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March 15, 2026Open Access

P=NP via Deterministic Oracle Machine Resolving NP via the Implicit Binary Decision Tree

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Authors

KKKaoru Aguilera Katayama

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Overview

Demonstrates that a deterministic Turing machine resolves NP-complete problems in linear time, implying P=NP.

Key Points

  • To demonstrate that a deterministic Turing machine can resolve NP-complete problems in linear time using an oracle.
  • Constructed a deterministic Turing machine with an oracle for 3-SAT and NP-complete problems.
  • Analyzed the Boolean assignment space as a complete binary tree.
  • Formalized the oracle function and proved its O(n) complexity.
  • The oracle traverses the binary tree in O(n) time steps.
  • Each variable corresponds to a level in the binary tree, encoding complete assignments.
  • Implication established that P=NP.

Cite This Study

Kaoru Aguilera Katayama (2026) studied this question.

synapsesocial.com/papers/69b5ff8d83145bc643d1c652https://doi.org/10.5281/zenodo.18992841
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