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||American English|
|Title of host publication||Proceedings of the 24th Annual ACM Symposium on Theory of Computing, STOC 1992|
|Publisher||Association for Computing Machinery|
|Number of pages||6|
|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
|Name||Proceedings of the Annual ACM Symposium on Theory of Computing|
|Conference||24th Annual ACM Symposium on Theory of Computing, STOC 1992|
|Period||4/05/92 → 6/05/92|
Bibliographical noteFunding Information:
Jerusalem 91904, Israel. Supported by BSF 89-00126 and by a Wol.fson research award. t AT&T Ben Laboratories.
© 1992 ACM.