Mutually compatible and incompatible merges for the search of the smallest consistent DFA

Abstract

State Merging algorithms, such as Rodney Price’s EDSM (Evidence-Driven State Merging) algorithm, have been reasonably successful at solving DFA-learning problems. EDSM, however, often does not converge to the target DFA and, in the case of sparse training data, does not converge at all. In this paper we argue that is partially due to the particular heuristic used in EDSM and also to the greedy search strategy employed in EDSM. We then propose a new heuristic that is based on minimising the risk involved in making merges. In other words, the heuristic gives preference to merges, whose evidence is supported by high compatibility with other merges. Incompatible merges can be trivially detected during the computation of the heuristic. We also propose a new heuristic limitation of the set of candidates after a backtrack to these incompatible merges, allowing to introduce diversity in the search.