We describe an approach that is related to a number of existing algorithms for the inference of a regular language from a set of positive (and optionally also negative) examples. Variations on this approach provide a family of algorithms that attempt to minimise the complexity of a description of the example data in terms of a finite state automaton model. Experiments using a standard set of small problems show that this approach produces satisfactory results when positive examples only are given, and can be helpful when only a limited number of negative examples is available. The results also suggest that improved algorithms will be needed in order to tackle more challenging problems, such as data mining and exploratory sequential analysis applications.