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Automatic Program Development
Assume a partially ordered set (S, ≤) 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 elementdoi:10.1007/978-1-4020-6585-9_14 fatcat:eghnt4nbmvgqjmokaw2z3ro6cy