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- W2022226854 abstract "Equations of the form X=φ(X) are considered, where the unknown X is a set of natural numbers. The expression φ(X) may contain the operations of set addition, defined as S+T={m+n|m∈S,n∈T}, union, intersection, as well as ultimately periodic constants. An equation with a non-periodic solution of exponential growth rate is constructed. At the same time it is demonstrated that no sets with super-exponential growth rate can be represented. It is also shown that restricted classes of these equations cannot represent sets with super-linearly growing complements nor sets that are additive bases of order 2. The results have direct implications on the power of unary conjunctive grammars with one nonterminal symbol." @default.
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- W2022226854 date "2012-03-01" @default.
- W2022226854 modified "2023-09-27" @default.
- W2022226854 title "On the expressive power of univariate equations over sets of natural numbers" @default.
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- W2022226854 doi "https://doi.org/10.1016/j.ic.2012.01.004" @default.
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