From onbehalfof@manuscriptcentral.com Thu Jun 10 15:37:56 2021 Date: Thu, 10 Jun 2021 18:07:47 +0000 From: Transactions on Human Robotics Interaction Reply-To: ocj@umich.edu To: harold@mun.ca Subject: Transactions on Human-Robot Interaction - Decision on Manuscript ID THRI-2020-0056 10-Jun-2021 Dear Dr. Wareham: Manuscript ID THRI-2020-0056 entitled "Swarm Control for Distributed Construction: A Computational Complexity Perspective" which you submitted to the Transactions on Human-Robot Interaction, has been reviewed. The comments of the reviewer(s) are included at the bottom of this letter. The reviewer(s) have recommended that your manuscript has the potential for publication. Publication of this manuscript would require major revisions to address critical issues raised in the review process. Therefore, I invite you to respond to the reviewer(s)' comments and revise your manuscript. 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If it is not possible for you to submit your revision by this date, we may have to consider your paper as a new submission. Once again, thank you for submitting your manuscript to the Transactions on Human-Robot Interaction and I look forward to receiving your revision. Sincerely, Dr. Odest Chadwicke Jenkins Editor-in-Chief, Transactions on Human-Robot Interaction ocj@umich.edu Editorial Board Comments to Author: Please accept our sincerest apologies for the delay in providing this review feedback, due in part to the global public health situation for COVID-19. In addition, a conflict of interest in the review process was discovered, which necessitated additional time to recruit new reviewers. We greatly appreciate your consideration of ACM THRI for publication of your work. We aim to provide quality and timely review feedback, a goal we continually strive to achieve. This manuscript went through the full review process of ACM THRI. This process included recruiting three external reviews followed by in depth discussion among the editorial board. The comments of the editorial board represents the consensus feedback of the journal. From this consensus opinion, the editorial board is in agreement with the feedback provided by the Associate Editor. The editorial board is interested in this topic and the prospect of publishing a high quality survey that clarifies thought in the area. However, this current manuscript would require major revisions to address critical issues raised in the review process. The editorial board has confidence this manuscript can meet the standards of publication for ACM THRI with a thorough revision that is responsive to the review feedback. In preparing this resubmission, please provide responses to the review feedback, as well as giving specific attention to the items raised by the Associate Editor. The Editors-in-Chief are available to address any points of clarification you may have about this review feedback and its necessary revisions. The Editors-in-Chief are available to address any points of clarification you may have about this review feedback and its necessary revisions. Associate Editor Comments to Author: Senior AE: 1 Comments to the Author: The submission is of significant relevance to the journal, however several significant areas of improvement have been identified by reviewers. We encourage the authors to revise and resubmit the article. Associate Editor: 2 Comments to the Author: This paper seeks to analyze the computational complexity of swarm control. The four well-qualified reviewers express a wide range of opinions about the paper. The reviewers collectively saw value in it. Each reviewer felt that the perspective of computational complexity in human-swarm interaction was welcome, important, and interesting. They feel this is a significant and neglected problem for which additional insights *can be* important to researchers in human-swarm interaction. The reviewers did have a variety of different concerns that I believe should be addressed. First, all reviewers provided a variety of recommendations for making the paper more understandable and assessable. Second, both reviewers 2 and 3 found the paper in its current form to have a rather narrow contribution. They were concerned that the way the proofs were constructed hurt the generality of the results. Reviewer 2 also felt the proofs should be better formulated to “demonstrate the correspondence between its version of the problem & those in the literature.” Third, reviewer 3 was concerned that the paper was not relevant to the HRI community, though reviewers 1 and 2 disagreed with this sentiment (and I agree with them). Finally, reviewer 2 felt that the current paper does not currently express good separation from prior work by the authors. I believe this paper has potential for being published in THRI, but believe the reviewers’ comments need to be addressed thoroughly and satisfactorily before that is possible. Reviewer(s)' Comments to Author: Reviewer: 1 Recommendation: Minor Revision Comments: p4l20: One might argue that poly-time approximate restricted solvability (as characterized by complexity classes such as BPFPT [1] or PPPT [2] can be consider efficient as well! [1] Montoya, J.A., Müller, M.: Parameterized random complexity. Theory of Computing Systems 52, 221-270 (2013) [2] Donselaar, N.: Probabilistic Parameterized Polynomial Time. Proceedings of SOFSEM 2019: 179-191 (2019) p7, l23: So they are part of the problem definition, rather than the input. Can the authors elaborate on their decision to make c1 and c3 constants, rather than inputs in unary notation; and how this might influence the complexity results? p10l41: I do understand the relevance of explicating these results for the intended audience, but they are trivial corollaries of the NP-hardness of these problems and the assumption that P=BPP. I think it is fair to mention implicitly that A4 and A5 are corollaries of widely-believed complexity theoretic assumptions and not necessarily reveal great theoretical insights. p12l45: I was a bit puzzled by this notation. This does mean the same as 'are in XP'? Or am I missing a subtlety? In either case it might be nice to comment on that in a footnote. I do appreciate the consideration of |x|^k and the treatment of sub-linear k as an arguably feasible result. p17l37: Just as an aside here: generalizing to probabilistic models invites using parameters that are not natural numbers (e.g., an error rate) which introduces various interesting consequences for the formal results, but might also generate interesting additional tractability results. Additional Questions: Condense the contribution of the manuscript to 1 sentence maximum: The manuscript contributes novel computational complexity results that show when swarm control can and cannot be tractable. Summarize the contribution, methods, and findings of the manuscript in at least one paragraph.: The manuscript focuses on the computational complexity of various problems related to human control of robot swarms, in particular algorithm selection, environment adaptation and leader selection. The methodology is formal in nature and is based on formalization of concepts and deriving formal properties thereof. The manuscript shows that the problems at hand are intractable in general, and remain intractable despite several constraints on complexity of the problems. About a dozen of different problem parameters are considered, ranging from the maximum number of states a robot can be in to number of two-dimensional cells relevant in the problems. For most combinations or such parameters the problems remain intractable. On as positive note, the authors do show that when specific parameters are constrained the problems enjoy tractable algorithms. Summarize your overall assessment of the manuscript (1 paragraph recommended): In general this is a thorough, well-worked out paper that provides insightful results to swarm robotics theory and practice. While the complexity theoretic framework by necessity requires several simplifying assumptions the results show what the most prominent sources of complexity are in swarm robot control that deny efficient control. Were you able to clearly understand the research from the composition of the manuscript?: Yes Is your working knowledge of the manuscript (to your best understanding) sufficient to approximately reproduce the methods described?: Yes Clarity comments, including any detailed author feedback and justification for the assessment given above: In general the manuscript is well-readible; the appendix by necessity requires detailed knowledge of parameterized complexity theory necessary to verify or replicate the results. In some cases, brevity makes the manuscript less self-contained; see below. Detailed comments: P2l41 this is a very complex sentence, consider breaking it down. On p3l14, it might be good to inform the reader at this point that this notation is not to be understood as 'number of elementary operations as a function of the input size' which would be the traditional computer science interpretation. p3l37 introduces a different concept relative to the cognitive complexity - emphasize to help the reader appreciate that these are different concepts. In p6l39 the symbol '*' appears without formal definition. p8l14: unsure about notation here? p9l25 insert such/these before issues p9l42: I understand the definition, and the c1 constant is needed to cover for 'start-up costs', but I'm a bit unhappy with both the deviation from the traditional (assymptotical) big-Oh definition and the re-use of c1 and c2 here, as I think their interpretation is intuitively different than in (c1,c2) completion. p40l11 note the LaTeX typesetting error in Is the contribution of this manuscript sufficiently distinct from existing work?: Yes If this novelty of this work is not sufficiently distinct, provide at least 3 citations from independent sources that subsume the contribution of this manuscript along with a reasoned justification.: Does the manuscript provide a sufficient accounting and comparison regarding existing relevant research?: Yes Are the contributions of this manuscript a significant non-incremental advancement of the state-of-the-art, including the authors' own work?: Yes Novelty comments, including any detailed author feedback and justification for the assessment given above: The manuscript does build on previous work, notably by the first author, but the author team is novel, focuses on swarm control as a novel problem, and makes novel contributions with respect to parameterized complexity. Were the claims and findings of this manuscript supported in the description of its methods, results, and experimentation?: Yes Are the claimed contributions of the manuscript accurately depicted in its scope?: Yes If the claims and findings of the manuscript are not sufficiently supported, suggest the proper scope of contributions or the proper method for evaluation.: Validity comments, including any detailed author feedback and justification for the assessment given above: abstract, l19: The assumption of deterministic outcomes of actions is of course a very constrained real life situation. Natural extension to stochastic reliability. Did you find the work presented in this manuscript interesting or inspiring intellectually?: Yes Are the findings of this manuscript of significant interest to the advancement of physical robotic systems or autonomous robotic computation?: Yes Are the findings of this manuscript of significant interest to the understanding and/or design of human interaction with robotic systems?: Yes Relevance comments, including any detailed author feedback and justification for the assessment given above: The assessment of the constraints needed to make human control of swarm robot systems feasible is relevant beyond the immediate application area. Are the findings of this manuscript reproducible and/or replicable by an independent researcher or practitioner with reasonable training in human-robot interaction (e.g, a competent graduate student)?: Yes Have the findings of this manuscript already been reproduced and/or replicated by an independent research or practitioner?: No Reproducibility comments, including any detailed author feedback and justification for the assessment given above: The findings are formal, not experimental, in nature and so the reproducibility aspect is not entirely applicable here. If this manuscript were accepted for publication, would you be willing to write a published critique of this work?: Yes Do you affirm this review was performed without the influence of a conflict of interest and in accordance with the policies of the Transactions on Human-Robot Interaction and of the Association for Computing Machinery?: Yes Most ACM journal papers are researcher-oriented. Is this paper of potential interest to developers and engineers?: Maybe Reviewer: 2 Recommendation: Major Revision Comments: This is an important problem. I hope comments, etc. are helpful. Additional Questions: Condense the contribution of the manuscript to 1 sentence maximum: This paper seeks to provide an analysis of the computational complexity of swarm control Summarize the contribution, methods, and findings of the manuscript in at least one paragraph.: The analysis of swarm control was discussed in the context of three types of problems: robot algorithm selection (SelAlg), environmental influence selection (SelEnvInf), and leader selection (SelLead). Providing appropriate input to the swarm was identified as the critical problem. Summarize your overall assessment of the manuscript (1 paragraph recommended): This paper addresses a significant and neglected problem. However, depending solely on a computational complexity analysis, it needs to: demonstrate the correspondence between its version of the problem & those in the literature. The analysis is voluminous but largely recapitulates an earlier paper. Were you able to clearly understand the research from the composition of the manuscript?: No Is your working knowledge of the manuscript (to your best understanding) sufficient to approximately reproduce the methods described?: Yes Clarity comments, including any detailed author feedback and justification for the assessment given above: This paper seeks to provide an analysis of the computational complexity of swarm control. In particular, the analysis was discussed in the context of three types of problems: robot algorithm selection (SelAlg), environmental influence selection (SelEnvInf), and leader selection (SelLead). Unlike conventional analysis of computational complexity for concrete algorithms, the discussion in this paper is based on the abstract combinatorial computation with various swarm control inputs in 2D grid-based environment. Results on the complexity as polynomial-time solvability was provided for each one of the three problems under different parameter settings. The question of what and how much we can expect of human supervised robots is important to HRI because it lets us focus on, and advance the feasible. Some results, such as the advantages of homogeneity and restriction on numbers of algorithms suggest that restrictions in the current state of the field may be more features than bugs. The issues addressed in this paper are important and therefore require close scrutiny. The paper was not technically written and very hard to follow. First, it seems the contribution was built upon the authors’ previous work in [49] and it is unclear what are the main incremental contributions developed in this paper. Moreover, there are no detailed formulations of the three computation problems: algorithm selection, environmental influence selection and leader selection, which should be critical to evaluate the effectiveness of the complexity analysis. The provided discussion also requires a lot of preliminary knowledge from a number of other papers, hence making the paper not self-contained and difficult to read. The authors are strongly encouraged to give more details on the definitions used in the paper and connect the complexity analysis with concrete problem settings and candidate algorithms that help readers to better understand the use case and implications of the contribution. Another primary concern is that most of the proofs are from other existing literature and contextualized with specific values of parameters. Hence the generality of the results is questionable and the reviewer found limited insights from the provided results. Some detailed comments are as follows. - Contribution and problem set-up: By reading over [49], the reviewer found the discussed complexity analysis set-up in this paper is very similar to those in [49] and many results remain the same, e.g. p12 in this paper and p11 in [49]. It is suggested to clearly separate the contribution discussion in the introduction part and elaborate on the incremental contribution compared to [49]. On the other hand, the lack of detailed explanation on the three problem set-up makes it difficult to understand the generality of the complexity analysis. For example, what are the transition model (dynamics) involved in each of the problems and what algorithms to use in order to construct the structure X in an environment? I could not find descriptions of the concrete swarm tasks until I read [49]. It is also unclear why the swarm control should be classified into the three types: algorithm selection, environmental influence selection and leader selection in the way defined in this paper. Common sense is that by switching the robot algorithm for each one of the swarm members, one could demonstrate the diverse roles for the robots (e.g. leader, follower) and the resulting environmental changes based on the position of the robot and the controller being executed. Moreover, in the robot leader selection problem in this paper, only the selected leader will be able to move, which is not the leader selection problem commonly studied in the community. The dependence between swarm members and leader/non-leader agents is not discussed at all, which is supposed to play a key role in the discussion of complexity. For example, as discussed in [22] the consensus swarm algorithm will have O(1) complexity and a robot team with linearly independent robot members will have O(n) complexity. Under the ill-posed problem set-up in this paper, the reviewer found the results very limited compared to other literature in the field, e.g. [22]. - The generality of the results: In the provided parametric results in table 3 and 5 , there are certain specific numbers such as |f| = 38 for SA. 1 and |E_T| =6 for SA. 1. As a formal discussion for computation complexity, why are fixed parameters used in the theoretical reasoning? Another example is the Lemma A.7 in line 41 on page 27. Why is a particular instance with specific value discussed to represent the polynomial-time tractability, e.g. h=2, |Q|=1, d=3, etc.. Almost all of the proofs in the appendix come from other papers with example-based explanations, which to the reviewer is inadequate. - Mathematical notations: there are many notations used in the paper that are duplicate or never properly defined, which prevents the smooth understanding of the underlying concept. For example, in line 34-43 on page 6, what is f, x and *, and what does trigger-formula mean exactly? Is the contribution of this manuscript sufficiently distinct from existing work?: Yes If this novelty of this work is not sufficiently distinct, provide at least 3 citations from independent sources that subsume the contribution of this manuscript along with a reasoned justification.: I do not consider self-citation particularly in a distinct venue where it would not otherwise be noted as 'non-novel' Does the manuscript provide a sufficient accounting and comparison regarding existing relevant research?: Yes Are the contributions of this manuscript a significant non-incremental advancement of the state-of-the-art, including the authors' own work?: Yes Novelty comments, including any detailed author feedback and justification for the assessment given above: Were the claims and findings of this manuscript supported in the description of its methods, results, and experimentation?: Yes Are the claimed contributions of the manuscript accurately depicted in its scope?: Yes If the claims and findings of the manuscript are not sufficiently supported, suggest the proper scope of contributions or the proper method for evaluation.: Validity comments, including any detailed author feedback and justification for the assessment given above: Did you find the work presented in this manuscript interesting or inspiring intellectually?: Yes Are the findings of this manuscript of significant interest to the advancement of physical robotic systems or autonomous robotic computation?: Yes Are the findings of this manuscript of significant interest to the understanding and/or design of human interaction with robotic systems?: Yes Relevance comments, including any detailed author feedback and justification for the assessment given above: Are the findings of this manuscript reproducible and/or replicable by an independent researcher or practitioner with reasonable training in human-robot interaction (e.g, a competent graduate student)?: Yes Have the findings of this manuscript already been reproduced and/or replicated by an independent research or practitioner?: No Reproducibility comments, including any detailed author feedback and justification for the assessment given above: If this manuscript were accepted for publication, would you be willing to write a published critique of this work?: Yes Do you affirm this review was performed without the influence of a conflict of interest and in accordance with the policies of the Transactions on Human-Robot Interaction and of the Association for Computing Machinery?: Yes Most ACM journal papers are researcher-oriented. Is this paper of potential interest to developers and engineers?: Yes Reviewer: 3 Recommendation: Reject Comments: Some more specific comments: - Many (if not most) of the swarm behaviours are based on neighbours’ interaction through communication. Removing communication from the problem is a big piece of what makes robotic swarms, and that is not solely related to communication latency problems... - The authors mention the need to restrict the model to use defined numerical values of c1 and c2, but they don't explain why and how they selected the values 3 and 10. - On pages 9 and 10, many results turn out to be inapplicable to the problem studied... but from the text it isn't clear why these results are quickly discarded. Additional Questions: Condense the contribution of the manuscript to 1 sentence maximum: The authors study in detail the computational complexity of simplified and generalized swarm control schema. Summarize the contribution, methods, and findings of the manuscript in at least one paragraph.: The authors build on their previous work to assess computational complexity of distributed systems and extend the reasoning to swarm control. They suggest that the funding can help future development of swarm controller and swarm interaction design. Their theoretical proofs, based on sound reasoning, lead to the conclusion that human-swarm interaction must be limited : in terms of the number of robots, workspace and/or available behaviours. Summarize your overall assessment of the manuscript (1 paragraph recommended): The reviewer really enjoyed the perspective of computational complexity onto the issues of swarm control. The paper is merely giving an overview of the reasoning, most of the method is available in the appendix. This strategy makes the paper easier to go through, but harder to assess the validity and fundament of the results. Thus, one need to go through the whole appendix in detail and the method is tedious to the non-expert in theoretical computational complexity assessments (as the reviewer). From the limited expertise of the reviewer, the reasoning and results are based on thorough analysis and sound method. However, the topic and method are rather far from the common THRI publications. Furthermore, the conclusions applied to human-swarm interaction are really narrowed and do not bring any major contribution to the field. The reviewer suggests Autonomous Robots or Swarm Intelligence journals as better venue for this work. Were you able to clearly understand the research from the composition of the manuscript?: No Is your working knowledge of the manuscript (to your best understanding) sufficient to approximately reproduce the methods described?: No Clarity comments, including any detailed author feedback and justification for the assessment given above: The level of expertise required to clearly understand the methods and theoretical proofs is pretty high and requires a good grasp of all the theoretical works on which the authors based their work. For instance to cope with concepts that "are widely believed to be true within the Computer Science community". Is the contribution of this manuscript sufficiently distinct from existing work?: Yes If this novelty of this work is not sufficiently distinct, provide at least 3 citations from independent sources that subsume the contribution of this manuscript along with a reasoned justification.: Based on the previous works discussed and the knowledge of the reviewer, this take on swarm control is completly novel. Does the manuscript provide a sufficient accounting and comparison regarding existing relevant research?: Yes Are the contributions of this manuscript a significant non-incremental advancement of the state-of-the-art, including the authors' own work?: Yes Novelty comments, including any detailed author feedback and justification for the assessment given above: Were the claims and findings of this manuscript supported in the description of its methods, results, and experimentation?: No Are the claimed contributions of the manuscript accurately depicted in its scope?: Yes If the claims and findings of the manuscript are not sufficiently supported, suggest the proper scope of contributions or the proper method for evaluation.: The authors claimed to shed light on the real challenge of human-swarm interaction based on the theoretical derivation. The conclusion (to limit the operator degrees of complexity) is nothing new, even if the method to draw this conclusion is new. They use HSI work to show their finding can explain what was already observed. While this strategy is certainly interesting, it limits the scope of applicability of their finding. The reviewer suggests they conduct their own experiment to better support and illustrate their findings. Validity comments, including any detailed author feedback and justification for the assessment given above: Did you find the work presented in this manuscript interesting or inspiring intellectually?: No Are the findings of this manuscript of significant interest to the advancement of physical robotic systems or autonomous robotic computation?: Yes Are the findings of this manuscript of significant interest to the understanding and/or design of human interaction with robotic systems?: No Relevance comments, including any detailed author feedback and justification for the assessment given above: In general, the findings can be useful to the autonomous robotic computation field, but not, in its current state, to the HRI community. Are the findings of this manuscript reproducible and/or replicable by an independent researcher or practitioner with reasonable training in human-robot interaction (e.g, a competent graduate student)?: Yes Have the findings of this manuscript already been reproduced and/or replicated by an independent research or practitioner?: No Reproducibility comments, including any detailed author feedback and justification for the assessment given above: The annex is well detailed to follow step by step the reasoning behind all proofs. Since no experiments were conduct, the purely theoretical results can be reproduce. If this manuscript were accepted for publication, would you be willing to write a published critique of this work?: No Do you affirm this review was performed without the influence of a conflict of interest and in accordance with the policies of the Transactions on Human-Robot Interaction and of the Association for Computing Machinery?: No Most ACM journal papers are researcher-oriented. Is this paper of potential interest to developers and engineers?: No Reviewer: 4 Recommendation: Minor Revision Comments: I report a number of minor edits to fix typos and minor grammar issues: P0:3L38: "designing such systems for tasks." -> remove the period P0:4L17: "Leader Selection (SelAlg)" -> "Leader Selection (SelLead)" P0:9L14: "for all intensive purposes" -> "for all intents and purposes" P0:9L37: "meaning of and patterns in of" -> rephrase P0:10L15: "polynomial-time promise solvable" -> not clear what "promise" means here P0:11L37: "four easily-proven lemmas" -> "four lemmas" P0:17L26: "intractability results" -> add period P0:18L13: "in this endeavor" -> add period P0:18L33: double period at the end of the line Additional Questions: Condense the contribution of the manuscript to 1 sentence maximum: This paper provides a careful analysis of the computational tractability of swarm control, in the context of human-swarm interaction and swarm construction. Summarize the contribution, methods, and findings of the manuscript in at least one paragraph.: The main novelty of this paper is the focus on the computational tractability of the problem of swarm control, as opposed to the more conventional algorithmic analysis. The authors provide a number of fundamental results that show how swarm control is difficult because of the combinatorial explosion of possible control inputs, rather than because of factors such as heterogeneity and timing aspects. The paper includes a discussion of the consequences of the reported results on the power of software tools for robot swarms and on the design of effective human-swarm interfaces. Summarize your overall assessment of the manuscript (1 paragraph recommended): This paper is overall excellent. The authors managed to provide rigorous, important results in an accessible and engaging manner. I particularly appreciated the discussion in Section 4, which offered a much needed tie between the theoretical results discussed in Section 3 and more practical aspects. Were you able to clearly understand the research from the composition of the manuscript?: Yes Is your working knowledge of the manuscript (to your best understanding) sufficient to approximately reproduce the methods described?: Yes Clarity comments, including any detailed author feedback and justification for the assessment given above: The paper is extremely well written. The text is clear and well structured. The content is conducted in rigorous, but accessible manner, and the tone of the paper help making the more theoretical aspects less intimidating for non-theoreticians such as myself. I have a few of suggestions for improvement: 1. A few symbols are used before they are formally defined. For example n at line 13 of page 0:3 and h at line 39 of page 0:4. 2. The meaning of the * symbols at page 0:6, line 39, is not defined and was not clear to me. 3. I appreciate the effort made in Section 1.2 to provide a quick glance at the main results offered in the paper. I enjoyed most of this section, but I found the discussion in the bullet points quite hard to grasp (lines 39-onwards of page 0:6). This was due to the symbols being used before definition, and to the excessively formal tone of the text. I would suggest to provide a more descriptive summary, or at least more verbose one, to make the main points more easily understandable. 4. The title of the paper mentions "distributed construction", but this theme is marginal in the paper. I understood that the construction angle stems from the ability of the robots to modify their surrounding grid cells; however, the paper lacks a dedicated subsection in Section 4 that justifies the use of catchy keywords such as distributed construction. I would suggest the authors to drop these keywords in the title, or to explicitly add a discussion section on this topic. 3. How were the values c1=10 and c2=3 chosen? Is the contribution of this manuscript sufficiently distinct from existing work?: Yes If this novelty of this work is not sufficiently distinct, provide at least 3 citations from independent sources that subsume the contribution of this manuscript along with a reasoned justification.: Does the manuscript provide a sufficient accounting and comparison regarding existing relevant research?: Yes Are the contributions of this manuscript a significant non-incremental advancement of the state-of-the-art, including the authors' own work?: Yes Novelty comments, including any detailed author feedback and justification for the assessment given above: In terms of novelty and incrementality, this paper builds upon previous work by some of the authors, but it is a convincing stand-alone contribution because of the wider and more general results offered. Were the claims and findings of this manuscript supported in the description of its methods, results, and experimentation?: Yes Are the claimed contributions of the manuscript accurately depicted in its scope?: Yes If the claims and findings of the manuscript are not sufficiently supported, suggest the proper scope of contributions or the proper method for evaluation.: Validity comments, including any detailed author feedback and justification for the assessment given above: The paper is theoretical in nature. I have very limited background in the methods used by the authors in this paper, but I could follow the main points of both the results and the proofs. To the best of my understanding, the methodology is sound. Did you find the work presented in this manuscript interesting or inspiring intellectually?: Yes Are the findings of this manuscript of significant interest to the advancement of physical robotic systems or autonomous robotic computation?: Yes Are the findings of this manuscript of significant interest to the understanding and/or design of human interaction with robotic systems?: Yes Relevance comments, including any detailed author feedback and justification for the assessment given above: I found Section 4 of this paper particularly enjoyable and thought-provoking. I am confident this manuscript is likely to become a highly-cited work in our field. Are the findings of this manuscript reproducible and/or replicable by an independent researcher or practitioner with reasonable training in human-robot interaction (e.g, a competent graduate student)?: Yes Have the findings of this manuscript already been reproduced and/or replicated by an independent research or practitioner?: No Reproducibility comments, including any detailed author feedback and justification for the assessment given above: The paper does not provide an experimental evaluation, so in that sense it is not technically reproducible. However, the provided proofs seem correct. If this manuscript were accepted for publication, would you be willing to write a published critique of this work?: No Do you affirm this review was performed without the influence of a conflict of interest and in accordance with the policies of the Transactions on Human-Robot Interaction and of the Association for Computing Machinery?: No Most ACM journal papers are researcher-oriented. Is this paper of potential interest to developers and engineers?: Yes