Evolutionary complexity is measured here by the number of trials/evaluations needed for evolving a logical gate in a nonlinear medium. Behavioral complexity of the gates evolved is characterized in terms of cellular automata behavior. We speculate that hierarchies of behavioral and evolutionary complexities are isomorphic up to some degree, subject to substrate specificity of evolution, and the spectrum of evolution parameters.2009 Wiley Periodicals, Inc. Complexity 14: 15-20, 2009 Key Words: logic gates; evolution; cellular automata; complexity T here are many ways to measure the complexity of a system [1-3]. For example, having a problem we can estimate its complexity as the number of steps a computer takes to solve the problem (computational complexity). A descriptive complexity of a system is evaluated by the length of a minimal program/ model representing the system. Complexity of a finite state machine can be classified in sets of regular languages accepted by the machine. There are also measures based on how difficult it is to predict the evolution of a system.There are, however, few-if any-results related to the comparison of different measures of complexity. This short article aims to raise readers' awareness of the subject and to invite them to undertake research in ''comparative complexity.'' We compare the evolutionary complexity of logical functions (time required to evolve the functions) with the behavioral complexity of the functions (complexity of sequences of data iteratively processed by the functions).Nonlinear spatial extended media-liquid crystal [4] and Belousov-Zhabotinsky system [5]-were chosen as substrates of various logical gates' evolution because these media are possibly the best prototypes of nonclassical, unconventional, computing devices [6]. One-dimensional cellular automata were then selected as substrates to implement the gates evolved because the automata are good approximators of the real world [7], the space-time dynamic of the automata is easy to visualize, and methods for exploring complexity of the automata are well-established [8][9][10][11][12].
EVOLUTIONARY COMPLEXITY OF BOOLEAN GATESWe infer hierarchies of evolutionary complexity from computational and experimental laboratory studies of evolving of logic gates in liquid crystal [4] and excitable chemical medium [5]. See full details in the article cited, here we provide only a very brief overview of the results.