Siphon-Based Deadlock Prevention of Complex Automated Manufacturing Systems Using Generalized Petri Nets
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe article presents a theoretical and methodological review for the prevention of deadlocks in Automated Manufacturing Systems, based on the structure of Petri net models, specifically in the computation of minimal siphons. For each minimal siphon, a monitor place is added along with the corresponding relationships this place must have with the transitions to ensure the system remains deadlock-free. The work builds on the formalization of previous studies and extends it to a subclass of generalized Petri nets.
It is important to note that the paper lacks a more detailed explanation of the theorems and proofs where the extension of their previous work is developed. At first glance, it reads as if it were merely a survey of related works. Therefore, I suggest adding a dedicated section with the formalization and proof of their own results. It is also important to include a comparison of the computational complexity with respect to previous works. This would help to better highlight the theoretical contribution of the paper.
Some comments to enhance your document are described below:
Explain in a general and more detailed way the operation of the system in Figure 7 to give a better interpretation to the model.Line 696 “to” is twice.
Line 1079, that is twice.
Correct “i.e.” by “i.e.,” in all the paper.
REFERENCES
Please add the DOI link in the following references:
1: https://doi.org/10.1109/TSMCA.2011.2147308
2, https://doi.org/10.1007/3-540-61363-3_4
5 : https://doi.org/10.1109/ACCESS.2021.3072892
6. https://theses.hal.science/tel-01288919/
7 : https://doi.org/10.1155/2016/8219424
9 : https://doi.org/10.1002/asjc.801
10: https://doi.org/10.1007/978-1-4615-4493-7_14
12, 14, 15, 18. Those are references are missing in the document corpus.
- https://doi.org/10.1109/TSMCA.2008.2007947
16: https://doi.org/10.1109/TSMCA.2003.820576
17: https://doi.org/10.1109/70.37050020:
- https://doi.org/10.1007/s00170-008-1684-1
- https://doi.org/10.1002/rnc.1421
Correct the reference information from the journal. It does not match the article.
20: https://doi.org/10.1109/TSMCA.2006.878966
23 : https://doi.org/10.1007/978-1-84882-244-3
25: DOI : https://doi.org/10.1093/comjnl/bxl019
26: https://doi.org/10.1137/0201010
28: https://doi.org/10.6688/JISE.2009.25.6.13
29: https://doi.org/10.1109/ROBOT.2005.1570131
30: https://doi.org/10.1109/9.956052
31: https://doi.org/10.1007/BF01438223
32: No DOI was found.
38: https://doi.org/10.1109/ICSMC.1995.538436
39: https://doi.org/10.1109/ACCESS.2018.2868981
41: http://dx.doi.org/10.4236/ica.2011.24036
42: https://doi.org/10.1002/asjc.217
44: https://doi.org/10.1109/COASE.2006.326915
42: DOI: https://doi.org/10.1093/comjnl/bxp081. Revise the order of authors: Yu-Ying Shih; Daniel Chao
43: https://doi.org/10.1093/comjnl/bxp081
45: https://doi.org/10.3390/pr8010021
48: https://doi.org/10.1049/iet-cta:20070399
49: https://doi.org/10.1080/00207721.2013.827257
50: https://doi.org/10.3182/20140514-3-FR-4046.00078
53: https://doi.org/10.1080/0951192X.2013.800233
57: DOI does not find.
63: https://doi.org/10.1007/s10626-012-0132-4
65: https://doi.org/10.1109/TAC.2017.2677859
66: https://doi.org/10.1007/s00170-007-1125-6
68: https://doi.org/10.1109/JAS.2020.1003210
71: https://doi.org/10.1049/iet-cta:20060218
75: https://doi.org/10.3182/20130619-3-RU-3018.00549
76: https://doi.org/10.1016/j.ins.2019.09.018
77: https://doi.org/10.1109/IECON.2004.1431873
78: https://doi.org/10.1109/ICCAIS.2017.8217583
Broken DOI links in the following references
3, ,7, 9, 53, 63, 78, 48
Reference 71 and 74 are duplicated.
Correct reference information:
9: Tricas, F., García-Vallés, F., Colom, J.M., Ezpeleta, J. (2000). An Iterative Method for Deadlock Prevention in FMS. In: Boel, R., Stremersch, G. (eds) Discrete Event Systems. The Springer International Series in Engineering and Computer Science, vol 569. Springer, Boston, MA.
Please revise that all references are cited into the curpus´s paper.
Author Response
Reviewer 3: I suggest adding a dedicated section with the formalization and proof of author´s own results. It is also important to include a comparison of the computational complexity with respect to previous works to see the practical and theorical proposal. This would help to better highlight the theoretical contribution of the paper.
Answer:
(i) The Subsection 1.2 was added to the Introduction
1.2. Aim of the paper
The main aim of this paper is to resolve situations at the AMS control when there exists only a minimal capacity of resources at disposal. In case of OPN models of AMS these are the situations when marking of places representing resources are equal to one. In case of GPN models of AMS these are the situations when marking of the place representing resource, is equal to the weight of the arc, which is greatest out of all weights of arcs directed to output transitions.
In such cases, it is not so much a matter of computational complexity as it is of finding a solution that exists at all when other approaches to its finding fail.
The sub-goal is also to compare the results obtained in such a case with the results obtained using complementary siphons.
While Example 1 demonstrates the case of an OPN model of AMS with limited resources using siphons to prevent deadlocks, Example 2 uses complementary siphons for the same case. By comparing the results in the form of reachability graphs, it was found that the results obtained in Example 1 for deadlock prevention are better than those obtained in Example 2.
As it was mentioned above, this paper is a free continuation of the paper [3], where a case of deadlock prevention of ES3PR model of AMS was presented. Here, five examples are presented. Three of them - Examples 1, 2, 4 concern S3PR kinds of OPN models while remaining two - Examples 3, 5 concern S4PR kinds of GPN models.
(ii) As to the demand of formalization and proof:
The synthesis of results of Theorem 5 proved in [13] and results of the paper [73] was performed. This is explained inside of the Example 1.
Reviewer 3: In Introduction: add, at the end of the section, a paragraph detailing more precisely the contribution in relation to their work in [3] or related works, since those studies present results for OPN and GPN. Describe in more detail what the contribution is.
Answer: There is the corresponding last paragraph in the Subsection 1.2 mentioned above.
Reviewer 3: Line 344- 346, those definitions were previously defined (in basic of Petri nets). Please remove them.
Answer: removed
Reviewer 3: In section “3. Examples of PN Models with a Simpler Structure”, write a brief paragraph explaining why you are introducing that example, what it means “simple structure”?
Answer: There was added the second paragraph into beginning of the Section 4.
Reviewer 3: Line 348-355 remove them, those were defined (definition 6).
Answer: removed
Table 1: Please siphon places should be numerated as in Figure 1. p1,p2, …,p9. instead of p01, p02, to homogenize the notation.
Answer: corrected
Line 439, write a dot at the end of the sentence.
Answer: corrected
Line 462-463 is redundant, from previous definitions.
Answer: corrected
Line 583 and 585 referencing Figure 4, but should be Figure 5. Because Figure 4 only presents the supervisor net.
Answer: corrected
Line 644, please explain in a general way the operation of the system in Figure 7 to give a better interpretation of the model.
Answer: corrected
In the title of figure 9, it should be reference to Figure 8 instead of Figure7.
Answer: corrected
Line 871 and 872, Figure 11 should be Figure 10 instead of Figure 11.
Answer: corrected
Line 696 “to” is twice.
Answer: corrected
Line 1079, that is twice.
Answer: corrected
Correct “i.e.” by “i.e.,” in all the paper.
Answer: corrected
Reviewer 3: In reference section I have the following comments:
Please add the DOI link in the following references: 1: https://doi.org/10.1109/TSMCA.2011.2147308
2, https://doi.org/10.1007/3-540-61363-3_4
5: https://doi.org/10.1109/ACCESS.2021.3072892 6. https://theses.hal.science/tel-01288919/1
7 : https://doi.org/10.1155/2016/8219424
9 : https://doi.org/10.1002/asjc.801
10: https://doi.org/10.1007/978-1-4615-4493-7_14
12, 14, 15, 18 are missing in the document corpus.
- https://doi.org/10.1109/TSMCA.2008.2007947
16: https://doi.org/10.1109/TSMCA.2003.820576
17: https://doi.org/10.1109/70.37050020:
- https://doi.org/10.1007/s00170-008-1684-1
- https://doi.org/10.1002/rnc.1421
Correct the reference information from the journal. It does not match the article.
20: https://doi.org/10.1109/TSMCA.2006.878966
23: https://doi.org/10.1007/978-1-84882-244-3
25: DOI: https://doi.org/10.1093/comjnl/bxl019
26: https://doi.org/10.1137/0201010
28: https://doi.org/10.6688/JISE.2009.25.6.13
29: https://doi.org/10.1109/ROBOT.2005.1570131
30: https://doi.org/10.1109/9.956052
31: https://doi.org/10.1007/BF01438223
32: No DOI was found.
38: https://doi.org/10.1109/ICSMC.1995.538436
39: https://doi.org/10.1109/ACCESS.2018.2868981
41: http://dx.doi.org/10.4236/ica.2011.24036
42: https://doi.org/10.1002/asjc.217
44: https://doi.org/10.1109/COASE.2006.326915
42: DOI: https://doi.org/10.1093/comjnl/bxp081. Revise the order of authors: Yu-Ying Shih; Daniel Chao
43: https://doi.org/10.1093/comjnl/bxp081
45: https://doi.org/10.3390/pr8010021
48: https://doi.org/10.1049/iet-cta:20070399
49: https://doi.org/10.1080/00207721.2013.827257
50: https://doi.org/10.3182/20140514-3-FR-4046.00078
53: https://doi.org/10.1080/0951192X.2013.800233
57: DOI does not find.
63: https://doi.org/10.1007/s10626-012-0132-4
65: https://doi.org/10.1109/TAC.2017.2677859 66: https://doi.org/10.1007/s00170-007-1125-6
68: https://doi.org/10.1109/JAS.2020.1003210 71: https://doi.org/10.1049/iet-cta:20060218
75: https://doi.org/10.3182/20130619-3-RU-3018.00549
76: https://doi.org/10.1016/j.ins.2019.09.018
77: https://doi.org/10.1109/IECON.2004.1431873
78: https://doi.org/10.1109/ICCAIS.2017.8217583
Broken DOI links in the following references
3, ,7, 9, 53, 63, 78, 48
Reference 71 and 74 are the same.
Correct reference information:
9: Tricas, F., García-Vallés, F., Colom, J.M., Ezpeleta, J. (2000). An Iterative Method for Deadlock Prevention in FMS. In: Boel, R., Stremersch, G. (eds) Discrete Event Systems. The Springer International Series in Engineering and Computer Science, vol 569. Springer, Boston, MA.
Please revise that all references are cited into the curpus´s paper.
Answer: corrected
Comment 1: Line 460 missing subsection number.
Response 1: The subsection number was corrected
Comment 2: Figures in line 694 and 695-698 cannot be seen, please verify the correct view
Response 2: These Figures can be seen (TEX file has to be translate to PDF twice in a row)
Comment 3: In Reference 16, DOI it does not correspond to the paper information. Please, correct it.
Response 3: This DOI was corrected
Comment 4: Revise DOI link of reference 38(line 1392).
Response 4: This DOI was revised
Comment 5: Revise link of reference 51, it is broken down (line 1421).
Response 5: This DOI link for reference 51 is not listed in WEB
Comment 6: DOI link for reference 57,60, and 73 are missing. Please add them for those.
Response 6: DOI link for reference 57 is not listed in WEB, DOI links for references 60, 73 were introduced
Comment 7: DOI in reference 80 is broken down (line 1488), please correct it
Response 7: DOI link for reference 80 was introduced
As to quality of Figures and Tables:
All images, except for the state reachability trees, are in 300 DPI quality. The availability those trees are the product of a graphics system that provides them in the stated quality. Unfortunately, this quality cannot be influenced from the outside.
Tables were constructed in the sense of the LaTeX standards for MDPI journals.
Answer: All recommended changes were performed.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe submitted manuscript deals with siphon based deadlock prevention for manufacturing systems specified with Petri nets. The author has already published some papers on the topic, this is the continuation of his research.
The following comments need to be taken into account in the revised version of the paper:
#1: The group of citations [1]-[78] in line 27 is inacceptable. Instead, the author should try to select some representative citations here, or just state that most of the research described in related work use siphons.
(The same applies for group citation in line 42)
#2: Deadlock control is usually realized either by deadlock prevention or deadlock recovery. The author deals here with deadlock prevention, not even mentioning about deadlock recovery, although there are some recent approaches to deadlock recovery with Petri nets (as e.g. https://doi.org/10.3390/app10072332 or 10.1109/INFOTEH53737.2022.9751283). At least a short discussion of the other type of deadlock control should be added.
#3: I would suggest to move the basics of Petri nets to a separate section.
#4: The structure of the paper is a little bit hard to follow. The main contribution of the article is an enormous set of definitions – it is valuable – but then the aim of the paper gets lost.
#5: The related work has to be better described. There are a lot of references that are useful but not commented. The presentation of state-of-the-art is especially important, as it makes it then possible for the reader to place the new contribution within the existing knowledge.
#6: The proposed prevention methods should be clearly introduced. The text placed in Section 5 (Results) would actually fit better earlier – as the introduction of the methods.
#7: The discussion is rather vague and should be extended.
#8: The last sentence of the paper is not clear: “In the future we would like to be paying attention not only to deadlock prevention based on siphons, when the necessity to know all siphons, but also to dedicate ourselves another currents which will appear in this area.”
#9: The section with conclusion is just symbolic. Without the last sentence, it has only two sentences. Must definitely be extended.
Summary: The contribution might be interesting, but the presentation must be improved a lot.
Author Response
Comment #1: The group of citations [1]-[78] in line 27 is inacceptable. Instead, the author should try to select some representative citations here, or just state that most of the research described in related work use siphons.
(The same applies for group citation in line 42)
Answer: This well-founded comment was fulfilled in the whole paper
Comment #2: Deadlock control is usually realized either by deadlock prevention or deadlock recovery. The author deals here with deadlock prevention, not even mentioning about deadlock recovery, although there are some recent approaches to deadlock recovery with Petri nets (as e.g. https://doi.org/10.3390/app10072332 or 10.1109/INFOTEH53737.2022.9751283). At least a short discussion of the other type of deadlock control should be added.
Answer: The following segment was added into the Section Introduction (lines 43-48), where both papers [82], [84] are cited:
It is necessary to notice that there are distinguished three principal strategies how to deal with deadlocks: (i) deadlock detection and recovery [4,81,82,84] - which is used in cases where deadlocks are infrequent and their consequences are not too serious; (ii) deadlock prevention - it imposes restrictions on the interactions among resources and their users to prevent resource requests that may lead to deadlocks; and (iii) deadlock avoidance[13,16,30,31,62,79,81,83] - it grants a resource to a user only if the resulting state is not a deadlock. In this paper only deadlock prevention will be investigated.
Comment #3: I would suggest to move the basics of Petri nets to a separate section.
Answer: The suggestion was fulfilled. The separated section was built – Section 2: Basics of Petri nets. It starts on the page 4. Consequently, numbering of other sections was shifted.
Comment #4: The structure of the paper is a little bit hard to follow. The main contribution of the article is an enormous set of definitions – it is valuable – but then the aim of the paper gets lost.
Answer: Introduced definitions together with proved Lemmas and Theorems represent (create) the theoretical background of the given topic. The sources from which they come are listed directly at their captions. They can help the reader orient himself in the issue.
Of course, it is possible to eliminate some of them, but then the interpretation of the issue will be only rough.
The specific aims of the article are stated in the individual examples. It is necessary to mention Examples 1 and 2, respectively. In the former example is solved the problem how to control the OPN based S3PR model when marking of resource places is strictly prescribed and cannot be changed. It was shown that in spite of the fact that the standard method presented in the Subsection 3.1 (described by Definitions and Theorems introduced there) failed to resolve such problem. By adding further monitor (based on the theory introduced inside of the Example 1) the solution close to optimal was found. In the latter example was shown, that the supervisor synthesized by means of complementary siphons [S] described in the Subsection 3.2 as well as in the Subsection 4.2 and inside of Example 2 itself, is not so effective like that in Example 1. Namely, the state space of the controlled plant is a little bit poorer (more restricted).
Comment #5: The related work has to be better described. There are a lot of references that are useful but not commented. The presentation of state-of-the-art is especially important, as it makes it then possible for the reader to place the new contribution within the existing knowledge.
Answer: The situation was improved (in my opinion), because the state-of-the-art was introduced in the section Introduction and all references were commented there. The references introduced at captions of Definitions, Lemmas and Theorems cannot be commented, because they are facts already proved and published by their authors themselves.
Comment #6: The proposed prevention methods should be clearly introduced. The text placed in Section 5 (Results) would actually fit better earlier – as the introduction of the methods.
Answer; The proposed prevention method for S3PR modelled by OPN is described in details in Example 1 and the defined specific task is resolved there too. The proposed prevention method based on complementary siphons is described in details in Example 2 and the supervisor is synthesized at solution of the same task like in Example 1. The obtained supervisor is compared with that obtained in Example 1. It was shown by comparing reachability graphs that the supervisor obtained in Example 1 is more effective, because it restricts behaviour of controlled plant less. The proposed prevention methods are introduced in details also in further examples.
Comment #7: The discussion is rather vague and should be extended.
Answer: Although the Discussion is not mandatory section in the sense of instructions for the structure of MDPI papers, to satisfy the comment the Discussion was amended and extended.
Comment #8: The last sentence of the paper is not clear: “In the future we would like to be paying attention not only to deadlock prevention based on siphons, when the necessity to know all siphons, but also to dedicate ourselves another currents which will appear in this area.”
Answer: The sentence was amended into: “In the future we would like to be paying attention not only to deadlock prevention when is necessary to know all siphons, but also to dedicate ourselves another trends where is not necessary to know absolute all siphons.”
Moreover, some other sentences were added as to the future works.
Comment #9: The section with conclusion is just symbolic. Without the last sentence, it has only two sentences. Must definitely be extended
Answer: Conclusion was extended for sentences:
Also approaches based on optimization by means of MIP (Mixed-Integer Programming) and MILP (Mixed-Integer Linear Programming) are an interesting area for further research for deadlock prevention. In our opinion the robust deadlock control for AMS seems to be also very perspective. The approach based on extended elementary siphons applicable on GPN models of AMS seems to be very useful too.
Date: August 15, 2025
Reviewer 3 Report
Comments and Suggestions for AuthorsIn Electronics-3816914, authors presented a comprehensive Petri-net-based deadlock prevention framework for complex automated manufacturing systems (AMS). They covered both ordinary (OPN) and generalized (GPN) Petri nets, using siphon theory as the backbone. The methodology was demonstrated on progressively complex net subclasses (S3PR, ES3PR, S4PR) through five examples. The paper is interesting and followings are my comments for authors in Electronics-3816914.
[1]. Some key numeral results can be mentioned or added in the Abstract.
[2]. As there are so many abbreviations in this paper such as SMS, AMS, GPN and so on. Some of them even appear more than once, thus a Nomenclature table is suggested.
[3]. The proposed method remains within the classical siphon monitor framework. It is suggested that the authors clearly point out the theoretical or algorithmic innovations of this article, such as whether new siphon classifications, new monitor construction conditions, or new complexity upper bounds have been proposed? Has the siphon control of a certain type of GPN (such as weighted S4PR) been fully systematized for the first time?
[4]. Sufficient and necessary conditions for the control of ‘weakly dependent siphon’ (Theorem 14) are not discussed and please supplement counterexamples or prove that its necessity is not valid.
[5]. Authors’ introduced algorithm relied on enumerating all SMS, and the number/count of SMS grew exponentially with resources. Please provide the worst-case complexity and discuss how to mitigate it.
[6]. How about the CPU runtime and memory statistics when executing examples?
[7]. Examples in this paper just verified deadlock absence by reachability graphs. Some quantitative metrics can also be considered and analyzed.
Author Response
Answers to comments of the Reviewer 2
Comment [1]: Some key numeral results can be mentioned or added in the Abstract.
Answer: It was done. The next sentence was added to the Abstract.
The principal results are introduced, explained and illustrated in Examples. Key results are introduced especially in Example 1 and Example 2.
Comment [2]: As there are so many abbreviations in this paper such as SMS, AMS, GPN and so on. Some of them even appear more than once, thus a Nomenclature table is suggested.
Answer: The Table 1 was introduced on the page 3. There are explained all of the abbreviations.
Comment [3]: The proposed method remains within the classical siphon monitor framework. It is suggested that the authors clearly point out the theoretical or algorithmic innovations of this article, such as whether new siphon classifications, new monitor construction conditions, or new complexity upper bounds have been proposed? Has the siphon control of a certain type of GPN (such as weighted S4PR) been fully systematized for the first time?
Answer: The specific aims of the article are stated in the individual examples. It is necessary to mention Examples 1 and 2, respectively. In the former example the problem how to control the OPN based S3PR model when marking of resource places is strictly prescribed and cannot be changed. It was shown that in spite of the fact that the standard method presented in the Subsection 3.1 failed to resolve such problem, adding further monitor it was found the solution close to optimal. In the latter example was shown, that the supervisor synthesized by means of complementary siphons [S] is not so effective like that in Example 1.
Comment [4]: Sufficient and necessary conditions for the control of ‘weakly dependent siphon’ (Theorem 14) are not discussed and please supplement counterexamples or prove that its necessity is not valid.
Answer: This Theorem was proved in [23]. Since S4P is well-initially-marked, the controllability of a weakly dependent siphon depends on S1 - Sn only. (N, M0) is said to be well-initially-marked iff for all siphons S from Π, Mmax(S) = M0(S). In the sense of this, several sentences were introduced in the wake of the Theorem 14.
Comment [5]: Authors’ introduced algorithm relied on enumerating all SMS, and the number/count of SMS grew exponentially with resources. Please provide the worst-case complexity and discuss how to mitigate it.
Answer: In this paper siphons and traps were computed by the Matlab based tool GPenSIM elaborated and supported in [37]. No own algorithm for enumeration of siphons was performed.
Comment [6]: How about the CPU runtime and memory statistics when executing examples?
Answer: The CPU runtime and memory statistics at computing siphons in examples of smaller PN models in general were not unfavourable neither on PC with Intel(R)Core(TM)i7-10700CPU@2,96 GHz, 16 GB RAM with Windows 11. At larger PN models in critical cases the Lenovo Think System SD630 v2 + SR670 v2, CPU cores 221184CUDA + 13824 Tensor, 38 TB with CentOS 7.x was at disposal. The measurement of such statistics was not the aim of this paper.
Comment [7]: Examples in this paper just verified deadlock absence by reachability graphs. Some quantitative metrics can also be considered and analysed
Answer: The following text was introduced into the Section 1. Introduction: The deadlock prevention will be in all cases based on siphons. Siphons are [24] closely related to deadlocks. Some authors in older literature e.g. in [85] even identify siphons with deadlocks. Hence, siphons are extensively utilized in analysis and control of deadlocks. To any Petri net unambiguously belongs the reachability tree/graph. Hence, such a tree/graph is very suitable for verifying the deadlock absence. It follows also from Definition 19 introduced below in the Subsection 3.2. In this paper no other quantitative metrics are utilized. Of course, there exist papers - see e.g. [86,87] – where such research is performed. It is based on logical inconsistency measures. Observable PN liveness is analysed in [88]. Some other papers devoted to deadlock detection are presented e.g. in [67] where PN decomposition techniques are applied, in [92], and in [93],[94] where transitive matrix of resource share places is used.
Here, in this paper, in order to verify the deadlock absence, the reachability trees/graphs will be used. There are two reasons for this: (i) Matlab based tool GPenSIM is able to compute and draw the reachability trees; (ii) we have own Petri net simulator able to compute and draw the reachability trees. Just these trees are introduced in the paper.
As to quality of figures: All figures are 300 DPI exclusive of reachability tree figures produced by Petri nets simulator tool. Their quality cannot be influenceable from outside.
Date: August 15, 2025
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe article presents the theoretical and methodological background for the prevention of deadlocks in Automated Manufacturing Systems, based on the structure of Petri net models, specifically in the computation of strict minimal siphons. For each strict minimal siphon, a monitor place is added along with the corresponding relationships with the corresponding monitor place and the making of each monitor is computed to ensure the system remains deadlock-free, that ensures the deadlock prevention for Ordinary Petri Nets and Generalized Petri Nets. The work builds on the formalization of previous studies and extends it to a subclass of generalized Petri nets.
I appreciate, that all comments and recommendations to enhance the paper had been done.
Below, I present some minors mistakes that I fould. Please, revised them carefully.
Line 460 missing subsection number.
Figures in line 694 and 695-698 cannot be seen, please verify the correct view.
In Reference 16, DOI it does not correspond to the paper information. Please, correct it.
Revise DOI link of reference 38(line 1392).
Revise link of reference 51, it is broken down (line 1421).
DOI link for reference 57,60, and 73 are missing. Please add them for those.
DOI in reference 80 is broken down (line 1488), please correct it.
Author Response
Comment 1: Line 460 missing subsection number.
Response 1: The subsection number was corrected
Comment 2: Figures in line 694 and 695-698 cannot be seen, please verify the correct view
Response 2: These Figures can be seen (TEX file has to be translate to PDF twice in a row)
Comment 3: In Reference 16, DOI it does not correspond to the paper information. Please, correct it.
Response 3: This DOI was corrected
Comment 4: Revise DOI link of reference 38(line 1392).
Response 4: This DOI was revised
Comment 5: Revise link of reference 51, it is broken down (line 1421).
Response 5: This DOI link for reference 51 is not listed in WEB
Comment 6: DOI link for reference 57,60, and 73 are missing. Please add them for those.
Response 6: DOI link for reference 57 is not listed in WEB, DOI links for references 60, 73 were introduced
Comment 7: DOI in reference 80 is broken down (line 1488), please correct it
Response 7: DOI link for reference 80 was introduced
As to quality of Figures and Tables:
All images, except for the state reachability trees, are in 300 DPI quality. The availability those trees are the product of a graphics system that provides them in the stated quality. Unfortunately, this quality cannot be influenced from the outside.
Tables were constructed in the sense of the LaTeX standards for MDPI journals.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsI appreciate the efforts of the author to improve paper’s quality. I have no other comments.
Author Response
Reviewer has no comments.
Reviewer 3 Report
Comments and Suggestions for AuthorsAuthors have well addressed my raised comments and accept is recommended.
Author Response
Reviewer has no comments
