How considering incompatible state mergings may reduce the DFA induction search tree

A simple and effective method for DFA induction from positive and negative samples is the state merging method. The corresponding search space may be tree-structured, considering two subspaces for a given pair of states: the subspace where states are merged and the subspace where states remain different. Choosing different pairs leads to different sizes of space, due to state mergings dependencies. Thus, ordering the successive choices of these pairs is an important issue. Starting from a constraint characterization of incompatible state mergings, we show that this characterization allows to achieve better choices, i.e. to reduce the size of the search tree. Within this framework, we address the issue of learning the set of all minimal compatible DFA's. We propose a pruning criterion and experiment with several ordering criteria. The prefix order and a new entropy based criterion have exhibit the best results in our test sets.