Dexter Kozen: A Winning Combination of Brilliance, Depth, and Elegance
نویسنده
چکیده
This is a somewhat non-standard piece about Dexter Kozen, longtime colleague and friend. I am sure that the praise of Dexter’s research will have been sung by many of the people contributing to this volume. I could probably have added my own perspective, talking at length about the enormous impact of his most profound work. For example, the wonderful paper on alternation influenced my work on seemingly unrelated topics years later, in many unexpected ways. However, on second thoughts, I decided to do it a little differently. I’m going to tell you why I decided not to write a paper for this volume in honor of Dexter, but instead to write a laudatio. A paper would have been easy, right? We all do research and write papers, and it shouldn’t be too much of a problem to select a fitting one for the occasion. So, why not? Well, there are two reasons: The first is that any paper I could have written, which would have been in some way relevant to a volume in honor of Dexter Kozen, would have fallen short, in the following sense: Dexter would have read it and would probably have thought: “Oh yea, that’s kind of interesting, and yes, I can see how those proofs go; and, by the way, here is how to continue the work and get far stronger results, and in a much nicer way”. (This is the best case, of course; it could be a lot worse. Dexter sees errors, gaps in proofs, shaky arguments, etc., very quickly...) The second reason is a lot more acute. I simply can’t write a paper befitting this volume, because I stopped doing theory of computation almost twenty years ago. Why? Well, that’s an easy one: It’s Dexter. He’s the one to blame. Let me explain: Dexter Kozen is absolutely amazing! IMHO, he is one of the most brilliant theoretical computer scientists of our generation. But it’s not just his cleverness and depth and the wonderful work he’s been able to produce, but also the unparalleled beauty of his thinking and of the way he goes about doing his research. A work session with Dexter was always a combination of exhilaration and frustration. He had the uncanny ability to bring in, out of the blue, unexpected notions from seemingly unrelated branches of mathematics – often from algebra or topology – which either you’d have never heard of, or you’d have long-forgotten. And these then turned out not only to be relevant but to make everything you wanted to do fall into place, and in a concise, exotically elegant and often stunning way. Such collaboration
منابع مشابه
Brzozowski's Algorithm (Co)Algebraically
We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on the duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to further generalizations. This paper is dedicated to Dexter Kozen on the occasion ...
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