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.
Supported by the Academy of Finland under grant 118540.
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Lehtinen, T., Okhotin, A. (2009). On Equations over Sets of Numbers and Their Limitations. In: Diekert, V., Nowotka, D. (eds) Developments in Language Theory. DLT 2009. Lecture Notes in Computer Science, vol 5583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02737-6_29
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DOI: https://doi.org/10.1007/978-3-642-02737-6_29
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