We study the computational complexity of the problem of computing a complem
ent representation for a set of terms. Depending on the class of sets consi
dered, some sets are shown to have an exponential complement representation
in the worst case, and some are shown to have a polynomial one. The comple
xity of deciding if a set has an empty complement is also studied. (C) 1999
Elsevier Science B.V. All nights reserved.