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Three elementary logics for compound control

This paper is concerned with the regulatory mechanisms used for compound control, the characteristic mode of control in biological systems, to administer appropriate regulations in response to the simultaneous occurrence of a huge number of environmental changes. The restricted resources of cells strictly limit the number of their regulatory methods, so cells must adopt, as compensation, special mechanisms to deal with the simultaneous occurrence of environmental changes. We hypothesize that cells use various control logics to integrate information about independent but functionally related environmental changes. Using the notion of equivalent classes in set theory, we demonstrate that the regulatory mechanisms used for compound control, represented by logical functions, can be mathematically classified into three functionally different elementary control logics.