Polynomial Solvability of the Subset Sum Problem

Б. Синчев; Aksulu Mukhanova; Anel Auezova; Tolkynai Sadykova

doi:10.1109/sist54437.2022.9945761

April 28, 2022

Polynomial Solvability of the Subset Sum Problem

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Key Points

To establish the polynomial-time solvability of the NP-complete subset sum problem by connecting subset cardinalities to number theory principles.
Formulated the subset sum problem algebraically using polynomial representations and Waring's hypothesis for polynomials.
Applied the Classical Waring Problem from number theory to determine conditions under which a target sum certificate can be represented by a subset.
Derived Lemma 1 to define the cardinality relationships and variation ranges between full integer sets and target subsets.
Established Lemma 2 demonstrating representation of a target certificate as a subset sum via Waring's problem.
Concluded that polynomial solvability of the subset sum problem extends to all NP-complete problems, implying that P equals NP.

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Implication

Theoretical analysis demonstrates polynomial-time solvability of the subset sum problem using Waring's problem formulations, suggesting equivalence of complexity classes P and NP.

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Синчев et al. (2022) studied this question.

synapsesocial.com/papers/6a153a5979ff98d0de4e48a4 https://doi.org/10.1109/sist54437.2022.9945761

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Polynomial Solvability of the Subset Sum Problem

Key Points

No abstract yet

Implication

Discussion

Cite This Study

Polynomial Solvability of the Subset Sum Problem

Key Points

No abstract yet

Implication

Discussion

Cite This Study

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