Review Paper
Year: 2021 | Month: May | Volume: 8 | Issue: 5 | Pages: 379-388
DOI: https://doi.org/10.52403/ijrr.20210547
The Equation of the Set of Natural Numbers Just to Sum
Tulus Nadapdap1, Tulus2, Opim Salim3
1Posgraduate Students Faculty of Mathematics and Natural Sciences Universitas Sumatera Utara, Indonesia
2,3Postgraduate Lecturer Faculty of Mathematics and Natural Sciences Universitas Sumatera Utara, Indonesia
Corresponding Author: Tulus Nadapdap
ABSTRACT
Systems of equations of the form X = Y + Z and X = C, in which the unknowns are sets of integers,”+” denotes pairwise sum of sets S + T = m + n m S, n T , and C is an ultimately periodic constant. When restricted to sets of natural numbers, such equations can be equally seen as language equations over a one-letter alphabet with concatenation and regular constants, and it is shown that such systems are computationally universal, in the sense that for every recursive set S N there exists a system with a unique solution containing T with S = n 16n + 13 T. For systems over sets of all integers, both positive and negative, there is a similar construction of a system with a unique solution S = {n|16n ∈ T} representing any hyper-arithmetical set S ⊆ N.
Keywords: Language equations, Natural numbers, Equations of natural number.
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