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Succinct Representations of Functions

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Book cover Automata, Languages and Programming (ICALP 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3142))

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Abstract

We investigate the problem of succinctly representing an arbitrary function, f: [n] →[n] so that f k(i) can be computed quickly for any i and any (positive or negative) integer power k. We give a representation that takes \((1+\epsilon) n \lg n + O(1)\) bits and computes arbitrary positive powers in constant time. It can also be used to compute f k(i), for any negative integer k, in O(1+|f k(i)|) time.

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Author information

Authors and Affiliations

  1. School of Computer Science, Univ. of Waterloo, Waterloo, ON, Canada, N2L 3G1

    J. Ian Munro & S. Srinivasa Rao

Authors
  1. J. Ian Munro
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  2. S. Srinivasa Rao
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Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Campus Nord - Ed. Omega, 240 Jordi Girona Salgado, 1-3 E-08034, Barcelona

    Josep Díaz

  2. Department of Mathematics and Turku Centre for Computer Science TUCS, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  3. Department of Mathematics, University of Turku, Turku, Finland

    Arto Lepistö

  4. Laboratory for Foundations of Computer Science, University of Edinburgh,  

    Donald Sannella

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© 2004 Springer-Verlag Berlin Heidelberg

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Munro, J.I., Rao, S.S. (2004). Succinct Representations of Functions. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds) Automata, Languages and Programming. ICALP 2004. Lecture Notes in Computer Science, vol 3142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27836-8_84

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  • DOI: https://doi.org/10.1007/978-3-540-27836-8_84

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22849-3

  • Online ISBN: 978-3-540-27836-8

  • eBook Packages: Springer Book Archive

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