This article is cited in 5 papers

On complexity measures for complexes of faces in the unit cube

I. P. Chukhrov

Institute for Computer Aided Design, RAS, 19/18 2nd Brestskaia St., 123056 Moscow, Russia

Abstract: We study the problem of proving that the complex of faces is minimal in the unit $n$-dimensional cube. We formulate sufficient conditions which enable us to prove that a complex of faces is minimal using the ordinal properties of the complexity measure functional and structural properties of Boolean functions. It makes it possible to expand the set of complexes of faces which are proven to be minimal with respect to complexity measures satisfying certain properties. We prove the strict inclusion for the following sets of complexes of faces: kernel, minimal for any complexity measure and minimal for any complexity measure, which is invariant under the replacement faces on isomorphic faces. Ill. 2, bibliogr. 10.

Keywords: face, complex of faces in the $n$-dimensional unit cube, Boolean function, complexity measure, minimal complex of faces.

UDC: 519.714.7

Received: 09.11.2012

 English version: Journal of Applied and Industrial Mathematics, 2014, 8:1, 9–19

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