Before revision: We establish and build theoretical and numerical connections between the theories and methods of integrated information and algorithmic complexity. We introduce a method for estimating integrated information performing a programmability test rooted in algorithmic information dynamics quantifying the change in program size of a system subject to perturbations.
After revision: The concept of information has emerged as a language in its own right, bridging several disciplines that analyze natural phenomena and man-made systems. Integrated information has been introduced as a metric to quantify the amount of information generated by a system beyond the information generated by its elements. Yet, this intriguing notion comes with the price of being prohibitively expensive to calculate, since the calculations require an exponential number of sub-divisions of a system. Here we introduce a novel framework to connect algorithmic randomness and integrated information and a numerical method for estimating integrated information performing a programmability test rooted in algorithmic information dynamics quantifying the change in program size of a system subject to perturbations.