63-74
ϕj
such systems
set
system of equations
basic decision problems
2008-01-01
2022-08-04T17:14
false
decision problem
recursive sets
family
operations of union
constants
https://scigraph.springernature.com/explorer/license/
unique solution
chapters
On the Computational Completeness of Equations over Sets of Natural Numbers
Systems of equations of the form ϕj(X1, ..., Xn) = ψj(X1, ..., Xn) with \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$1 \leqslant j \leqslant m$\end{document} are considered, in which the unknowns Xi are sets of natural numbers, while the expressions ϕj,ψj may contain singleton constants and the operations of union (possibly replaced by intersection) and pairwise addition . 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.
addition
pairwise addition
chapter
computational completeness
operation
system
arithmetical hierarchy
problem
2008-01-01
unknowns Xi
solution
https://doi.org/10.1007/978-3-540-70583-3_6
completeness
form
natural numbers
Union
XI
number
equations
hierarchy
family of sets
Halldórsson
Magnús M.
Igor
Walukiewicz
Goldberg
Leslie Ann
Department of Mathematics, University of Turku, Finland
Department of Mathematics, University of Turku, Finland
Academy of Finland
978-3-540-70582-6
978-3-540-70583-3
Automata, Languages and Programming
Mathematical Sciences
Springer Nature - SN SciGraph project
pub.1009467480
dimensions_id
Applied Mathematics
Okhotin
Alexander
Institute of Computer Science, University of Wrocław, Poland
Institute of Computer Science, University of Wrocław, Poland
Ingólfsdóttir
Anna
10.1007/978-3-540-70583-3_6
doi
Jeż
Artur
Aceto
Luca
Ivan
Damgård
Springer Nature