On the learnability of shuffle ideals

Dana Angluin, James Aspnes, Sarah Eisenstat, Aryeh Kontorovich

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


PAC learning of unrestricted regular languages is long known to be a difficult problem. The class of shuffle ideals is a very restricted subclass of regular languages, where the shuffle ideal generated by a string u is the collection of all strings containing u as a subsequence. This fundamental language family is of theoretical interest in its own right and provides the building blocks for other important language families. Despite its apparent simplicity, the class of shuffle ideals appears quite difficult to learn. In particular, just as for unrestricted regular languages, the class is not properly PAC learnable in polynomial time if RP ≠ NP, and PAC learning the class improperly in polynomial time would imply polynomial time algorithms for certain fundamental problems in cryptography. 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
Pages (from-to)1513-1531
Number of pages19
JournalJournal of Machine Learning Research
StatePublished - 1 Jun 2013


  • Deterministic finite automata
  • PAC learning
  • Regular languages
  • Shuffle ideals
  • Statistical queries
  • Subsequences

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence


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