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On Equations X+X+C=X+X+D and X+E=F with Unknown X Subseteq N

Tommi Lehtinen, Alexander Okhotin, On Equations X+X+C=X+X+D and X+E=F with Unknown X Subseteq N. TUCS Technical Reports 952, Turku Centre for Computer Science, 2009.

Abstract:

It is shown that the recently discovered computational universality in systems of equations over sets of numbers occurs already in systems of the simplest form, with one unknown X and two equations X+X+C=X+X+D and X+E=F, where C, D, E, F \subseteq \mathbb{N} are four ultimately periodic constants and + denotes the operation of elementwise addition of sets, S+T = {m+n | m \in S, n \in T}.

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BibTeX entry:

@TECHREPORT{tLeOk09a,
  title = {On Equations X+X+C=X+X+D and X+E=F with Unknown X Subseteq N},
  author = {Lehtinen, Tommi and Okhotin, Alexander},
  number = {952},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2009},
  keywords = {Language equations, equations over sets of numbers, computational univesality},
  ISBN = {978-952-12-2329-7},
}

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

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