The Computational Complexity of Finding Arithmetic Expressions With and Without Parentheses

10/26/2021

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by   Jayson Lynch, et al.

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We show NP-completeness for various problems about the existence of arithmetic expression trees. When given a set of operations, inputs, and a target value does there exist an expression tree with those inputs and operations that evaluates to the target? We consider the variations where the structure of the tree is also given and the variation where no parentheses are allowed in the expression.