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On Equations Over Sets of Numbers and Their Limitations

Tommi Lehtinen, Alexander Okhotin, On Equations Over Sets of Numbers and Their Limitations. International Journal of Foundations of Computer Science 22(2), 377–393, 2011.

http://dx.doi.org/10.1142/S012905411100809X

Abstract:

Systems of equations of the form X = Y + Z and X = C, in which the unknowns are sets of natural numbers, "+" denotes elementwise sum of sets S + T = {m + n | m ∈ S, n ∈ T}, and C is an ultimately periodic constant, have recently been proved to be computationally universal (Jeż, Okhotin, "Equations over sets of natural numbers with addition only", STACS 2009). This paper establishes some limitations of such systems. A class of sets of numbers that cannot be represented by unique, least or greatest solutions of systems of this form is defined, and a particular set in this class is constructed. The argument is then extended to equations over sets of integers.

BibTeX entry:

@ARTICLE{jLeOk11a,
  title = {On Equations Over Sets of Numbers and Their Limitations},
  author = {Lehtinen, Tommi and Okhotin, Alexander},
  journal = {International Journal of Foundations of Computer Science},
  volume = {22},
  number = {2},
  editor = {Ibarra, Oscar H.},
  pages = {377–393},
  year = {2011},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

Publication Forum rating of this publication: level 2

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