Decomposition-Based Representation of Symmetric Multiple-Valued Functions

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Symmetric multiple-valued functions are a basic class of multiple-valued functions such that function values are unchanged by any permutation of input variable labels. They appear in various situations such as arithmetic operations. A compact representation of symmetric multiple-valued functions benefits many applications. To represent symmetric multiple-valued functions compactly, this paper focuses on functional decomposition and decision diagrams. We propose a method that decomposes a symmetric multiple-valued function into three parts, and represents the three parts using suitable decision diagrams. This paper also derives theorems on sizes of the decision diagrams. Experimental results using randomly generated symmetric multiple-valued functions show the effectiveness of the proposed method.