Addressing Design for testability of digital structures requires performing complex studies of phenomena at the frontiers of scientific directions as mathematical logic, physics, chemistry, biology. Half a century passed from the moment of issue of Integrated Circuits Design for testability has not yielded the expected results, which confirms the need for a new paradigm based on the principles of the very nature of existence. Creating the design for testability paradigm involves research, analysis, and use of certain functional aspects between logical functions of different structures. This can lead to the creation of new types of elementary structures and properties intrinsic to the development of modern theories and efficient design for testability. Are highlighted and considered various functional forms of logical functions: equivalent, reverse duality complementary. These functional aspects can be considered as a small step towards establishing innovative concepts of the future transition to the new state of knowledge. The paper is based on analysis of reference works in research logic algebra functions and design for testability.