The Computational Complexity of Finding Arithmetic Expressions With and Without Parentheses
Jayson Lynch, Yan (Roger) Weng
TL;DR
This paper investigates the computational difficulty of constructing arithmetic expressions with specific inputs and operations, demonstrating NP-completeness in various scenarios including with and without parentheses.
Contribution
It establishes the NP-completeness of several problems related to arithmetic expression tree existence, considering different structural constraints.
Findings
NP-completeness for expression tree existence problems
Difficulty persists with fixed tree structures
Parentheses restrictions impact computational complexity
Abstract
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.
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Taxonomy
TopicsAlgorithms and Data Compression · Natural Language Processing Techniques · Machine Learning and Algorithms