On the Boundedness Property of Semilinear Sets

  • Oscar H. Ibarra
  • Shinnosuke Seki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7876)


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.


semilinear set generator without states generator with states bounded multitape NFA decidable undecidable 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Oscar H. Ibarra
    • 1
  • Shinnosuke Seki
    • 2
    • 3
  1. 1.Department of Computer ScienceUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Helsinki Institute of Information Technology (HIIT)Aalto UniversityAaltoFinland
  3. 3.Department of Information and Computer ScienceAalto UniversityAaltoFinland

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