comput. complex. 21 (2012), 193 – 195

c© Springer Basel AG 2012

1016-3328/12/020193-3

published online April 28, 2012

DOI 10.1007/s00037-012-0041-9 computational complexity

SPECIAL ISSUE

“CONFERENCE ON

COMPUTATIONAL

COMPLEXITY 2011”

GUEST EDITOR’S FOREWORD

Anup Rao

This special issue contains the full versions of four papers thatwere presented at the 26th Annual IEEE Conference on Computa-tional Complexity (CCC 2011) held in San Jose, California, fromJune 8 to June 10, 2011. The papers were selected by the pro-gram committee from all the papers presented at the conference.They were invited for submission to this special issue and weresubsequently subjected to the standard refereeing process of thejournal.

The first paper deals with the direct product question, whichasks how the difficulty of computing k copies of a function scaleswith k. For many computational models, this question is notori-ously hard to answer, and successful attempts to answer it oftenprovide new insights. In Improved direct product theorems for ran-domized query complexity, Andrew Drucker gives essentially opti-mal bounds showing that if every algorithm that makes T queriesto the input has at most (1− ε) probability of success in determin-ing the value of a function, then for every α, the success probabilityusing αεTk queries is at most (2αε(1− ε))k. The results are partic-ularly interesting because the techniques used seem fairly generaland widely applicable.

In the paper Bounded-depth circuits cannot sample good codes,Shachar Lovett and Emanuele Viola continue a beautiful line ofwork investigating the complexity of sampling problems. Theyshow that any constant depth circuit using AND, OR, and NOT

194 Rao cc 21 (2012)

gates cannot accurately sample a random codeword from a gooderror correcting code. Previous work on the noise sensitivity of con-stant depth circuits shows that one cannot use a constant depthSPcircuit to compute the encoding function of a good code. In thiswork, the authors use isoperimetric inequalities on the hammingcube in addition to the noise sensitivity characterization to obtaintheir results.

The third paper is about the problem of constructing locallytestable codes, namely codes where the membership in the codecan be certified by a randomized algorithm making only a con-stant number of queries into a purported codeword. Locally test-able codes are relevant to the study of probabilistically checkableproofs and property testing. Despite much effort, we do not yetknow many useful lower bounds on the parameters of locally test-able codes. In Towards lower bounds on locally testable codes viadensity arguments, Eli Ben-Sasson and Michael Viderman outlinea strategy for obtaining such lower bounds and makes partial pro-gress toward obtaining such lower bounds.

The final paper makes interesting connections between twowell-studied areas of complexity theory. In Property testing lowerbounds via communication complexity, Eric Blais, Joshua Brodyand Kevin Matoulef show how to reduce communication problemsto property testing problems, and so obtain lower bounds for prop-erty testing. The connection is elegant and novel and provides newlower bounds, for example, for testing whether a function is theparity of k-variables, or a k-junta.

I wish to thank the authors of the above papers for acceptingthe invitation to the special issue and for revising their manuscriptswithin a short time frame. I am also grateful to the referees fortheir thorough and timely reviews. Finally, I want to thank OmerReingold and Joachim von zur Gathen for inviting me to edit thisspecial issue.

Anup RaoGuest Editor

cc 21 (2012) Special issue 195

Anup RaoUniversity of Washington,Seattle, WA,USA.anuprao@cs.washington.eduhttp://www.cs.washington.edu/homes/anuprao/