Delay models for binary logic circuits have been proposed and clarified their mathematical properties. Kleene's ternary logic is one of the simplest delay models to express transient behavior of binary logic circuits. Goto first applied Kleene's ternary logic to hazard detection of binary logic circuits in 1948. Besides Kleene's ternary logic, there are many delay models of binary logic circuits, Lewis's 5-valued logic etc. On the other hand, multiple-valued logic circuits recently play an important role for realizing digital circuits. This is because, for example, they can reduce the size of a chip dramatically. Though multiple-valued logic circuits become more important, there are few discussions on delay models of multiple-valued logic circuits. Then, in this paper, we introduce a delay model of multiple-valued logic circuits, which are constructed by Min, Max, and Literal operations. We then show some of the mathematical properties of our delay model.

This review presents research topics and results on digital signal processing in the last twenty years in Japan. The main parts of the review consist of design and analysis of multidimensional digital filters, multiple-valued logic circuits and number systems for signal processing, and general purpose signal processors.