Towards Abstract Memristic Machines

I just published a new paper about "time- and history-dependent" machines at my MemRistics website:

 http://memristors.memristics.com/Machines/Memristic%20Machines.html
http://memristors.memristics.com/Machines/Memristic%20Machines.pdf

This is a very first attempt to propose the new possibilities of computation offered by the discovery/invention of memristors and memristive systems.

A comparision with different types of machines is presented:

trivial machines

non-trivial machines

self-organizing machines

co-creative autonomous machines.

The framework of monomorphy-based morphogrammatics is used to demonstrate some mechanisms of memristic machines.

Time-dependence is modeled as a retro-grade evolvement (prolongation, succession, disremption, recursion) of morphograms with simultaneous outcomes.

With that, the characterization of the behavior of memristors as time-dependent devices of nanoscale is taken seriously and is interpreted as second-order events, which demands for a specific, non-classical, formalization.

A few basic operations, like "successor", "addition" (coalitions) and "multiplication" (cooperations) of memristive constellations are developed.

Abstract
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 some further operations, like “addition" (coalition), "multiplication” (cooperation), “reflection”, etc. 

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. 

FULL TEXT
 http://memristors.memristics.com/Machines/Memristic%20Machines.html
http://memristors.memristics.com/Machines/Memristic%20Machines.pdf