On the parity complexity measures of Boolean functions

The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Boolean function is polynomially related to the non-deterministic complexity of the function or its comp...

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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Zhang, Zhiqiang, Shi, Yaoyun
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 03.04.2010
Subjects:	Boolean algebra Boolean functions Complexity Decision trees Parity
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Boolean function is polynomially related to the non-deterministic complexity of the function or its complement. We also show that they are polynomially related to an analogue of the block sensitivity. We further study parity decision trees in their relations with an intermediate variant of the decision trees, as well as with communication complexity.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.1004.0436