Complexity of Equations over Sets of Natural Numbers

@article{Je2011ComplexityOE,
  title={Complexity of Equations over Sets of Natural Numbers},
  author={Artur Jeż and Alexander Okhotin},
  journal={Theory of Computing Systems},
  year={2011},
  volume={48},
  pages={319-342}
}
AbstractSystems of equations of the form Xi=φi(X1,…,Xn) (1≤i≤n) are considered, in which the unknowns are sets of natural numbers. Expressions φi 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… 

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