An exact algorithm to minimize mixed-radix exclusive sums of products for incompletely specified Boolean functions

Efficient search methods for obtaining exact minimum AND-EXOR expressions

“…It is important to reveal the exact minimum ESOPs of benchmark functions since the results are the basic data for studies of logic synthesis using EXORs. The minimum ESOP of t481 obtained by S DF is F =x 16 …”

“…However, these algorithms do not guarantee the minimality of the resulting ESOPs. On the other hand, studies of algorithms for minimizing ESOPs are fewer [16,20,24]; so far, no efficient minimization algorithms for ESOPs are known. It is considered difficult to minimize ESOPs.…”

Reversible Circuits Synthesis Based on EXOR-sum of Products of EXOR-sums

“…To achieve this goal authors of SOP tools compare their algorithm to exact minimum solutions obtained from exact minimizers such as Quine-McCluskey based ones. It is well known that the area of EXOR-based synthesis is much more difficult than the area of SOP-based synthesis and for ESOP the exact algorithms have been found [91,92] for not more than 6 inputs functions. The paper [91] created the first general method to solve this kind of problems, Concluding, my method of evaluating results includes several independent methods and is more comprehensive than those used by all other authors that publish results in the subarea of reversible and quantum logic synthesis.…”

Reversible Logic Synthesis

“…Reed-Muller-like spectral transforms [240] have found a variety of useful applications in minimizing Exclusive Sum-Of-Products (ESOP) and Galois field SOP (GFSOP) expressions [9,76,77,79,80,171,264], creation of new forms [4,78,104,173,265,266], binary decision diagrams [2,45,142], spectral decision diagrams [82,238,239], regular structures [5,7,13,18,50,51,84,177], besides their well-known uses in digital communications [125], digital signal processing [89,257,260], digital image processing [90], and fault detection (testing) [99,124,147,198,199,204,218]. Ternary Reduced Post Galois field Sum-Of-Products (RP-GFSOPs), their generalized Green/Sasao hierarchies, and the extensions of such hierarchies to the case of quaternary Galois field hierarchy were recently developed [4,9].…”