We introduce some restricted models of symport/antiport P systems that are used as acceptors (respectively, generators) of sets of tuples of non-negative integers and show that they characterize precisely the semilinear sets. Specifically, we prove that a set
is accepted (respectively, generated) by a restricted system if and only if
is a semilinear set. We also show that “slight” extensions of the models will allow them to accept (respectively, generate) non-semilinear sets. In fact, for these extensions, the emptiness problem is undecidable.