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. © 2012 Springer-Verlag.
CITATION STYLE
Angluin, D., Aspnes, J., & Kontorovich, A. (2012). On the learnability of shuffle ideals. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7568 LNAI, pp. 111–123). https://doi.org/10.1007/978-3-642-34106-9_12
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