Polynomial Representations of Symmetric Partial Boolean Functions
For Boolean polynomials in $\mathbb{Z}_p$ of sufficiently low degree we derive a relation expressing their values on one level set in terms of their values on another level set. We use this relation to derive linear upper and lower bounds, tight to within constant factor, on the degrees of various a...
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| Published in: | SIAM journal on discrete mathematics Vol. 19; no. 2; pp. 481 - 488 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Philadelphia
Society for Industrial and Applied Mathematics
01.01.2005
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| Subjects: | |
| ISSN: | 0895-4801, 1095-7146 |
| Online Access: | Get full text |
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| Summary: | For Boolean polynomials in $\mathbb{Z}_p$ of sufficiently low degree we derive a relation expressing their values on one level set in terms of their values on another level set. We use this relation to derive linear upper and lower bounds, tight to within constant factor, on the degrees of various approximate majority functions, namely, functions that take the value 0 on one level set, the value 1 on a different level set, and arbitrary 0-1 values on other Boolean inputs. We show sublinear upper bounds in the case of moduli that are not prime powers. |
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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 |
| ISSN: | 0895-4801 1095-7146 |
| DOI: | 10.1137/S0895480103433562 |