Pair algebras and Galois connections

Most studies of Galois connections begin with a function and ask the question: when is there a second function that is connected to the first? In possibly the first application of Galois connections directly related to the digital computer, Hartmanis and Stearns posed a subtly different question: when does a relation define two functions that are Galois connected? Such a relation they called a "pair algebra". We derive a general, necessary and sufficient condition for a relation between complete posets to define a Galois connection. We give examples of pair algebras illustrating why this notion is relevant to the science of computing