TY  - RPRT
A1  - Desharnais, Jules
A1  - Möller, Bernhard
T1  - Least reflexive points of relations
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 relationalgebraic 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.
T3  - Reports / Technische Berichte der Fakultät für Angewandte Informatik der Universität Augsburg - 2002-13 
KW  - Least reflexive point
KW  - greatest reflexive point
KW  - fixed point
KW  - lattice
KW  - partial order
KW  - relation
KW  - inflationary relation
Y1  - 2006
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/257
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-2080
PB  - Institut für Informatik, Universität Augsburg
CY  - Augsburg
ER  -