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Learning Finite Variants of Single Languages from Informant

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Algorithmic Learning Theory (ALT 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9925))

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Abstract

We show that the family \(\mathrm {S}^+_L=\{L \cup \{x\}: x \in \omega \} \cup \{L\}\) consisting of the languages obtained from a given language (i.e., computably enumerable set) L by adding at most one additional element can be explanatorily learned from informant (i.e., is \(\mathrm {InfEx}\)-learnable) if and only if L is autoreducible. Similarly, the subfamily \(\hat{\mathrm {S}}^+_L=\{L \cup \{x\}: x \not \in L\}\) of \(\mathrm {S}^+_L\) consisting of the languages obtained from L by adding exactly one additional element can be learned from informant without mind changes (i.e., is \(\mathrm {InfFin}\)-learnable) if and only if L is autoreducible.

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Acknowledgements

We would like to thank Wolfgang Merkle for some very helpful discussions and one of the anonymous referees for his very useful comments and suggestions.

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Authors and Affiliations

  1. Institut für Informatik, Heidelberg University, 69120, Heidelberg, Germany

    Klaus Ambos-Spies

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  1. Klaus Ambos-Spies
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Correspondence to Klaus Ambos-Spies .

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Editors and Affiliations

  1. Montanuniversität Leoben , Leoben, Austria

    Ronald Ortner

  2. Ruhr-Uni-Bochum , Bochum, Germany

    Hans Ulrich Simon

  3. University of Regina , Regina, Saskatchewan, Canada

    Sandra Zilles

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Ambos-Spies, K. (2016). Learning Finite Variants of Single Languages from Informant. In: Ortner, R., Simon, H., Zilles, S. (eds) Algorithmic Learning Theory. ALT 2016. Lecture Notes in Computer Science(), vol 9925. Springer, Cham. https://doi.org/10.1007/978-3-319-46379-7_11

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  • DOI: https://doi.org/10.1007/978-3-319-46379-7_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46378-0

  • Online ISBN: 978-3-319-46379-7

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