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Any Monotone Function Is Realized by Interlocked Polygons
Suppose there is a collection of n simple polygons in the plane, none of which overlap each other. The polygons are interlocked if no subset can be separated arbitrarily far from the rest. It is natural to ask the characterization of the subsets that makes the set of interlocked polygons free (not interlocked). This abstracts the essence of a kind of sliding block puzzle. We show that any monotone Boolean function f on n variables can be described by m = O(n) interlocked polygons. We also showdoi:10.3390/a5010148 fatcat:bzk5z2tplfdgbb3hc6rlyjjgzu