15-399 Constructive Logic
Assignment 10, Addendum

In Problem 1, a fourth condition is needed to ensure that each valuation of the "path" variables pij 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. (pij implies for all k != j. not pik)

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