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

The Computational Complexity of Finding Arithmetic Expressions With and Without Parentheses