Abstract
Every boolean function may be represented as a real polynomial. In this paper we characterize the degree of this polynomial in terms of certain combinatorial properties of the boolean function. Our first result is a tight lower bound of Ω(log n) on the degree needed to represent any boolean function that epends on n variables. Our second result states that for every boolean function f the following measures are all polynomi-ally related: The decision tree complexity of f. The degree of the polynomial representing f. The smallest degree of a polynomial approximating f in the Lmax norm.
Original language | English |
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Title of host publication | Proceedings of the 24th Annual ACM Symposium on Theory of Computing, STOC 1992 |
Publisher | Association for Computing Machinery |
Pages | 462-467 |
Number of pages | 6 |
ISBN (Electronic) | 0897915119 |
DOIs | |
State | Published - 1 Jul 1992 |
Event | 24th Annual ACM Symposium on Theory of Computing, STOC 1992 - Victoria, Canada Duration: 4 May 1992 → 6 May 1992 |
Publication series
Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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Volume | Part F129722 |
ISSN (Print) | 0737-8017 |
Conference
Conference | 24th Annual ACM Symposium on Theory of Computing, STOC 1992 |
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Country/Territory | Canada |
City | Victoria |
Period | 4/05/92 → 6/05/92 |
Bibliographical note
Publisher Copyright:© 1992 ACM.