Any Monotone Boolean Function Can Be Realized by Interlocked Polygons
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Demaine_Any monotone.pdf
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Author(s)
Demaine, Erik D.
Demaine, Martin L.
Uehara, Ryuhei
Date Issued
2010
Journal
Canadian Conference on Computational Geometry (CCCG). Proceedings
Publisher
University of Manitoba
Citation
Demaine, Erik D., Martin L. Demaine, Ryuhei Uehara. "Any Monotone Boolean Function Can Be Realized by Interlocked Polygon" Canadian Conference on Computational Geometry, Aug. 9-11, 2010.
Version
Author's final manuscript
Abstract
We show how to construct interlocked collections of simple
polygons in the plane that fall apart upon removing
certain combinations of pieces. Precisely, interior-disjoint
simple planar polygons are interlocked if no
subset can be separated arbitrarily far from the rest,
moving each polygon as a rigid object as in a sliding-block
puzzle. Removing a subset S of these polygons
might keep them interlocked or free the polygons, allowing
them to separate. Clearly freeing removal sets
satisfy monotonicity: if S S [prime] and removing S frees
the polygons, then so does S [prime]. In this paper, we show
that any monotone Boolean function f on n variables
can be described by m > n interlocked polygons: n of
the m polygons represent the n variables, and removing
a subset of these n polygons frees the remaining
polygons if and only if f is 1 when the corresponding
variables are 1.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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http://www.cs.umanitoba.ca/~cccg2010/accepted.html
