Program derivation by fixed point computation
Science of Computer Programming
Relations and graphs: discrete mathematics for computer scientists
Relations and graphs: discrete mathematics for computer scientists
Information Processing Letters - Special issue on the calculational method
Language Polynomial in the Input Plus Output
AMAST '91 Proceedings of the Second International Conference on Methodology and Software Technology: Algebraic Methodology and Software Technology
Acta Cybernetica
A Theory of Synchronous Relational Interfaces
ACM Transactions on Programming Languages and Systems (TOPLAS)
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Assume a partially ordered set (S, 驴) and a relation R on S. We consider various sets of conditions in order to determine whether they ensure the existence of a least reflexive point, that is, a least x such that xRx. This is a generalization of the problem of determining the least fixed point of a function and the conditions under which it exists. To motivate the investigation we first present a theorem by Cai and Paige giving conditions under which iterating R from the bottom element necessarily leads to a minimal reflexive point; the proof is by a concise relation-algebraic calculation. Then, we assume a complete lattice and exhibit sufficient conditions, depending on whether R is partial or not, for the existence of a least reflexive point. Further results concern the structure of the set of all reflexive points; among other results we give a sufficient condition that these form a complete lattice, thus generalizing Tarski's classical result to the nondeterministic case.