Degree complexity of Boolean functions and its applications to relativized separations

It is shown that a simple function in AC/sup 0/, OR of square root n disjoint ANDs, cannot be computed by decision trees of depth log/sup O(1)/n where each node asks whether or not p(x/sub 1/, . . .,x/sub n/)=0 for some polynomial p of degree log/sup O(1)/n. This is in contrast to recent results tha...

Full description

Saved in:
Bibliographic Details
Published in[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference pp. 382 - 390
Main Author Tarui, J.
Format Conference Proceeding
LanguageEnglish
Published IEEE Comput. Soc. Press 1991
Subjects
Application software
Artificial intelligence
Boolean functions
Circuits
Computer science
Decision trees
Polynomials
Online AccessGet full text

Cover

More Information
Summary:It is shown that a simple function in AC/sup 0/, OR of square root n disjoint ANDs, cannot be computed by decision trees of depth log/sup O(1)/n where each node asks whether or not p(x/sub 1/, . . .,x/sub n/)=0 for some polynomial p of degree log/sup O(1)/n. This is in contrast to recent results that every function in AC/sup 0/ can be computed probabilistically by just one such query and can be deterministically computed by such decision trees if each node asks whether or not p(x/sub 1/, . . .,x/sub n/)>0. The proofs are based on simple algebraic arguments that also provide alternative proofs for some known results.< >
ISBN:9780818622557
0818622555
DOI:10.1109/SCT.1991.160282