  We study the computational complexity of finite intersections and unions of
deterministic context-free (dcf) languages. Earlier, Wotschke [J. Comput.
System Sci. 16 (1978) 456--461] demonstrated that intersections of $(d+1)$ dcf
languages are in general more powerful than intersections of $d$ dcf languages
for any positive integer $d$ based on the intersection hierarchy separation of
Liu and Weiner [Math. Systems Theory 7 (1973) 185--192]. The argument of Liu
and Weiner, however, works only on bounded languages of particular forms, and
therefore Wotschke's result is not directly extendable to disprove any given
language to be written in the form of $d$ intersection of dcf languages. To
deal with the non-membership of a wide range of languages, we circumvent the
specialization of their proof argument and devise a new and practical technical
tool: two pumping lemmas for finite unions of dcf languages. Since the family
of dcf languages is closed under complementation and also under intersection
with regular languages, these pumping lemmas help us establish a non-membership
relation of languages formed by finite intersections of non-bounded languages
as well. We also refer to a relationship to deterministic limited automata of
Hibbard [Inf. Control 11 (1967) 196--238] in this regard.
