Dear Guo,
yes, most active learning algorithms (including L*) construct complete hypotheses and require the membership oracle to answer queries for all posible words over the given alphabet. However, you can also handle partially defined systems under learning when you fallback to some default behavior in these cases.
For example, if a DFA can no longer transition to a state upon reading an input (undefined transition) the word will be rejected. So in a membership oracle you could simply return "false". This will then result in a sink state in the hypothesis which collects all undefined transitions.
Similarly for Mealy machines, you can (repeatedly) emit a special "undefined" output symbol which will then also result in a "undefined" sink.
Kind regards,
Markus
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