The complexities of the possible rendezvous and the lockout problems f
or propositional concurrent programs are investigated in detail. We de
velop a unified strategy, based on domino tiling, to show that the abo
ve two problems with respect to a variety of propositional concurrent
programs are complete for a broad spectrum of complexity classes, rang
ing from NLOGSPACE, PTIME, NP, PSPACE to EXPTIME. Our technique is nov
el in the sense that it demonstrates how two seemingly unrelated model
s, namely, propositional concurrent programs and dominoes, can be link
ed together in a natural and elegant fashion.