Structural Pattern Recognition for Factored XOR-AND-OR Minimization of Multivariable Boolean Functions

We present a structural-atom-recognition algorithm for Booleanfunction minimization that produces factored exclusive-OR / AND /OR algebraic output directly, without an intermediate sum-of-products representation. The algorithm recognizes a library often compound structural atoms - including AND-pair-XOR-literal,paired complemented AND-pairs, complemented AND-pair timesOR-pair, nested AND-pair-XOR-literal, and all-AND-with-nested-NOTforms - matched against the input minterm specification. Everycandidate expression is truth-table-verified against the originalspecification before emission, guaranteeing zero incorrectoutput. On a hand-verified test corpus of 254 N=3 Booleanfunctions, the implementation matches or improves upon handexpressions in 100% of cases (189 ties, 65 strict wins, 0 losses,0 errors). The technique is particularly suited to Booleanfunctions with internal exclusive-OR structure, includingcryptographic operations, error-correction codes, parityfunctions, and Galois field arithmetic. This work is companionto the foundational M-Maps paper (DOI 10.5281/zenodo.20498821).