Abstract
A method for studying the qualitative dynamical properties of abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm is presented. It is shown that the compression-based approach classifies cellular automata (CA) into clusters according to their heuristic behavior, with these clusters showing a correspondence with Wolfram's main classes of CA behavior. A compression based method to estimate a characteristic exponent to detect phase transitions and measure the resiliency or sensitivity of a system to its initial conditions is also proposed. A conjecture regarding the capability of a system to reach computational universality related to the values of this phase transition coefficient is formulated. These ideas constitute a compression-based framework for investigating the dynamical properties of cellular automata and other systems.
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