  The paper explores the correspondence between balanced incomplete block
designs (BIBD) and certain linear CNF formulas by identifying the points of a
block design with the clauses of the Boolean formula and blocks with Boolean
variables. Parallel classes in BIBDs correspond to XSAT solutions in the
corresponding formula. This correspondence allows for transfers of results from
one field to the other. As a new result we deduce from known satisfiability
theorems that the problem of finding a parallel class in a partially balanced
incomplete block design is NP-complete.
