doi
10.1007/s00224-009-9246-y
form xi
paper
system
set
arithmetization
319-342
natural numbers
Complexity of Equations over Sets of Natural Numbers
addition
article
equations
operation
problem
articles
least solution
operations of union
membership problem
number
conjunctive grammars
consequences
intersection
Systems 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
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\begin{document}$S+T=\{m+n\mid m\in S$\end{document}
, 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 membership problem for these equations is proved to be EXPTIME-complete. Among the consequences of the result is EXPTIME-completeness of the compressed membership problem for conjunctive grammars.
system of equations
https://scigraph.springernature.com/explorer/license/
general membership problem
https://doi.org/10.1007/s00224-009-9246-y
unknowns
results
2022-08-04T16:58
true
time
EXPTIME
XI
grammar
expression
solution
same time
2009-12-23
such systems
complexity of equations
Union
complexity
2009-12-23
Pure Mathematics
Okhotin
Alexander
Springer Nature
Theory of Computing Systems
1432-4350
1433-0490
Institute of Computer Science, University of Wrocław, Wrocław, Poland
Institute of Computer Science, University of Wrocław, Wrocław, Poland
2
pub.1003872386
dimensions_id
Academy of Finland, Helsinki, Finland
Academy of Finland, Helsinki, Finland
Department of Mathematics, University of Turku, Turku, Finland
Mathematical Sciences
Jeż
Artur
Springer Nature - SN SciGraph project
48