Approximations of algorithmic and structural complexity validate cognitive-behavioral experimental results.

Abstract

Being able to objectively characterize the intrinsic complexity of behavioral patterns resulting from human or animal decisions is fundamental for deconvolving cognition and designing autonomous artificial intelligence systems. Yet complexity is difficult in practice, particularly when strings are short. By numerically approximating algorithmic (Kolmogorov) complexity (K), we establish an objective tool to characterize behavioral complexity. Next, we approximate structural (Bennett's Logical Depth) complexity (LD) to assess the amount of computation required for generating a behavioral string. We apply our toolbox to three landmark studies of animal behavior of increasing sophistication and degree of environmental influence, including studies of foraging communication by ants, flight patterns of fruit flies, and tactical deception and competition (e.g., predator-prey) strategies. We find that ants harness the environmental condition in their internal decision process, modulating their behavioral complexity accordingly. Our analysis of flight (fruit flies) invalidated the common hypothesis that animals navigating in an environment devoid of stimuli adopt a random strategy. Fruit flies exposed to a featureless environment deviated the most from Levy flight, suggesting an algorithmic bias in their attempt to devise a useful (navigation) strategy. Similarly, a logical depth analysis of rats revealed that the structural complexity of the rat always ends up matching the structural complexity of the competitor, with the rats' behavior simulating algorithmic randomness. Finally, we discuss how experiments on how humans perceive randomness suggest the existence of an algorithmic bias in our reasoning and decision processes, in line with our analysis of the animal experiments. This contrasts with the view of the mind as performing faulty computations when presented with randomized items. In summary, our formal toolbox objectively characterizes external constraints on putative models of the "internal" decision process in humans and animals.