In this paper two algorithms for the synthesis and minimization of a CA (cellular array architecture) are proposed. Starting from a completely specified single-output switching function, our methods produce rectangularly shaped arrays of cells, interconnected in chains, with an effort to minimize the number of the produced chains (cascades). This kind of cellular topology is known throughout the bibliography as Maitra cellular arrays. The significance of those algorithms is underlined by the fact that this particular type of cellular architecture can be mapped to reversible circuits and gates (generalized Toffoli gates), which are the type of logic used in quantum circuits. The proposed methodologies include use of ETDDs (EXOR ternary decision diagrams), and switching function decompositions (including new types of boolean expansions).

In this paper, an efficient approach to the synthesis of CA (Cellular Architecture) -type FPGAs is presented. To exploit the array structure of cells in CA-type FPGAs, logic expressions called Maitra terms which can be mapped directly to the cell arrays are generated by using ETDDs (EXOR Ternary Decision Diagrams). Since a traversal of the ETDD is sufficient to generate a Maitra term which takes O (n) steps where n is the number of nodes in the ETDD, Maitra terms are generated very efficiently. The experiments show that the proposed method generates better results than existing methods.