15399 Constructive Logic
Assignment 10, Addendum
In Problem 1, a
fourth condition is needed to ensure that each valuation of the "path"
variables p_{ij} actually represents a path in the
graph:
(d) Each node of the path is assigned to at most one node of the
graph.
On the Boolean variables, this translates to
for all i, j. (p_{ij} implies for all k != j.
not p_{ik})
Together with condition (c) this ensures that each node of the
path is assigned to exactly one node of the graph.
Most solutions did not state this condition, but since the
formulation of the problem was misleading, suggesting
that the three conditions are sufficient, we did not take off
any points.
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Frank Pfenning
