Beigel, Reingold, and Spielman (J. Comput System Sci 50, 191-202 (1995
)) showed that PP is closed under intersection and a variety of specia
l cases of polynomial-time truth-table closure. We extend their techni
ques to show that PP is closed under general polynomial-time truth-tab
le reductions. We also show that PP is closed under constant-round tru
th-table reductions. (C) 1996 Academic Press, Inc.