Degree reduction and recursive parity queries for explicit Boolean polynomials
Year: 2026
Type: preprint
Abstract: Research preprint containing the PDF, LaTeX source and document checks. Attributed algorithmic corollaries of Zhang and Moshkovitz-Zhu construct one degree-reducing parity batch in polynomial time and a complete on-demand recursive parity policy from an explicit Boolean ANF. For each fixed hidden input, correctness and min(n,O(1+4^d log(s) log(nd))) parity queries hold jointly with probability at least 1-delta. Recursion uses 2^O(d log(d+1))*poly(n,S,log(1/delta)) bit time with an explicit precision interface and polynomial working space; n queries is an unconditional cap. Boolean finite differences followed by scalar extension avoid expanded residual ANFs. This does not improve the stronger existential depth bound or construct an all-input correct sampled tree. No established priority, implementation, independent peer review or formal certification is claimed. OpenAI Codex assisted derivation, source comparison, drafting and package preparation.
Author: Fredriksen, Daniel
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225646098
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