This paper deals with two well discussed, but largely open problems on E-pattern languages, also known as extended or erasing pattern languages: primarily, the learnability in Gold's learning model and, secondarily, the decidability of the equivalence. As the main result, we show that the full class of E-pattern languages is not inferrable from positive data if the corresponding terminal alphabet consists of exactly three or of exactly four letters - an insight that remarkably contrasts with the recent positive finding on the learnability of the subclass of terminal-free E-pattern languages for these alphabets, As a side-effect of our reasoning thereon, we reveal some particular example patterns that disprove a conjecture of Ohlebusch and Ukkonen (Theoretical Computer Science 186, 1997) on the decidability of the equivalence of E-pattern languages.
CITATION STYLE
Reidenbach, D. (2004). On the learnability of E-pattern languages over small alphabets. In Lecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science) (Vol. 3120, pp. 140–154). Springer Verlag. https://doi.org/10.1007/978-3-540-27819-1_10
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