Ilan Newman

Private vs. common random bits in communication complexity

Abstract We investigate the relative power of the common random string model vs. the private random string model in communication complexity. We show that the models are essentially equal.

A combinatorial characterization of the testable graph properties: it's all about regularity

A common thread in recent results concerning the testing of dense graphs is the use of Szemerédis regularity lemma. In this paper we show that in some sense this is not a coincidence. Our first result is that the property defined by having any given Szemerédi-partition is testable with a constant number of queries. Our second and main result is a purely combinatorial characterization of the graph properties that are testable with a constant number of queries. This characterization (roughly) says that a graph property P can be tested with a constant number of queries if and only if testing P can be reduced to testing the property of satisfying one of finitely many Szemerédi-partitions. This means that in some sense, testing for Szemerédi-partitions is as hard as testing any testable graph property. We thus resolve one of the main open problems in the area of property-testing, which was raised in the 1996 paper of Goldreich, Goldwasser and Ron [25] that initiated the study of graph property-testing. This characterization also gives an intuitive explanation as to what makes a graph property testable.

Regular Languages are Testable with a Constant Number of Queries

We continue the study of combinatorial property testing, initiated by Goldreich, Goldwasser, and Ron in [J. ACM, 45 (1998), pp. 653--750]. The subject of this paper is testing regular languages. Our main result is as follows. For a regular language

A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity

L\in \{0,1\}^*

On grid intersection graphs

and an integer n there exists a randomized algorithm which always accepts a word w of length n if

Regular languages are testable with a constant number of queries

w\in L

Hot-potato algorithms for permutation routing

and rejects it with high probability if

Combinatorial characterization of read-once formulae

w

Testing versus Estimation of Graph Properties

has to be modified in at least

Testing versus estimation of graph properties

\epsilon n