Equations X + A = B and (X + X) + C = (X − X) + D over Sets of Natural Numbers

  • Tommi Lehtinen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7464)


It has recently been shown, that hyper-arithmetical sets can be represented as the unique solutions of language equations over sets of natural numbers with operations of addition, subtraction and union. It is shown that the same expressive power, under a certain encoding, can be achieved by systems of just two equations, X + A = B and (X + X) + C = (X − X) + D, without using union. It follows that the problems concerning the solutions of systems of the general form are as hard as the same problems restricted to these systems with two equations, it is known that the question for solution existence is \(\Sigma^1_1\) complete.


Natural Number Formal Language Expressive Power Unary Word Periodic Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Tommi Lehtinen
    • 1
    • 2
  1. 1.Turku Centre for Computer ScienceFinland
  2. 2.Department of MathematicsUniversity of TurkuFinland

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