Signal conservation logic (SCL) is a model of logic for the physical world subject to the matter conservation law. This letter proves that replication, complementary replication, and computational universality called elemental universality are equivalent in SCL. Since intelligence has a close relation to computational universality, the presented theorem may mean that life under the matter conservation law eventually acquires some kind of intelligence.

This paper is concerned with a concept called universality or completeness of sets of logic devices. Universality characterizes sets of logic devices which can be used for the construction of arbitrary logic circuits. The elemental universality proposed here is the most general condition of universality which covers logic devices with/without delay time and combinational/sequential circuits. The necessary and sufficient condition of elemental universality shows that nonlinearity and nonmonotonicity are essential conditions for the realization of various digital mechanisms.