Howdy! It's been some time since I posted last. Being a graduate student, I don't think it is possible for me to post 3 - 4 times per week without sacrificing the quality of the posts. [Maybe, successful bloggers, like Professor Lance Fortnow, would care to tell me how they manage to cope well with both blogging and academic life.] However, my dear readers, rest assured! I do love posting here, and will try to post at least once a week.
Anyway, I just remembered that Stephen Cook told me some time ago that Michael Taitslin claimed to have a proof that NL is different from P, and at that time Steve was checking his proof. His paper can be found here. I am not quite sure of the progress. Incidentally, when I was in Los Alamos a couple of months back, a complexity theorist briefly looked at the paper and told me that it looks "fishy". Of course, in view of the many fallacious proofs that P != NP claimed by some novices (as discussed in here, people often tend to avoid reading "proofs" of this type of statements. Again, I am not sure of Taitslin's "proof". I read the first few pages, and all I can say is that he definitely uses some logic. One thing I can say though is that he has published some nice results in the areas of database theory and finite model theory in well-known journals and conference proceedings. This gives him some credentials, which perhaps will attract some of the readers to read his manuscript and find subtle bugs in his proof or verify the validity of his proof. In any case, if you decide to do so, please keep me informed :-)