Hierarchical Decomposition of Large-Variable Boolean Functions Using Recursive Fundamental-Block Minimization

We present a hierarchical decomposition architecture for Booleanfunction minimization that extends single-output structural-atomrecognition from a base engine of K input variables (typicallyK=4) to arbitrarily large N (16, 32, 64, 128+). The architecturepartitions an N-variable specification into 2^ (N-K) cofactorsub-specifications indexed by the upper N-K variables; identifiesequivalence classes of cofactors that share the same minterm set;invokes the K-variable base engine once per unique cofactor;constructs a selector function over the upper variables for eachcofactor group; recursively minimizes each selector function bythe same architecture; and composes the result as a sum ofproducts selector * cofactor. Verification of the composedexpression against the original specification ensurescorrectness. The architecture is intrinsically parallelizable: the 2^ (N-K) cofactor minimizations are independent. Tested atN=8 and N=16 with single-recursion-level decomposition and a4-variable base engine. The architecture extends to N=32, 64, and 128 by additional recursion levels with computational costthat grows polynomially in the number of unique cofactor groupsrather than exponentially in N. Companion to the foundationalM-Maps paper (DOI 10. 5281/zenodo. 20498821) and the structural-atom engine paper (DOI 10. 5281/zenodo. 20499264).