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According to the comments of reviewers and the author's reply, after comprehensive consideration, it is decided that accept.
[# PeerJ Staff Note - this decision was reviewed and approved by Jyotismita Chaki, a PeerJ Section Editor covering this Section #]
The author successfully fixed the problems I identified in the previous round, and the new additions are appropriate. I recommend acceptance.
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Fine.
Fine.
Fine.
Fine.
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Thank you for the revision based on the comments in my previous review.
I, personally, am not fully convinced with the claim of "helps compose high-quality puzzles" from the text, but judge the current paper satisfies the requirements for the journal publication.
Please follow the reviewers' comments to revise the paper.
Based on the tracked changes, the author successfully fixed all of the problems I found.
However, it seems that the main review pdf file that I'm able to download contains an outdated version of the manuscript.
Regarding the new additions, I have only extremely minor comments:
- "pokers" should be "poker" (or something like "the various variants of poker")
- "In the Method section of this study": the section being referred to is actually titled "Methods"
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3-1) The author claimed (in title and in text) that we can use the results of retrograde analysis for "composing high-quality puzzles". The evidence provided in the paper was that the author found a set of states in which sacrificing move is necessary to win. However, to find those states/moves are usually a part of strongly-solving game. The claim is too strong and misleading if the author does not have other evidences for "composing" puzzles. I simply suggest to remove the claim from the title and the text.
3-2) Some of results should be described more in detail and/or more precisely. For the sizes of output files in lines 318 and 328, show the breakdown (or some reasoning). The author should provide all the seven states taking 147 plies to win, not just saying "two positions with some restricted move", in line 322.
4-1) Lines 212-215: Can we treat repetition correctly if we only consider the states with Black's turn?
4-2) Misc:
- In line 113: f_{square} takes two arguments, m and p (BTW, what is this bar?), but only one argument in the example in the same line.
- In line 115: The same as above. In addition, the function should be f_{direction} not f_{square} in the example.
- In line 126: Where is this p_s defined? I guess it is a position corresponding to the state....
- In line 161: "transition" has no v.t. use.
From the reviewers, I got feedback from two different perspectives. One of the reviewers was dissatisfied with your rebuttal and thought that your reply was not professional enough. But the other two reviewers gave a positive response. Therefore, I think this paper needs to be further modified.
Generally speaking, the reply letter is not professionally written.
Besides, it does not matter whether the journal is online or not. The authors should know the instructions provided by the journal before submission.
Unfortunately, the manuscript’s content and modifications do not live up to the expectations. There is no discussion of their strengths and weaknesses, what the current state of the art actually is, which are the open questions, or which are the most promising future directions. Instead, some introductory (undergraduate level) general information is provided on topics unrelated to each other and simple lists of papers are given, which is not enough for a journal paper. Overall, I fail to see what the contribution of the article is, i.e. how a reader would become wiser.
It is a bit frustrating because the authors lost an opportunity to improve the overall quality of the paper considering previous suggestions. Thus, there is no more to discuss and the reviewer's recommendation is to keep the same comments as the paper is unsuitable for publication.
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The author successfully fixed the problems I identified in the previous round.
It's still unclear to me why there is a vertical bar in the parameter list of function D, but this is a very minor detail.
Regarding the new additions, I have only a minor comment:
In line 125 of the new file (without change tracking), the list of elements should be enclosed in curly braces {} rather than quotation marks.
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I strongly agree with the author's suspicion that the first round's Reviewer 1 has misunderstood what the paper is about, resulting in misguided suggestions regarding the content.
The manuscript has been improved sufficiently.
The manuscript has been improved sufficiently.
The manuscript has been improved sufficiently.
The manuscript has been improved sufficiently.
Modify according to the reviewers' opinions.
[# PeerJ Staff Note: Please ensure that all review comments are addressed in a rebuttal letter and any edits or clarifications mentioned in the letter are also inserted into the revised manuscript where appropriate. It is a common mistake to address reviewer questions in the rebuttal letter but not in the revised manuscript. If a reviewer raised a question then your readers will probably have the same question so you should ensure that the manuscript can stand alone without the rebuttal letter. Directions on how to prepare a rebuttal letter can be found at: https://peerj.com/benefits/academic-rebuttal-letters/ #]
The proposed model is utilized to strongly solve Ostle by retrograde analysis relying on a zero-sum game. The model integrated several techniques such as bit boards and succinct indexable dictionaries significantly reducing the memory consumption in the analyses.
The paper has many concerns that should be considered before publication as follows:
- Paper presentation is not well prepared.
- It is recommended to add a related work section.
- The authors should readapt the introduction organization.
- It is recommended to locate the figures at the top or the bottom of any page.
- The authors have to do enough surveys about the other types of trust models and show the outperforming benefits of the proposed one based on game theory among the other methodologies. The following papers are strongly recommended which extensively show the role of each methodology: https://doi.org/10.1049/iet-wss.2018.5114; https://doi.org/10.1016/j.asoc.2017.07.033; https://doi.org/10.1109/JIOT.2020.2996671; https://doi.org/10.1016/j.asoc.2006.11.002; https://doi.org/10.1109/ISCC.2017.8024586; https://doi.org/10.1016/j.asoc.2009.11.025; https://doi.org/10.1109/ACCESS.2019.2940699
- All the sections should be numbered.
- The letters used above figures are not the same size. All figures should be consistent.
- The authors should move throughout the English structure of the whole manuscript
- Generally speaking, it would be better to use bold notation when you mention a set, while the normal font is used for a scalar value.
- It seems that the authors propose a zero-sum game. Therefore, they should clearly reveal that in both the abstract and introduction.
- The authors mentioned that their game model is based on zero-sum game (two opposing players). Accordingly, the authors should clearly define those players.
- No mathematical analysis is provided.
- It is better for the authors to add a table of notations.
- The authors should clearly define the game parameters e.g., utility function, players’ actions, etc.
- What are the real-world actions of the players?
- It would be better to add a table of the simulation parameters showing the main game parameters, simulation time, etc.
- The authors did not present the proof of the obtained Nash equilibrium and the uniqueness of their optimal solution.
- The author should compare their obtained results based on the proposed mode to the existing ones in the literature to show their enhanced performance.
The English is not perfect, but still easy to comprehend.
Some of the definitions are a bit unclear, listed below.
In line 106 (definition of f_square), I believe you meant to write "source square" instead of "target square".
In lines 106 and 108, in the examples, what is "m3L"? (Did you mean "e3L"?)
In line 108, you accidentally used "f_quare" instead of "f_direction".
Some functions use a vertical bar ("|") in their argument lists; its meaning is not clear.
Functions f_quare and f_direction do not seem to depend on the position.
I fail to see the difference between Theorem 4 and the definition of a checkmate position.
In Theorem 5, the first half of the condition ("m1!=m2") seems redundant (it follows from the second half).
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In lines 365-366, you write "Because the initial position is a draw, such software never loses unless the opponent makes a mistake."
I suspect you meant something like "Because the initial position is a draw, such software never loses. However, it can't win unless the opponent makes a mistake."
The level of English expression and structure of the paper are in general very good.
I just saw a few minor problems with the writing, e.g.
• The first paragraph (lines 23-29) is brief, clumsy and does not read smoothly. The paper could start with a nicer introductory paragraph.
• Figure 1 caption "Another example of position." => "Another example of a position."
• Some section headings are oddly phrased, e.g. "Preliminary about move generation" might be better as "Move generation preliminaries" and "Preliminary about symmetricity" might be better as "Positional Symmetry".
• The word "symmetricity" is used several times. Is this a word? Or do you mean just "symmetry"?
• Line 250 "It is equals" => "it equals"
• Line 367 underscore "_" breaks the URL in my Safari browser.
• The syntax "[0, i)" is unusual but is used consistently in several places (e.g. line 251) so does not seem to be a mistake. I assume that this means the range 0, ..., i-1? This could be stated unless this syntax really is widely used. However, it does get a bit messy and make the text harder to read in places, e.g. "... and [0, |P| x 25)." on line 240.
It's good to see the source code provided for the study. I was surprised that the entire program was implemented as a single .cpp class, but coding style is beyond this review.
The Discussion section is extremely short. I would expect a much longer and more in-depth discussion for a paper of this length.
The key result of the paper – that the initial state is a draw – is buried in page 12 (line 301)! Instead, I would have though that this nice result should be stated more obviously, perhaps in a subsection of its own rather than buried in text on retrograde analysis. Also, I would move the tables that show this result closer to this announcement where they are relevant rather than listing them after the References.
I like the level of detail in which the program is described. Going down to the bit-level to describe the encoding of the game state etc. is useful for others wanting to implement such programs.
I like the extensive use of pseudocode to describe the key aspects of the approach. However, the code might be condensed or simplified in parts, e.g. the similar append operations in lines 6–17 might be better described as a single statement with direction as a parameter.
The section on composing puzzles is interesting but is brief and seems a bit of an afterthought. Some more in-depth discussion is warranted here. Why are such states "interesting"? What defines a good puzzles, in this context and in general? Do the puzzles generated require that the owner make one correct move at each step of their solution, or are they less strict?
The automated puzzle aspect is very interesting and I believe an important benefit of solving a game. Much more could be made of this aspect in the paper.
The research question is not stated outright, but is implied in lines 54–55 and well defined. It is clear what this paper is about.
The theorems and proofs on pages 4 and 5 are useful.
More care should be taken with the terms used. for example, the very first sentence of the Abstract describes Chess as a combinatorial game. If you are thinking of the strict definition of "combinatorial game" provided by Combinatorial Game Theory, then Chess is *not* a combinatorial game as the last move does not always win the game. INstead, you might describe the relevant class of games as "pure strategy board games".
In the Conclusion (lines 370–371), the following statement is made: "Therefore, to solve a wider variety of games at a more detailed level, it is essential to use techniques to reduce memory consumption and computation time for each game." This is indeed a valid point but it seems to come out of nowhere; this point is alluded to briefly in the Introduction but it is an important point that could be made much more strongly. The authors could cite the recent deep learning work from Google DeepMind that achieved superhuman levels of play for complex games such as Go, Chess and Shogi but at the expense of astronomical amounts of computational power. Estimating the huge power consumption required to achieve such results would be an interesting exercise...
I found this paper to be a generally well written and interesting account of solving a recent board game
that should be of benefit to readers. However, the paper ends somewhat abruptly with the puzzle generation, Discussion and Conclusion sections all brief and not sufficient.
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