Evolution and Computational Learning Theory: A survey on Valiant's paper (1312.4599v1)

Abstract: Darwin's theory of evolution is considered to be one of the greatest scientific gems in modern science. It not only gives us a description of how living things evolve, but also shows how a population evolves through time and also, why only the fittest individuals continue the generation forward. The paper basically gives a high level analysis of the works of Valiant[1]. Though, we know the mechanisms of evolution, but it seems that there does not exist any strong quantitative and mathematical theory of the evolution of certain mechanisms. What is defined exactly as the fitness of an individual, why is that only certain individuals in a population tend to mutate, how computation is done in finite time when we have exponentially many examples: there seems to be a lot of questions which need to be answered. [1] basically treats Darwinian theory as a form of computational learning theory, which calculates the net fitness of the hypotheses and thus distinguishes functions and their classes which could be evolvable using polynomial amount of resources. Evolution is considered as a function of the environment and the previous evolutionary stages that chooses the best hypothesis using learning techniques that makes mutation possible and hence, gives a quantitative idea that why only the fittest individuals tend to survive and have the power to mutate.