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On the completeness of the polymorphic gate set

Polymorphic gates are special kinds of logic gates that can exhibit different functions under the control of environmental parameters, such as light, temperature, and VDD. These polymorphic gates can be used to build polymorphic circuits that perform different functions under different environments. Because polymorphic gates are different from traditional logic gates, the existent completeness theory for the traditional logic gate set is not suitable for the polymorphic gate set. So far, only the definition of the complete polymorphic gate set is given. There is no approach to judging whether a given polymorphic gate set is complete. The contributions of this article include three aspects. First, the impact of logic-1 and logic-0 on the completeness of the polymorphic gate set is discussed. Second, the theory and two related algorithms for judging the completeness of polymorphic gate sets with two modes are given. Finally, the theory and related algorithms for complete polymorphic gate sets with more than two modes are proposed.