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**:** 52
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**:** 2014
**:** . . / . 52. .: , 2014. .23-36.

** :** , , ,

** (.):** artificial intelligence, columns-based intelligent systems, column, multiset.

**:** , , .. . . .

** (.):** We consider columns-based intelligent systems with patterns containing duplicates, i.e., representing the finite multisets. The representation of such patterns is suggested and solutions to the direct and the inverse problems are discussed. We use the intersections technique to solve both problems.

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