# Complexity of Equations over Sets of Natural Numbers

@article{Jez2009ComplexityOE,
title={Complexity of Equations over Sets of Natural Numbers},
author={Artur Jez and Alexander Okhotin},
journal={Theory of Computing Systems},
year={2009},
volume={48},
pages={319-342}
}
Systems of equations of the form X i =φ i (X 1,…,X n ) (1≤ i ≤ n) are considered, in which the unknowns are sets of natural numbers. Expressions φ i may contain the operations of union, intersection and elementwise addition $S+T=\{m+n\mid m\in S$ , n∈T}. A system with an EXPTIME-complete least solution is constructed in the paper through a complete arithmetization of EXPTIME-completeness. At the same time, it is established that least solutions of all such systems are in EXPTIME. The general… CONTINUE READING

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