Towards Abstract Memristic Machines
Memristic machines are time-tensed machines of the nanosphere. Their definition and their rules are not covered by ordinary logic, arithmetics and semiotics, basic for a theory of abstract automata. The difference to classical concepts of machines to tensed, i.e. memristive machines is elaborated. As an attempt to develop memristive machines, basic constructs from morphogrammatics are applied. Properties of retro-gradeness (antidromicity), self-referentiality, simultaneity and locality (positionality) of operations as they occur in kenogramamtic and morphogrammatic basic operations, like the successor operations, ‘addition’ and ‘multiplication’ have to be realized on all levels of operativity in memristive systems. Hence, the tiny memristive properties of time- and history-dependence for kenomic successors are presented for all further operations, like “addition" (coalition), "multiplication”, “reflection”, etc. Morphogrammatics will be further developed in Part II of the paper.
A new framework for design and analysis for memristive systems, i.e. memristics, shall be sketched as a complex methodology of Morphogrammatics, Diamond Category Theory, Diagrammatics and Nanotechnology.