Expected Compression Ratio for DFCA: experimental average case analysis

In this paper we investigate from a statistical point of view the expected compression ratio between the size of a minimal Deterministic Finite Cover Automaton (DFCA) and the size of the minimal corresponding Determinitic Finite Automaton (DFA). Using sound statistical methods, we extend the experimental study done in [16], thus obtaining a much better picture of the compression power of DFCAs. We compute the expected ratio for the family of all finite languages, but also for various subfamilies of finite languages, such as prefix, suffix-free languages prefix and suffix closed languages, or (un)balanced languages. We also give an example of a family for which the expected compression ratio is very high.