Pair algebras and Galois connections

Abstract

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 very first application of Galois connections directly related to the modern digital computer, Hartmanis and Stearns posed a. subtly different question, namely: when does a relation define two functions that are Ga'!ois connected? Such a relation they called a "pair algebra". In this paper we derive a general, necessary and sufficient condition for a relation between complete lattices to define a Galois connection between the lattices. We also give several examples of pair algebras illustrating why this seemingly forgotten notion is relevant to the science of computing.

DOI: 10.1016/S0020-0190(98)00107-0

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Cite this paper

@article{Backhouse1998PairAA, title={Pair algebras and Galois connections}, author={Roland Carl Backhouse}, journal={Inf. Process. Lett.}, year={1998}, volume={67}, pages={169-175} }