Persamaan Himpunan Bilangan Asli Hanya Terhadap Penjumlahan
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Institusion
Universitas Sumatera Utara
Author
Nadapdap, Tulus (STUDENT ID : 137021001)
(LECTURER ID : 0001096202)
(LECTURER ID : 0017086108)
(LECTURER ID : 0001096202)
(LECTURER ID : 0017086108)
Subject
Language equations
Datestamp
2022-11-30 04:13:04
Abstract :
Systems of equations of the form X = Y + Z dan XC, in which the unknowns are sets of integers, "+" denotes pairwise sum of sets S+T= {m + n|m ? S, ne 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 SCN 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 SC N.
Systems of equations of the form X = Y + Z dan XC, in which the unknowns are sets of integers, "+" denotes pairwise sum of sets S+T= {m + n|m ? S, ne 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 SCN 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 SC N.
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