Beautiful Structures: An Appreciation of the Contributions of Alan Selman

Abstract

Professor Alan Selman has been a giant in the field of computational complexity for the past forty years. This article is an appreciation, on the occasion of his retirement, of some of the most lovely concepts and results that Alan has contributed to the field. * This appreciation will appear, in slightly different form, in the Complexity Theory Column of the September 2014 issue of SIGACT News.† Supported in part by grant NSF-CCF-1101479.to the field are of such beauty and insight that they are as important to the field's future as they have been to its past and present. Any retirement is bittersweet, but Alan has mentioned that he will be keeping his hand in the field in retirement. That happy fact helped all of us at the celebration focus on the sweet side of the bittersweet event. Warm talks and memories were shared by everyone from the university's president, the department chair, and Alan's faculty colleagues all the way up to the people who are dearest of all to Alan-his postdocs and students.The warmth was no surprise. Alan is not just respected by but also is adored by those who have worked with him. Anyone who knows Alan knows why. Alan is truly kind, shockingly wise, and simply by his nature devoted to helping younger researchers better themselves and the field. But in fact, I think there is more to say-something far rarer than those all too rare characteristics. What one finds in Alan is a true belief in-an absolute, unshakable belief in-the importance of understanding of the foundations of the field. Now, one might think that Alan holds that belief as an article of faith. But my sense is that he holds the belief as an article of understanding. Like all the very, very best theoreticians, Alan has a terrific intuition about what is in the tapestry of coherent beauty that binds together the structure of computation. He doesn't see it all or even most of itno one ever has. But he knows it is there. And in these days when many nontheory people throw experiments and heuristics at hard problems, often without much of a framework for understanding behaviors or evaluating outcomes, not everyone can be said to even know that there is an organized, beautiful whole to be seen. Further, Alan has such a strong sense for what is part of the tapestry that-far more than most people-he has revealed the tapestry's parts and has guided his collaborators and students in learning the art of discovering pieces of the tapestry.And that brings us to the present article and its theme of the beauty of the structures and the structure that Alan has revealed-the notions, the directions, and the theorems. For all of us whose understanding isn't as deep as Alan's, the beauty of Alan's work has helped us to gain understanding, and to know that that tapestry really is out there, waiting to be increasingly discovered by the field, square inch by square inch, in a process that if it stretches beyond individual lifetimes nonetheless enriches the lifetimes of those involved in the pursuit of something truly important. To summarize Alan'...