Complexity of a Phenotype with Greater Plasticity for Digital Evolvable Hardware

 This paper analyzes the complexity of a new phenotype for evolvable hardware with more plasticity than the traditional phenotype. The plasticity is due to that fact that this phenotype is unstructured and that property allows it to perform combinational and sequential tasks. The complexity is evaluated in relation to Shannon’s limit (lower) and Lupanov’s limit (upper). These limits define a bounded and sufficient search space for the combinational circuits. However, in the studied case (multipliers with 2-bits word width operands) the lowest number of iterations is achieved when the number of cells available is around four-times the Shannon’s limit. Moreover, at calculate the mutation rate of digital organisms using the Lynch’s equation, which relates the mutation rate to the genome length of the species, the circuit size stays around Lupanov’s limit. Finally, it important to note that compact circuits are obtained directly, with an evolutionary algorithm that only follows a wished-for functionality, where the economy of the phenotypes is an emergent property of the process. Key-Words:  Circuit Size, Complexity Limits, Evolvable Hardware, Iterations, Lupanov’s limit, Phenotype, Shannon’s limit.