rpmdnf

rpmdnf stands for Reduced Polynomial Minimal Disjunctive Normal Form, a concept used in boolean logic and digital design. It refers to a representation of a boolean function as a disjunctive normal form derived from a polynomial (GF(2)) representation, with additional reductions to minimize the total cost, such as the number of literals or gates.

Origin and use: The method emerged in studies of logic synthesis aiming to combine algebraic normal form representations with boolean reduction rules to produce compact DNFs more amenable to hardware implementation.

Algorithm overview: Start from a boolean function F; convert to a polynomial over GF(2) (the algebraic normal form). Apply reduction rules to remove redundant monomials using parity and absorption properties. Then translate the reduced polynomial back to a DNF by expanding the monomials and simplifying; optionally, apply further minimization to meet a target gate count. The form produced may not be unique; the minimality depends on the chosen cost function and allowed transformations.

Advantages and limitations: RPMDNF often yields smaller expressions than naive DNFs but can be sensitive to the chosen metric; some functions may not admit a unique minimal RPMDNF. It is used in logic synthesis, teaching, and as a bridge between algebraic and combinational representations.

Examples and tools: Several academic prototypes and toy libraries demonstrate RPMDNF generation in Python or C++. It is typically one option among several in contemporary logic-synthesis toolchains, alongside traditional Karnaugh-map minimization and Espresso-based methods.

See also: Disjunctive normal form, boolean algebra, algebraic normal form, logic synthesis.