Abstract
The framework for the information dynamics of distributed computation introduced in Chaps. 3–5 has proven successful in locally identifying the component operations of information storage, transfer and modification. We have observed that while these component operations exist to some extent in all types of computation, complex computation is distinguished in having coherent structure in its local information dynamics profiles. We conjecture that coherent information structure is a defining feature of complex computation, particularly evolved computation that solves human-understandable tasks. We present a methodology for studying coherent information structure, consisting of state-space diagrams of the local information dynamics and a measure of structure in these diagrams. The methodology identifies both clear and “hidden” coherent structure in complex computation, most notably reconciling conflicting interpretations of the complexity of ECA rule 22. The measure is also used to demonstrate a maximisation of coherent information structure in the order-chaos phase-transition in RBNs.
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Notes
- 1.
The methodology for studying coherent information structure and the results of its application to CAs were first reported in [1].
- 2.
Also, in Sect. 8.3 we will observe the emergence of coherent particle-like information structures in a snake-like robot evolved to maximise transfer entropy between its segments.
- 3.
See also [10] for a discussion of the term “coherent structure” referring to particles (including blinkers) in this context.
- 4.
Indeed, the candidate measures considered in Appendix G did not capture its alignment with the known complex rules in this respect.
- 5.
For example, \(t^c(i,j=-1,n,k)\) is almost completely specified by \(a(i,n,k)\) and \(t(i,j=1,n,k)\) in ECAs, except for any difference in \(h(i,n)\) between the “0” and “1” states.
- 6.
Note we have altered our notation for mutual and multi-information expressions from \(I_{X;Y}\) to \(I(X;Y)\) here. This is simply for easier display of the complicated quantities over which the information is being calculated.
- 7.
This is similar to the manner in which the local information dynamics measures themselves reveal more about the underlying computation than their averages do.
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Lizier, J.T. (2013). Coherent Information Structure in Complex Computation. In: The Local Information Dynamics of Distributed Computation in Complex Systems. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32952-4_7
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