  Query equivalence is investigated for disjunctive aggregate queries with
negated subgoals, constants and comparisons. A full characterization of
equivalence is given for the aggregation functions count, max, sum, prod,
toptwo and parity. A related problem is that of determining, for a given
natural number N, whether two given queries are equivalent over all databases
with at most N constants. We call this problem bounded equivalence. A complete
characterization of decidability of bounded equivalence is given. In
particular, it is shown that this problem is decidable for all the above
aggregation functions as well as for count distinct and average. For
quasilinear queries (i.e., queries where predicates that occur positively are
not repeated) it is shown that equivalence can be decided in polynomial time
for the aggregation functions count, max, sum, parity, prod, toptwo and
average. A similar result holds for count distinct provided that a few
additional conditions hold. The results are couched in terms of abstract
characteristics of aggregation functions, and new proof techniques are used.
Finally, the results above also imply that equivalence, under bag-set
semantics, is decidable for non-aggregate queries with negation.
