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dissertation's Issues

SH comments

  • page 1, "sequential = inherently sequential??"

    I don't know what this means.

  • page 5, first paragraph, "urgency!?"

    I don't know what this means.

  • page 14, last paragraph, "?" and "does this matter? what does it say really?"

    This has been rephrased in commit ca2a8a6.

  • page 17, "capital G"

    Strunk & White doesn't suggest capitalization after a colon, so I'm leaving this as is.

  • page 18, Defn 2.4.1 "q-CSP?" and "put what is defined here"

    I have added some explanatory sentences in commit 73f687d.

  • page 19, "I don't know regular PCPs very well, especially the newer versions. Nothing to be done but this is not very self-contained."

    I know, but I'm not sure how to fix this.

  • page 19, in step 3 in Lemma 2.4.4 "Where does the NC in PCP^NC come in here? (Say a word about this?) Obvious?"

    I have added an analysis of the efficiency of the algorithm in commit e4b3f72.

  • page 20, "OK: here from quest on last page" and above logarithmic space "polylog? cite?"

    I'm not sure what this is asking.

  • page 22, at graph powering "transitive closure?"

    Added that graph powering is a generalization of transitive closure in commit 455d9cc.

  • page 23, "k and d are constants?"

    I have added quantifiers for these constants in commit 5c0902d.

BH comments

  • page 6, "Should you name them?" and "same"

    I have named the researchers in commit e3846bd.

  • page 8, remove 'The innitialism' and "Initials?"

    Incorporated abbreviation into definition in commit 93638ff.

  • page 9, change 'f in C' to "f in F"

    Fixed in commit 8a951ef.

  • page 12, on Thm 2.2.3 "Proof?"

    Adds an explanatory sentence explaining that the proof is in the preceding paragraph in commit 3f1a498.

  • page 17, "I like this section"

    Cool.

  • page 18, on i_k in {1, ..., n} "I don't understand is n, k? Is it just 1 <= i_k <= n?"

    Replaced confusing quantification with English in commit b1889d8.

  • page 21, on Prop 2.4.5 "good. new?"

    One direction of this was actually false. I have removed the offending direction of the biconditional in commit 685c9a1. Fortunately, it did not affect the results in the section. I have also noted explicitly that this proposition is new and potentially interesting in commit e260884.

  • page 23, "Conclusion, just 2 or 3 sentences"

    Not sure what you wanted here, but I added a concluding sentence and restated the theorem proven in this section in commit 408ad2a.

  • page 25, on Sec. 3.1, Definitions "Should this be earlier?" and on 'natural numbers' "different from earlier where you said positive or nonnegative"

    It seems silly to refactor such a small amount of repeated info from each chapter into its own little section. But I can do it if you think it's better.

  • page 26, "y in I?"

    No, y is a candidate solution, not an instance of the problem.

  • page 28, "????? Do this? Maybe not?"

    I can't read what this says.

  • page 29, 'intermediary' is circled

    I don't know what this means.

  • page 30, "Apx, PTAS, FPTAS, at least one direction"

    I have added a single sentence that states that APX, etc., are our guides when defining ApxNCO, etc. in commit 474af06.

  • page 46, "Aside: I don't remember this problem. What were the challenges to showing completeness?"

    The challenge is I don't how to do it.

  • page 48, on L reductions and MaxSNP "Defined earlier?"

    These were not defined earlier, should I mention that it is just another type of approximation-preserving reduction?

  • page 50, remove first Definitions paragraph "Just give definitions as you need them now"

    See comment about repeated definitions in my response to the comment on page 25 above.

  • page 51, "Multiple definitions in different chapters makes the reader think that the current definition is different. Say things like 'recall the definition of a circuit"

    I'm not sure where exactly you'd like me to say that.

  • page 53, Remove 'Can the lack of ...' "Repetition?" and remove 'In other words' in next sentence

    Fine, removed the extra sentence in commit 20e151d.

  • page 54, on 'the classes para AC^d\uparrow' "Classes?"

    I used the plural here because it is a family of classes, one for each number d, but I don't care too much about this so I have changed it in commit 4598d57.

  • page 55, first sentence of Sec. 4.2.2, "Slightly conversational? but OK"

    I'm not sure what to do about this.

  • page 58, instead of 'take' "takes?"

    This is fixed in commit 198682f.

  • page 60, nonuniformity description "good" and "Do you want to mention ??? between parameter and decision before"

    I can't read what this says.

  • page 61, replace O(log^d m) with O(log^d n)

    This is fixed in commit 65901c1.

  • page 63, circled 'with that is in' ?

    This is fixed in commit a92e6f5.

  • page 66, insert "the problem is" after 'but'

    This is fixed in commit 8e7387b.

  • page 74, circled 'silly' "somewhat trivial?"

    I have removed the word "silly" in commit 00a374d.

  • page 75, "paraEP new?"

    I state that this class is new both at the definition in the introduction to this section.

  • page 78, on 'useful in applications' "example usage?"

    Added reference to a similar function in GAP in commit cc03ab3.

  • page 83, first line of proof "is to" over 'we need' and "rephrase?"

    This is fixed in commit a5340ab.

  • page 93, remove "is" before 'to demonstrate'

    No, this sentence is correct as is.

  • page 94, "More conclusion. I think each chapter needs a few sentences (a small paragraph) of wrapup. Then maybe a 3 paragraph wrap to the thesis. It is repetition but nice."

    What you would call the "conclusion" is part of the "Introduction" section of each chapter. I am confident that this is the best way to present the motivation, findings, and the "so what". (The conclusion is the most important information, so it should be first.) So for the "conclusion", look in the second half of the introduction section in each chapter. For the conclusion of the whole thesis, look in the second half of the "Introduction" chapter.

  • page 101, on CV "Is this enough? the school might want more"

    The dissertation writer's guide is not very specific but these are the only things it says are explicitly required. Here is the relevant section of the guide.

    Both doctoral and master’s degree candidates must include a vita in their work.
    The vita is a short description of your professional life up to the point of being
    awarded your degree. The vita may be written in CV, résumé, or narrative
    format. Include the following basic information: your full name, your year of
    birth (not your birth date), and a contact address (e.g., your department) where
    you expect you can be reached for at least the next 1-­‐‐2 years. A vita may also
    include (but is not limited to) prior education, degrees, awards or honors,
    professional positions held, and publications. Please try to limit the vita to three
    of four pages.

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