Which formulae shrink under random restrictions?

Hana Chockler; Uri Zwick

Which formulae shrink under random restrictions?

Hana Chockler^*, Uri Zwick

^*Corresponding author for this work

School of Computer Science

Hebrew University of Jerusalem

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

We show that the shrinkage exponent, under random restrictions, of formulae over a finite complete basis B of Boolean functions is strictly greater than 1 if and only if all the functions in B are monotone increasing or monotone decreasing in each one of their variables. As a conseguence, we get non-linear lower bounds on the formula complexity of the parity function over any basis composed only of monotone increasing or decreasing functions.

Original language	English
Title of host publication	Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms
Pages	702-708
Number of pages	7
State	Published - 2001
Event	2001 Operating Section Proceedings, American Gas Association - Dallas, TX, United States Duration: 30 Apr 2001 → 1 May 2001

Publication series

Name	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference	2001 Operating Section Proceedings, American Gas Association
Country/Territory	United States
City	Dallas, TX
Period	30/04/01 → 1/05/01

Keywords

Algorithms
Theory
Verification

Cite this

@inproceedings{e73e59a2aa604f73b0c26d3f38743e73,

title = "Which formulae shrink under random restrictions?",

abstract = "We show that the shrinkage exponent, under random restrictions, of formulae over a finite complete basis B of Boolean functions is strictly greater than 1 if and only if all the functions in B are monotone increasing or monotone decreasing in each one of their variables. As a conseguence, we get non-linear lower bounds on the formula complexity of the parity function over any basis composed only of monotone increasing or decreasing functions.",

keywords = "Algorithms, Theory, Verification",

author = "Hana Chockler and Uri Zwick",

year = "2001",

language = "אנגלית",

isbn = "0898714907",

series = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

pages = "702--708",

booktitle = "Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms",

note = "2001 Operating Section Proceedings, American Gas Association ; Conference date: 30-04-2001 Through 01-05-2001",