Systemic computation: A model of interacting systems with natural characteristics

Abstract

Natural systems provide unique examples of computation in a form very different from contemporary computer architectures. Biology also demonstrates capabilities such as adaptation, self-repair and self-organisation that are becoming increasingly desirable for our technology. To address these issues a new computer model and architecture with natural characteristics is presented. Systemic computation is Turing Complete; it is designed to support biological algorithms such as neural networks, evolutionary algorithms and models of development, and shares the desirable capabilities of biology not found in conventional architectures. Systemic computation may also be implemented using natural systems, enabling the potential for future computational analysis and control of biology.

Keywords:

• Systemics
• Bio-inspired computation
• Unconventional computation
• Novel computation

Notes

¹And some useful systemic computation transformation functions resemble those widely used in membrane computing and brane calculus [38].

²The current model focuses on the interaction of two systems at any specific time t, in order to simplify analysis and implementation; this uses the notion that n-ary interactions are reducible to n − 1 combined binary interactions; nevertheless, it is recognised that future models may need to incorporate n-ary systemic interactions for practical reasons.

³Where “shape” means distinguishing properties and attributes and may encompass anything from morphology to spatial position.

⁴Akin to dynamic bigraph links [a].

⁵Akin to the views of Varela [16,27].

⁶The separation of context and scope is not essential, although it improves programmability; the model also supports one system acting as both scope and context for the same interacting systems. Indeed, scope can be regarded as another aspect of context, and context as another aspect of scope.

⁷The word-length is user-definable; here 16 characters was chosen.

⁸Systemic computation is a pseudo NTM unless a non-pseudo random number generator is used [36].

⁹Quantifying exactly what the theoretical penalties should be forms the basis of the well-known problem: “does P equal NP?” [37].

¹⁰Taking this view of computation, electronic computers provide a remarkably weak form of computation as their transformations are often confined to local patterns of electron flows. Biological systems are a much stronger form of computation as they are able to transform significant varieties and quantities of other systems.

¹¹There have been some claims that so-called Super-Turing Computation may be possible with certain models of computation [19], however detailed critiques suggest that such models rely on unimplementable features (e.g. infinite sensitivity in the Siegalman model [41]). Here it is seen as more useful to suggest that some biological processes may be Turing Complete and thus may be programmable and understood as computational devices, and not claim that systemic computation is a Super-Turing machine, which it may or may not be.

¹²Computation here means transformation of systems—where systems interact with no effect, no computation takes place.

¹³Assuming an energy source remains present and an absence of externally imposed destruction.

¹⁴And perhaps conventional computers, which consume electricity, emit heat as waste and have no more ability to recycle or integrate into a mutually supportive ecology than a rock.