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- W2086162968 abstract "Systems of finitely many equations of the form φ(X1,…,Xn)=ψ(X1,…,Xn) are considered, in which the unknowns Xi are sets of natural numbers, while the expressions φ,ψ may contain singleton constants and the operations of union and pairwise addition S+T={m+n|m∈S,n∈T}. It is shown that the family of sets representable by unique (least, greatest) solutions of such systems is exactly the family of recursive (r.e., co-r.e., respectively) sets of numbers. Basic decision problems for these systems are located in the arithmetical hierarchy. The same results are established for equations with addition and intersection." @default.
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- W2086162968 date "2014-10-01" @default.
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- W2086162968 title "Computational completeness of equations over sets of natural numbers" @default.
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- W2086162968 doi "https://doi.org/10.1016/j.ic.2014.05.001" @default.
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