Before revision:  On the basis of the perturbation test , we demonstrate how a system can be regarded as providing its own explanations for its own behavioursomething today highly sought in machine learning, helping us infer causal properties of a system while, if integrated, reducing the number of calculations required. We expect this approach to contribute toward a better understanding of integrated informationand of its connections to other, more established areas of science, such as dynamical systems and algorithmic information theory, and to help avoid some of the current abuses (e.g. relating \phi to lossless compression algorithms such as LZW) and limitations arising from the bottleneck principle which other approaches to \phi have been heavily subject to .
After revision:  On the basis of the perturbation test , we demonstrate how a system can be regarded as providing its own explanations for its own behavioursomething today highly sought in machine learning, helping us infer causal properties of a system while, if integrated, reducing the number of calculations to arrive at some bounds or estimations, as the algorithmic perturbation test guides an efficient search for estimating integrated information. Our work sets the stage for a systematic exploration of connections between algorithmic complexity and integrated information at the level of both theory and practice .