Properties of facets of full-dimensional polytopes P with binary vertices are studied. If Q is obtained from P by fixing some of the binary variables, then the facets of P that reduce to a given facet of Q are determined by the vertices of a certain polyhedron V . The case where V has a unique vertex is characterized. If P is completely monotonic and the facet of O has 0–1 coefficients, then the vertices of V lie in a hypercube of side 1, and the integer vertices correspond to the sequential lifts or extensions. The self facets, i. e. hyperplanes spanned by binary points, are connected to the hyperplanes spanned by non-negative integral points. Every threshold function can be labelled by its Chow parameter vector. The faces of the convex hull of all n -argument parameter vectors are characterized. This leads to a necessary and sufficient condition for a parameter vector to label a self dual threshold function having a self facet separator.
[1]
Calvin C. Elgot,et al.
Truth functions realizable by single threshold organs
,
1961,
SWCT.
[2]
Robert O. Winder,et al.
Chow Parameters in Threshold Logic
,
1971,
JACM.
[3]
Leslie E. Trotter,et al.
Properties of vertex packing and independence system polyhedra
,
1974,
Math. Program..
[4]
Laurence A. Wolsey,et al.
Faces for a linear inequality in 0–1 variables
,
1975,
Math. Program..
[5]
Manfred W. Padberg,et al.
On the facial structure of set packing polyhedra
,
1973,
Math. Program..
[6]
Leslie E. Trotter,et al.
A class of facet producing graphs for vertex packing polyhedra
,
1975,
Discret. Math..
[7]
Egon Balas,et al.
Facets of the knapsack polytope
,
1975,
Math. Program..
[8]
E. Balas,et al.
Facets of the Knapsack Polytope From Minimal Covers
,
1978
.
[9]
Peter L. Hammer,et al.
Facet of regular 0–1 polytopes
,
1975,
Math. Program..