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 work, a novel Multiple Valued Exclusive-Or Sum Of Products (MVESOP) minimization formulation is analyzed and an algorithm is presented that detects minimum MVESOP expressions when the weight of the function is less than eight. A heuristic MVESOP algorithm based on a novel cube transformation operation is then presented. Experimental results on MCNC benchmarks and randomly generated functions indicate that the algorithm matches or outperforms the quality of the state of the art in ESOP minimizers.