Well, I was just jotting down (almost completely on the fly—and at too much length, as it turned out), what _actually_ worked by me, in contrast to what “should have.” And among the things which worked for me, going through the chemistry books certainly was one of the most important aspects. It was only when I went through McQuarrie that I began to build some good confidence…

Self-study is different from studying from a teacher in a class-room. Perhaps even more importantly, studying all in isolation with no one to talk to is categorically different from learning with some 10–50 (or even more) class-mates, any one of whom you can always catch at any time to ask doubts, or work out things together….

Another point, what they teach in physics programs is different from the background of the other graduates (like engineers). That’s why, the best or the most suitable texts to follow also happen to be different. May be if I were to be a student majoring in physics in a university, I would have found some other texts to be suitable. But that, actually, was not the case, and I was writing only about my own experience, my own understanding. So, I just wrote what worked by me.

Just one more point. Though I did mention this point, I should have emphasized it even more, namely, that I still have _not_ finished all the books from my list, especially the more advanced ones. It is just that I _have_ read a good deal of them, and I find them neat. In any case, the books I list are the ones I am confident I could definitely come to finish. There were any number of other books on QM (with reportedly excellent credentials) which I did try, but which _I_ couldn’t hope to finish.

Anyway, thanks again!

Best,

–Ajit

]]>Another line of attack for making the many-one reductions weaker is to only allow isomorphisms.

…

I didnâ€™t read those papers yet, but … by Neil Immerman gives a nice survey of those results, which I read for a start.

Immerman’s survey presentation was from Jan 26, 2017. But the subject is actually much wider than I gathered from that survey presentation and the two papers I linked to. There are good recent survey papers which give a better impression how wide that subject really is:

The Isomorphism Conjecture for NP (23 pages)

https://www.cse.iitk.ac.in/users/manindra/survey/Isomorphism-Conjecture.pdf

by Manindra Agrawal – Dec 19, 2009

Investigations Concerning the Structure of Complete Sets (14 pages)

http://ftp.cs.rutgers.edu/pub/allender/isomorphism.pdf

by Eric Allender – 2014

(It should be clear that I didnâ€™t really try to read those texts, and just browsed through them.)

Well, I worked through the survey “Parallel Algorithms” by G. Blelloch and B. Maggs in the meantime, and finished the first quarter of “Thinking in Parallel: Some Basic Data-Parallel Algorithms and Techniques” by U. Vishkin. The terms EREW, CREW, CRCW (E=exclusive, C=concurent, R=read, W=write) are explained, but their detailed relation to NC^{1}, L, NL, SAC^{1}, and AC^{1} is not discussed. I found such a discussion (including the interesting fact that L is in EREW^{1} by viewing L as directed tree reachability) in section 3 “Models of Parallel Computation” of

A Survey of Parallel Algorithms for Shared-Memory Machines (70 pages)

https://www2.eecs.berkeley.edu/Pubs/TechRpts/1988/5865.html

https://www2.eecs.berkeley.edu/Pubs/TechRpts/1988/CSD-88-408.pdf

by Richard M. Karp and Vijaya Ramachandran – March 1988

What I want to say is that I have read Bussâ€™ paper in principle, but didnâ€™t yet work thoroughly enough through section 7, and I donâ€™t understand yet why Buss says (page 10): â€śHowever, we shall use the yet stronger property (c) of deterministic log time reducibility. Although it is not transitive, it is perhaps the strongest possible reasonable notion of reducibility.â€ť Why is DLogTime not transitive?

I worked thoroughly through section 7 in the meantime, and I understand now why DLogTime is not transitive. I also learned to appreciate Emil JeĹ™Ăˇbek’s detailed answer on the fine grained relation between LH and AC0 in this context. (Especially the part: “Additionally, we require that the ATM makes only *one* such query, at the very end of the computation, and returns the answer of the oracle as the result of the computation.”) And I found a later paper by S. Buss on the same subject:

Algorithms for Boolean Formula Evaluation and for Tree Contraction (19 pages)

https://www.math.ucsd.edu/~sbuss/ResearchWeb/Boolean3/paper.pdf

by S Buss – Oct 1991

Those papers would have been easy to find, if…

https://www.math.ucsd.edu/~sbuss/ResearchWeb/Boolean

https://www.math.ucsd.edu/~sbuss/ResearchWeb/Boolean2

https://www.math.ucsd.edu/~sbuss/ResearchWeb/Boolean3