Neutrality and epistasis in program space

Abstract

Neutral networks in biology often contain diverse solutions with equal fitness, which can be useful when environments (requirements) change over time. In this paper, we present a method for studying neutral networks in software. In these networks, we find multiple solutions to held-out test cases (latent bugs), suggesting that neutral software networks also exhibit relevant diversity. We also observe instances of positive epistasis between random mutations, i.e. interactions that collectively increase fitness. Positive epistasis is rare as a fraction of the total search space but significant as a fraction of the objective space: 9% of the repairs we found to look (and 4.63% across all programs analyzed) were produced by positive interactions between mutations. Further, the majority (62.50%) of unique repairs are instances of positive epistasis.