On the communication complexity of t-intersection problems in generalized boolean algebras

The authors consider the following game: Two players independently choose a chain in a partially ordered set. How many bits of information have to be communicated until at least one of the players knows whether the chains have exactly t elements in common? This model generalizes the t-intersection problem for subsets of a finite set. The authors establish the deterministic communication complexity in general. For the special cases of generalized Boolean algebra, they present improved nondeterministic and probabilistic protocols that are of optimal order of complexity for classes with fixed width q.