1234
EP - 1242
AU - Katsunori YAMASAKI
PY - 1993
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E76-D
IS - 10
JA - IEICE TRANSACTIONS on Information
Y1 - October 1993
AB - String grammars (languages) have been extensively studied from 60's. On the other hand, the transformational grammar, proposed by Chomsky, contains the transformation from the set of derivation trees of context-free language to the surface set. And the grammar regarded a tree as an input sentence to some transducer. After that from latter half of 60's, the studies of acceptor, transducer, and so on, whose input is a tree, have been done extensively. In this paper we propose, as a model, a new type of transducer which translates trees into trees and investigate its fundamental properties. The model proposed here is the pushdown tree transducer (for shortly PDTT) that is an extension of the finite state tree transducer discussed by J. W. Thacher, W. C. Rounds, J. Engelfriet, and so on. The main subjects discussed here (we consider only top-down case (t-PDTT)), are as follows: (1) final state t-PDTT translation is equivalent to empty stack t-PDTT translation and vice versa, (2) for any t-PDTT, a single state t-PDTT which is equivalent to it always exists, (3) as a standard form the symmetric stack form t-PDTT is proposed and based on this, it is shown that any single state t-PDTT can be always converted into a linear stack t-PDTT, and so on.
ER -