Sigact News Complexity Theory Column 6 Introduction to Complexity Theory Column 6 Guest Column: Semi-membership Algorithms: Some Recent Advances 1

I just attended the 9th Structure in Complexity Theory Conference, which was in Amsterdam this year. 100% of the rst three papers in the proceedings ;?) were devoted to the study of semi-membership algorithms! In fact, during the last half-decade, there has been a marked surge of interest in semi-membership algorithms. The article below surveys some of the recent results from this research area. Though it is hard to pinpoint what triggers research \surges," my own oo-hand guess is that, if one had to put one's nger on a single paper that restarted the interest in semi-membership algorithms, the paper one would nger would be Seinosuke Toda's wonderful 1991 paper Tod91], which set forth tricks (oops... techniques) that are used in many of the subsequent papers. Abstract A semi-membership algorithm for a set A is, informally, a program that when given any two strings determines which is logically more likely to be in A. A urry of interest in this topic in the late seventies and early eighties was followed by a relatively quiescent half-decade. However, in the 1990s there has been a resurgence of interest in this topic. We survey recent work on the theory of semi-membership algorithms.