Computational mechanics: from theory to practice

In the last fifty years, computational mechanics has gained the attention of a large number of disciplines, ranging from physics and mathematics to biology, involving all the disciplines that deal with complex systems or processes. With ϵ-machines, computational mechanics provides powerful models that can help characterizing these systems. To date, an increasing number of studies concern the use of such methodologies; nevertheless, an attempt to make this approach more accessible in practice is lacking yet. Starting from this point, this thesis aims at investigating a more practical approach to computational mechanics so as to make it suitable for applications in a wide spectrum of domains. ϵ-machines are analyzed more in the robotics scene, trying to understand if they can be exploited in contexts with typically complex dynamics like swarms. Experiments are conducted with random walk behavior and the aggregation task. Statistical complexity is first studied and tested on the logistical map and then exploited, as a more applicative case, in the analysis of electroencephalograms as a classification parameter, resulting in the discrimination between patients (with different sleep disorders) and healthy subjects. The number of applications that may benefit from the use of such a technique is enormous. Hopefully, this work has broadened the prospect towards a more applicative interest.