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On Generalized Constraints and Certificates
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| Venue: | DISCRETE MATHEMATICS |
| Citations: | 14 - 0 self |
BibTeX
@ARTICLE{Hellerstein_ongeneralized,
author = {Lisa Hellerstein},
title = {On Generalized Constraints and Certificates},
journal = {DISCRETE MATHEMATICS},
year = {},
volume = {226},
pages = {211--232}
}
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Abstract
Ekin, Foldes, Hammer, and Hellerstein showed that a set of Boolean functions is characterizable by a (possibly infinite) set of Boolean equations iff it is closed under permutation of variables, addition of dummy variables, and identification of variables. Subsequently, Pippenger introduced constraint characterizations, which generalize previous characterizations of clones. He showed that a set of finite functions can be characterized by a set of constraints iff it is characterizable by Boolean equations. He also developed a Galois theory for sets of finite functions characterizable by constraints. In this paper we generalize Pippenger's results by considering sets of finite functions, such as the unate functions, that are closed under permutation of variables and addition of dummy variables but not necessarily under identification of variables. We introduce the notion of a generalized constraint, and consider the question of which sets of functions can be characterized by...
