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On self-reducible sets of low information content

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Algorithms and Complexity (CIAC 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 778))

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Abstract

Self-reducible sets have a rich internal structure. The information contained in these sets is encoded in some redundant way. Therefore a lot of the information of the set is easily accessible. In this paper it is investigated how this self-reducibility structure of a set can be used to access easily all information contained in the set, if its information content is small. It is shown that P can be characterized as class of selfreducible sets which are “almost” in P (i.e. sets in APT′). Self-reducible sets with low instance complexity (i.e. sets in IC[log,poly]) are shown to be in NP ∩ co-NP, and sets which disjunctively reduce to sparse sets or which belong to a certain superclass of the Boolean closure of sets which conjunctively reduce to sparse sets are shown to be in PNP, if they are self-reducible in a little more restricted sense of self-reducibility.

Work done at Universität Ulm, Abt. Theoretische Informatik. Supported in part by the DAAD through Acciones Integradas 1992, 313-AI-e-es/zk.

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Authors and Affiliations

  1. Fachbereich IV - Informatik, Universität Trier, D-54286, Trier, Germany

    Martin Mundhenk

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  1. Martin Mundhenk
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M. Bonuccelli P. Crescenzi R. Petreschi

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© 1994 Springer-Verlag Berlin Heidelberg

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Mundhenk, M. (1994). On self-reducible sets of low information content. In: Bonuccelli, M., Crescenzi, P., Petreschi, R. (eds) Algorithms and Complexity. CIAC 1994. Lecture Notes in Computer Science, vol 778. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57811-0_17

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  • DOI: https://doi.org/10.1007/3-540-57811-0_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57811-6

  • Online ISBN: 978-3-540-48337-3

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