Ternary Galois field expansions for reversible logic and Kronecker decision diagrams for ternary GFSOP minimization [Galois field sum of products]

Ternary Galois field sum of products (TGFSOP) expressions are found to be good choice for ternary reversible, and especially quantum, logic design. In this paper, we propose 16 ternary Galois field expansions (TGFE) and introduce three ternary Galois field decision diagrams (TGFDD) using the proposed TGFEs, which are useful for reversible and quantum logic design. We also propose a heuristic for creating TGFDDs and a method for flattening the TGFDDs for determining TGFSOP expressions. We provide experimental results to show the effectiveness of the developed methods.