We Can't Come Close

How close can we come to a parity function when there isn't one?

Consider a group G such that there is no homomorphism f : G → {±1}. In that case, how close can we come to such a homomorphism? We show that if f has zero expectation, then the probability that f(xy) = f(x)f(y), where x, y are chosen uniformly and independently from G, is at most 1/2(1 + 1/ √ d), where d is the dimension of G’s smallest nontrivial irreducible representation. For the alternating...

Automated Debugging: Are We Close

2 Computer Automated Debugging: Are We Close? F or the past 50 years, software engineers have enjoyed tremendous productivity increases as more and more tasks have become automated. Unfortunately, debugging—the process of identifying and correcting a fail-ure's root cause—seems to be the exception, remaining as labor-intensive and painful as it was five decades ago. An engineer or programmer st...

Editorial : We ' ve Come a Long Way but Are We

The two-part article on the development and implementation of a resident classification system for long-term care facilities by Cathy Charles and Corinne Schalm in this issue of the Journal merits special attention. The description of the process and work involved in attempting to develop an equitable funding arrangement for these facilities provides a good example of the contribution applied r...

We Have Come a Long Way

Big Data Conferences, Here We Come!