On the Role of Equivalence Queries in Learning via Queries

Seiichi TANI

On the Role of Equivalence Queries in Learning via Queries

Seiichi TANI

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We consider the role of equivalence queries in learning unknown concepts using membership and equivalence queries. Equivalence queries have the following two roles: (R1) indicating whether a learning algorithm has succeeded to learn the unknown concept and (R2) providing counterexamples. In this paper, we consider the learning using membership and equivalence queries but using only the (R2) part of equivalence queries. In order to gain an insight into the learning membership and equivalence queries but using only the (R2) part of equivalence queries, we define equivalence-detecting problem". Let C be a representation class which is polynomial time learnable using membership and equivalence queries. We show that if the equivalence-detecting problem for C is polynomial time solvable then C is polynomial time learnable using membership and equivalence queries without using (R1). Moreover, we show that under certain conditions, the two notions, polynomial time solvability of equivalence-detecting problem" and polynomial time learnability using membership and equivalence queries without using (R1)", are equivalent. For concrete examples, we prove that dfas are polynomial time learnable using membership and equivalence queries without using (R1) in the learning situation where the algorithm is informed the number of states of the minimum states dfa accepting the target set in advance. On the other hand, we show that the equivalence-detecting problem for dfas are not solvable in the learning situation where the algorithm can use no additional information. This result together with our main result shows that, in this learning situation, the (R1) part of equivalence queries are necessary to learn dfas using membership and equivalence queries.

Publication: IEICE TRANSACTIONS on Information Vol.E75-D No.4 pp.435-441

Publication Date: 1992/07/25

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Type of Manuscript: Special Section PAPER (Special Issue on Algorithmic Learning Theory)

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Seiichi TANI, "On the Role of Equivalence Queries in Learning via Queries" in IEICE TRANSACTIONS on Information, vol. E75-D, no. 4, pp. 435-441, July 1992, doi: .
Abstract: We consider the role of equivalence queries in learning unknown concepts using membership and equivalence queries. Equivalence queries have the following two roles: (R1) indicating whether a learning algorithm has succeeded to learn the unknown concept and (R2) providing counterexamples. In this paper, we consider the learning using membership and equivalence queries but using only the (R2) part of equivalence queries. In order to gain an insight into the learning membership and equivalence queries but using only the (R2) part of equivalence queries, we define equivalence-detecting problem". Let C be a representation class which is polynomial time learnable using membership and equivalence queries. We show that if the equivalence-detecting problem for C is polynomial time solvable then C is polynomial time learnable using membership and equivalence queries without using (R1). Moreover, we show that under certain conditions, the two notions, polynomial time solvability of equivalence-detecting problem" and polynomial time learnability using membership and equivalence queries without using (R1)", are equivalent. For concrete examples, we prove that dfas are polynomial time learnable using membership and equivalence queries without using (R1) in the learning situation where the algorithm is informed the number of states of the minimum states dfa accepting the target set in advance. On the other hand, we show that the equivalence-detecting problem for dfas are not solvable in the learning situation where the algorithm can use no additional information. This result together with our main result shows that, in this learning situation, the (R1) part of equivalence queries are necessary to learn dfas using membership and equivalence queries.
URL: https://globals.ieice.org/en_transactions/information/10.1587/e75-d_4_435/_p

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@ARTICLE{e75-d_4_435,
author={Seiichi TANI, },
journal={IEICE TRANSACTIONS on Information},
title={On the Role of Equivalence Queries in Learning via Queries},
year={1992},
volume={E75-D},
number={4},
pages={435-441},
abstract={We consider the role of equivalence queries in learning unknown concepts using membership and equivalence queries. Equivalence queries have the following two roles: (R1) indicating whether a learning algorithm has succeeded to learn the unknown concept and (R2) providing counterexamples. In this paper, we consider the learning using membership and equivalence queries but using only the (R2) part of equivalence queries. In order to gain an insight into the learning membership and equivalence queries but using only the (R2) part of equivalence queries, we define equivalence-detecting problem". Let C be a representation class which is polynomial time learnable using membership and equivalence queries. We show that if the equivalence-detecting problem for C is polynomial time solvable then C is polynomial time learnable using membership and equivalence queries without using (R1). Moreover, we show that under certain conditions, the two notions, polynomial time solvability of equivalence-detecting problem" and polynomial time learnability using membership and equivalence queries without using (R1)", are equivalent. For concrete examples, we prove that dfas are polynomial time learnable using membership and equivalence queries without using (R1) in the learning situation where the algorithm is informed the number of states of the minimum states dfa accepting the target set in advance. On the other hand, we show that the equivalence-detecting problem for dfas are not solvable in the learning situation where the algorithm can use no additional information. This result together with our main result shows that, in this learning situation, the (R1) part of equivalence queries are necessary to learn dfas using membership and equivalence queries.},
keywords={},
doi={},
ISSN={},
month={July},}

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TY - JOUR
TI - On the Role of Equivalence Queries in Learning via Queries
T2 - IEICE TRANSACTIONS on Information
SP - 435
EP - 441
AU - Seiichi TANI
PY - 1992
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E75-D
IS - 4
JA - IEICE TRANSACTIONS on Information
Y1 - July 1992
AB - We consider the role of equivalence queries in learning unknown concepts using membership and equivalence queries. Equivalence queries have the following two roles: (R1) indicating whether a learning algorithm has succeeded to learn the unknown concept and (R2) providing counterexamples. In this paper, we consider the learning using membership and equivalence queries but using only the (R2) part of equivalence queries. In order to gain an insight into the learning membership and equivalence queries but using only the (R2) part of equivalence queries, we define equivalence-detecting problem". Let C be a representation class which is polynomial time learnable using membership and equivalence queries. We show that if the equivalence-detecting problem for C is polynomial time solvable then C is polynomial time learnable using membership and equivalence queries without using (R1). Moreover, we show that under certain conditions, the two notions, polynomial time solvability of equivalence-detecting problem" and polynomial time learnability using membership and equivalence queries without using (R1)", are equivalent. For concrete examples, we prove that dfas are polynomial time learnable using membership and equivalence queries without using (R1) in the learning situation where the algorithm is informed the number of states of the minimum states dfa accepting the target set in advance. On the other hand, we show that the equivalence-detecting problem for dfas are not solvable in the learning situation where the algorithm can use no additional information. This result together with our main result shows that, in this learning situation, the (R1) part of equivalence queries are necessary to learn dfas using membership and equivalence queries.
ER -