Dexter Kozen: An Appreciation

Abstract

I have known Dexter for 30 years, which, of course, means that I was 9 when I first met him. At that time, Dexter was already “the man”. Although he was only a few years ahead of me, he had already made his name by independently defining the notion of alternating Turing machines, a deep contribution to complexity theory that made it possible to connect time and space complexity. The results were viewed as so significant that it was already being taught in a graduate course on complexity theory that I attended. Of even more interest to me at the time was Dexter’s work on modal logic, since a large part of my thesis was on dynamic logic. Finding a sound and complete axiomatization for dynamic logic had been an open problem for many years. Krister Segerberg had suggested an obviously sound axiomatization, but couldn’t prove it complete. Rohit Parikh [7] showed that it was indeed complete, but his proof was rather complicated. Dexter then came up with a much simpler proof, one that got at the essence of Rohit’s ideas; this version was published as [6]. The proof is truly beautiful. I have taught it often, and used the ideas in a number of subsequent papers (e.g., [3,4]).