SIGACT News Complexity Theory Column 72 Lane A. Hemaspaandra Dept. of Computer Science, University of Rochester Rochester, NY 14627, USA Introduction to Complexity Theory Column 72 Small packages. Big packages. Powerful results sometime are established with short proofs. There is a danger here. It is important not to undervalue the contribution just because the proof has a striking simplicity. For example, the Immerman-Szelepcs´nyi Theorem, showing that nice nondetere ministic classes are closed under complementation, has a proof so simple that one can easily convey it not even just handwave it, but decently prove it in a part of a class session, on a single blackboard. But that shouldn t make us forget that before those two theoreticians had (independently) their breakthrough insight, this problem had stumped... well... absolutely everyone. On the other hand, powerful results sometimes are established through long proofs. There is a diï¬erent danger here: that the length of the proof/paper may keep people from learning as much as they would like to about the work and the proof its techniques, insights, and beauties. Happily, sometimes an expert will help us all regarding this second danger. In the area of Xi Chen s survey in this issue, some of the major advances have been achieved through proofs that would (to put it mildly) not ï¬t in full on a single blackboard; warmest thanks to Xi for writing this survey article making more broadly accessible the recent breakthroughs in achieving dichotomy results for counting problems. In the next issue this column will have an article by Dana Moshkovitz, and in the issue after that Bill Gasarch will present here (unless P versus NP has been resolved by then whether by a short proof or a long one I cannot guess) the results of his survey on P versus NP and related issues. ACM SIGACT News December 2011, vol. 42, no. 4
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SIGACT news complexity theory column 72
Hemaspaandra, Lane A.
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, Volume 42 (4)
Association for Computing Machinery – Dec 13, 2011
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