  We demonstrate that the algorithmic information content of a system is deeply
connected to its potential dynamics, thus affording an avenue for moving
systems in the information-theoretic space and controlling them in the phase
space. To this end we performed experiments and validated the results on (1) a
very large set of small graphs, (2) a number of larger networks with different
topologies, and (3) biological networks from a widely studied and validated
genetic network (e.coli) as well as on a significant number of differentiating
(Th17) and differentiated human cells from high quality databases (Harvard's
CellNet) with results conforming to experimentally validated biological data.
Based on these results we introduce a conceptual framework, a model-based
interventional calculus and a reprogrammability measure with which to steer,
manipulate, and reconstruct the dynamics of non- linear dynamical systems from
partial and disordered observations. The method consists in finding and
applying a series of controlled interventions to a dynamical system to estimate
how its algorithmic information content is affected when every one of its
elements are perturbed. The approach represents an alternative to numerical
simulation and statistical approaches for inferring causal
mechanistic/generative models and finding first principles. We demonstrate the
framework's capabilities by reconstructing the phase space of some discrete
dynamical systems (cellular automata) as case study and reconstructing their
generating rules. We thus advance tools for reprogramming artificial and living
systems without full knowledge or access to the system's actual kinetic
equations or probability distributions yielding a suite of universal and
parameter-free algorithms of wide applicability ranging from causation,
dimension reduction, feature selection and model generation.
