I have already asked this question in StackOverflow (open bounty closing on Aug 25th).
Let's say I have some finite sets: A, B, ..., K
I also have A1, A2, ... An, which are subsets of A; B1, B2, ... Bn, which are subsets of B, etc.
Let's say S is the cartesian product A x B x ... x K
and Sn is the cartesian product of An x Bn x ... x Kn
Is there an algorithm to efficiently determine if the union of all
Sn is equivalent to
Some pointers to literature where I can study this problem are greatly appreciated.