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• W1483620334 abstract "It is shown that equations of the form p(X) = ψ(X), in which the unknown X is a set of natural numbers and p, ψ use the operations of union, intersection and addition of sets S + T = {m + n |, m ∈ S, n ∈ T}, can simulate systems of equations pj(X1, …, Xn) = pj(X1, …, Xn) with 1 ≤ j ≤ e, in the sense that solutions of any such system are encoded in the solutions of the corresponding equation. This implies computational universality of least and greatest solutions of equations p(X) = ψ(X), as well as undecidability of their basic decision problems. It is sufficient to use only singleton constants in the construction. All results equally apply to language equations over a one-letter alphabet Σ = {a}." @default.
• W1483620334 created "2016-06-24" @default.
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• W1483620334 date "2010-01-01" @default.
• W1483620334 modified "2023-10-11" @default.
• W1483620334 title "Univariate Equations Over Sets of Natural Numbers" @default.
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• W1483620334 doi "https://doi.org/10.3233/fi-2010-352" @default.
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