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International Conference on Theory and Applications of Models of Computation

TAMC 2013: Theory and Applications of Models of Computation pp 156–168Cite as

On the Boundedness Property of Semilinear Sets

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7876))

Abstract

An additive system to generate a semilinear set is k-bounded if it can generate any element of the set by repeatedly adding vectors according to its rules so that pairwise differences between components in any intermediate vector are bounded by k except for those that have achieved their final target value. We look at two (equivalent) representations of semilinear sets as additive systems: one without states (the usual representation) and the other with states, and investigate their properties concerning boundedness: decidability questions, hierarchies (in terms of k), characterizations, etc.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara, CA, 93106, USA

    Oscar H. Ibarra

  2. Helsinki Institute of Information Technology (HIIT), Aalto University, P.O.Box 15400, FI-00076, Aalto, Finland

    Shinnosuke Seki

  3. Department of Information and Computer Science, Aalto University, P.O.Box 15400, FI-00076, Aalto, Finland

    Shinnosuke Seki

Authors
  1. Oscar H. Ibarra
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  2. Shinnosuke Seki
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Editor information

Editors and Affiliations

  1. The University of Hong Kong, Hong Kong

    T-H. Hubert Chan

  2. The Chinese University of Hong Kong, Hong Kong

    Lap Chi Lau

  3. Department of Computer Science, Stanford University, 94305, Stanford, CA, USA

    Luca Trevisan

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Ibarra, O.H., Seki, S. (2013). On the Boundedness Property of Semilinear Sets. In: Chan, TH.H., Lau, L.C., Trevisan, L. (eds) Theory and Applications of Models of Computation. TAMC 2013. Lecture Notes in Computer Science, vol 7876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38236-9_15

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  • DOI: https://doi.org/10.1007/978-3-642-38236-9_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38235-2

  • Online ISBN: 978-3-642-38236-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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