In this paper we extend the automaton synthesis paradigm to infinitary
languages, that is, to subsets of the set Sigma(omega) of all infinit
e sequences over some alphabet Sigma. Our main result is a polynomial
algorithm for learning a sub-class of the omega-regular sets from memb
ership queries and counter-examples based on the framework suggested b
y Angluin (Angluin, D. (1987), Inform. and Comput. 75, 87-106) for lea
rning regular subsets of Sigma. (C) 1995 Academic Press, Inc.