Two-Terminal Series Parallel (TTSP, for short) graphs are used as data models in applications for electric networks and scheduling problems. We propose a TTSP term graph which is a TTSP graph having structured variables, that is, a graph pattern over a TTSP graph. Let TGTTSP be the set of all TTSP term graphs whose variable labels are mutually distinct. For a TTSP term graph g in TGTTSP, the TTSP graph language of g, denoted by L(g), is the set of all TTSP graphs obtained from g by substituting arbitrary TTSP graphs for all variables in g. Firstly, when a TTSP graph G and a TTSP term graph g are given as inputs, we present a polynomial time matching algorithm which decides whether or not L(g) contains G. The minimal language problem for the class LTTSP={L(g) | g ∈ TGTTSP} is, given a set S of TTSP graphs, to find a TTSP term graph g in TGTTSP such that L(g) is minimal among all TTSP graph languages which contain all TTSP graphs in S. Secondly, we give a polynomial time algorithm for solving the minimal language problem for LTTSP. Finally, we show that LTTSP is polynomial time inductively inferable from positive data.
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Ryoji TAKAMI, Yusuke SUZUKI, Tomoyuki UCHIDA, Takayoshi SHOUDAI, "Polynomial Time Inductive Inference of TTSP Graph Languages from Positive Data" in IEICE TRANSACTIONS on Information,
vol. E92-D, no. 2, pp. 181-190, February 2009, doi: 10.1587/transinf.E92.D.181.
Abstract: Two-Terminal Series Parallel (TTSP, for short) graphs are used as data models in applications for electric networks and scheduling problems. We propose a TTSP term graph which is a TTSP graph having structured variables, that is, a graph pattern over a TTSP graph. Let TGTTSP be the set of all TTSP term graphs whose variable labels are mutually distinct. For a TTSP term graph g in TGTTSP, the TTSP graph language of g, denoted by L(g), is the set of all TTSP graphs obtained from g by substituting arbitrary TTSP graphs for all variables in g. Firstly, when a TTSP graph G and a TTSP term graph g are given as inputs, we present a polynomial time matching algorithm which decides whether or not L(g) contains G. The minimal language problem for the class LTTSP={L(g) | g ∈ TGTTSP} is, given a set S of TTSP graphs, to find a TTSP term graph g in TGTTSP such that L(g) is minimal among all TTSP graph languages which contain all TTSP graphs in S. Secondly, we give a polynomial time algorithm for solving the minimal language problem for LTTSP. Finally, we show that LTTSP is polynomial time inductively inferable from positive data.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E92.D.181/_p
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@ARTICLE{e92-d_2_181,
author={Ryoji TAKAMI, Yusuke SUZUKI, Tomoyuki UCHIDA, Takayoshi SHOUDAI, },
journal={IEICE TRANSACTIONS on Information},
title={Polynomial Time Inductive Inference of TTSP Graph Languages from Positive Data},
year={2009},
volume={E92-D},
number={2},
pages={181-190},
abstract={Two-Terminal Series Parallel (TTSP, for short) graphs are used as data models in applications for electric networks and scheduling problems. We propose a TTSP term graph which is a TTSP graph having structured variables, that is, a graph pattern over a TTSP graph. Let TGTTSP be the set of all TTSP term graphs whose variable labels are mutually distinct. For a TTSP term graph g in TGTTSP, the TTSP graph language of g, denoted by L(g), is the set of all TTSP graphs obtained from g by substituting arbitrary TTSP graphs for all variables in g. Firstly, when a TTSP graph G and a TTSP term graph g are given as inputs, we present a polynomial time matching algorithm which decides whether or not L(g) contains G. The minimal language problem for the class LTTSP={L(g) | g ∈ TGTTSP} is, given a set S of TTSP graphs, to find a TTSP term graph g in TGTTSP such that L(g) is minimal among all TTSP graph languages which contain all TTSP graphs in S. Secondly, we give a polynomial time algorithm for solving the minimal language problem for LTTSP. Finally, we show that LTTSP is polynomial time inductively inferable from positive data.},
keywords={},
doi={10.1587/transinf.E92.D.181},
ISSN={1745-1361},
month={February},}
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TY - JOUR
TI - Polynomial Time Inductive Inference of TTSP Graph Languages from Positive Data
T2 - IEICE TRANSACTIONS on Information
SP - 181
EP - 190
AU - Ryoji TAKAMI
AU - Yusuke SUZUKI
AU - Tomoyuki UCHIDA
AU - Takayoshi SHOUDAI
PY - 2009
DO - 10.1587/transinf.E92.D.181
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E92-D
IS - 2
JA - IEICE TRANSACTIONS on Information
Y1 - February 2009
AB - Two-Terminal Series Parallel (TTSP, for short) graphs are used as data models in applications for electric networks and scheduling problems. We propose a TTSP term graph which is a TTSP graph having structured variables, that is, a graph pattern over a TTSP graph. Let TGTTSP be the set of all TTSP term graphs whose variable labels are mutually distinct. For a TTSP term graph g in TGTTSP, the TTSP graph language of g, denoted by L(g), is the set of all TTSP graphs obtained from g by substituting arbitrary TTSP graphs for all variables in g. Firstly, when a TTSP graph G and a TTSP term graph g are given as inputs, we present a polynomial time matching algorithm which decides whether or not L(g) contains G. The minimal language problem for the class LTTSP={L(g) | g ∈ TGTTSP} is, given a set S of TTSP graphs, to find a TTSP term graph g in TGTTSP such that L(g) is minimal among all TTSP graph languages which contain all TTSP graphs in S. Secondly, we give a polynomial time algorithm for solving the minimal language problem for LTTSP. Finally, we show that LTTSP is polynomial time inductively inferable from positive data.
ER -