On the learnability of shuffle ideals

Dana Angluin, James Aspnes, Aryeh Kontorovich

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations


Although PAC learning unrestricted regular languages is long known to be a very difficult problem, one might suppose the existence (and even an abundance) of natural efficiently learnable sub-families. When our literature search for a natural efficiently learnable regular family came up empty, we proposed the shuffle ideals as a prime candidate. A shuffle ideal generated by a string u is simply the collection of all strings containing u as a (discontiguous) subsequence. This fundamental language family is of theoretical interest in its own right and also provides the building blocks for other important language families. Somewhat surprisingly, we discovered that even a class as simple as the shuffle ideals is not properly PAC learnable, unless RP=NP. In the positive direction, we give an efficient algorithm for properly learning shuffle ideals in the statistical query (and therefore also PAC) model under the uniform distribution.

Original languageEnglish
Title of host publicationAlgorithmic Learning Theory - 23rd International Conference, ALT 2012, Proceedings
Number of pages13
StatePublished - 30 Oct 2012
Event23rd International Conference on Algorithmic Learning Theory, ALT 2012 - Lyon, France
Duration: 29 Oct 201231 Oct 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7568 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference23rd International Conference on Algorithmic Learning Theory, ALT 2012

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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