TY - GEN

T1 - Learning pattern languages using queries

AU - Matsumoto, Satoshi

AU - Shinohara, Ayumi

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1997.

PY - 1997

Y1 - 1997

N2 - A pattern is a finite string of constant and variable symbols. For k≥1, we denote by kμΠ the set of all patterns in which each variable symbol occurs at most ktimes. In particular, we abbreviate μΠ for k=1. The language L(π) of a pattern πis the set of all strings obtained by substituting any non-null constant string for each variable symbol in π. In this paper, we show that any pattern π ∈ kμΠ is exactly identifiable in O(¦ω¦k+2) time from one positive example w ∈ L(π) using ¦ω¦k+1+¦π¦k membership queries. Moreover, we introduce the notion of critical pattern, and show that the number of membership queries can be reduced to ¦ω¦+¦π¦ if the target pattern π∈μΠ is not critical. For instance, any patternπ∈μΠ whose constant parts are of length at most 3 is not critical. Finally, we show a nontrivial subclass of μΠ that is identified using membership queries only, without any initial positive example.

AB - A pattern is a finite string of constant and variable symbols. For k≥1, we denote by kμΠ the set of all patterns in which each variable symbol occurs at most ktimes. In particular, we abbreviate μΠ for k=1. The language L(π) of a pattern πis the set of all strings obtained by substituting any non-null constant string for each variable symbol in π. In this paper, we show that any pattern π ∈ kμΠ is exactly identifiable in O(¦ω¦k+2) time from one positive example w ∈ L(π) using ¦ω¦k+1+¦π¦k membership queries. Moreover, we introduce the notion of critical pattern, and show that the number of membership queries can be reduced to ¦ω¦+¦π¦ if the target pattern π∈μΠ is not critical. For instance, any patternπ∈μΠ whose constant parts are of length at most 3 is not critical. Finally, we show a nontrivial subclass of μΠ that is identified using membership queries only, without any initial positive example.

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U2 - 10.1007/3-540-62685-9_16

DO - 10.1007/3-540-62685-9_16

M3 - Conference contribution

AN - SCOPUS:84949236283

SN - 3540626859

SN - 9783540626855

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 185

EP - 197

BT - Computational Learning Theory - 3rd European Conference, EuroCOLT 1997, Proceedings

A2 - Ben-David, Shai

PB - Springer Verlag

T2 - 3rd European Conference on Computational Learning Theory, EuroCOLT 1997

Y2 - 17 March 1997 through 19 March 1997

ER -