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Composition of polynomial many-one reductions

Abstract

Composition of polynomial many-one reductions.

Reduction transitivity composes total deterministic polynomial transducers and the two all-word membership equivalences. NP-hardness and completeness transfer consume that composition theorem; they supply no new SAT premise.

Theorem 1.1 (PolyRed.trans).

Lean statement: D5/S0/Computability/BinaryMachine/Reductions.trans

Proof. Machine-checked in Lean as D5/S0/Computability/BinaryMachine/Reductions.trans (✓ std3). ∎

Citation. RBarish-UTokyo (2026). NPCompleteness-Lean4 finite binary machine and composition source. URL: https://github.com/RBarish-UTokyo/NPCompleteness-Lean4/tree/3e603e795b44fedcf7d6dd65b7d1e30547ead925.

Commentary.

This declaration and its proof are attributed immutable source supply. The mathematical namespace and proof body are preserved. Full license, source correspondence and the finite retirement contract are recorded in docs/reports/licenses/RBarishBinaryMachine.md. This port supplies no new classification or independent mathematical escape content.

References