TY  - JOUR
A1  - Desharnais, Jules
A1  - Möller, Bernhard
T1  - Least reflexive points of relations
T2  - Higher-Order and Symbolic Computation
N2  - 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 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.
KW  - Software
KW  - Computer Science Applications
Y1  - 2005
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/54134
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-541340
SN  - 1388-3690
SN  - 1573-0557
VL  - 18
IS  - 1-2
SP  - 51
EP  - 77
PB  - Springer Nature
ER  -