We consider the inferability of linear single-tree languages. We are able t
o show that if the terminal productions of the corresponding grammars obey
a simple restriction, then the languages generated are inferable from posit
ive samples only. Moreover, we solve an open problem posed by Greibach, Shi
, and Simonson concerning the unambiguity of certain ultralinear single-tre
e grammars. (C) 2000 Elsevier Science B.V. All rights reserved.