TY  - CHAP
A1  - Desharnais, Jules
A1  - Möller, Bernhard
A2  - Danvy, Olivier
A2  - Mairson, Harry
A2  - Henglein, Fritz
A2  - Pettorossi, Alberto
T1  - Least reflexive points of relations
T2  - Automatic Program Development: A Tribute to Robert Paige
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 for these to form a complete lattice, thus generalizing Tarski's classical result to the nondeterministic case.
Y1  - 2008
UR  - https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/58792
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-587927
SN  - 9781402065842
SN  - 9781402065859
SP  - 215
EP  - 228
PB  - Springer Netherlands
CY  - Dordrecht
ER  -