Chemical Wave Computing from Labware to Electrical Systems

Round 1

Reviewer 1 Report

This paper presents chemical wave computing from labware to electrical systems using memristive system. The quality and novel approach are very very nice. I recommended the accepatance after small change.

I have two minor comments.

In Figure 20, Is it possible to operate at a low turn-on and hold voltage (0.25 V) for real threshold device? No effect of the amplitude of voltage for MemRC cell operation?

In Figure 22, font is very small and in many figures (20, 22), light yellow color cannot be recognized.

Author Response

This paper presents chemical wave computing from labware to electrical systems using memristive system. The quality and novel approach are very very nice. I recommended the acceptance after small change. I have two minor comments.

We thank the Reviewer for his/her encouraging comment and in the following we have tried to address the corresponding comments adequately.

In Figure 20, is it possible to operate at a low turn-on and hold voltage (0.25 V) for real threshold device? No effect of the amplitude of voltage for MemRC cell operation?

The Reviewer makes a nice point here. The mentioned operation is based on real threshold devices; this fact has been appropriately incorporated in the manuscript (page 17, lines 410-412): ”In order to integrate the threshold switching behaviour of the fabricated CBRAM device of [86] in the circuit simulation, a modified version of the VTEAM model [87] has been implemented as described in [85]”. Furthermore, the voltage amplitude effects directly to the MemRC cell oscillation, and more specifically, it is mentioned (page 18, lines 421-422): ”MemRC is continuously oscillating between V_ON and V_OFF”.

In Figure 22, font is very small and in many figures (20, 22), light yellow color cannot be recognized.

In order to comply with the Reviewer’s  comment, we have increased the font size, enlarged the figures and changed the color from light to dark yellow for readability reasons.

Reviewer 2 Report

I have read manuscript entitled “Chemical wave computing from labware to electrical systems” in a fairly detailed fashion. This paper deals with the mathematical simulation of the reaction-diffusion rules that govern the chemical computers and in order to enable a simpler and faster investigation of new logic architectures. Further, memristor-based wave propagating circuits have been designed that mimic the dynamics of the chemical computers. In general, the topic of this manuscript is academically and technologically relevant. However, there exist some points that need to be clarified.

Figure 10 shows the specific values of a modified transmission line circuit model including a memristor (R = 0.01Ω, L = 1mH, C = 10mF). The values for L and C are not even close to the values that are present in modern transmission lines realized in integrated technologies such as microstrip. Why these values? It is completely unclear in the text of the paper whether these values or some others were used in numerical simulations. Also, nothing has been said about the nature of memristors used in numerical simulations. It is completely unexplained how and why logical gates was realized on a 111x50 M-RLC grid with two output channels of 5x50 M-RLC units each. Further, Figure 14 is not mentioned anywhere in the text of the paper.

Generally, the paper is very interesting, but also a little confusingly written to be understandable to the general scientific community, especially to scientists in the field of electronics. Based on the above, I think that manuscript in this version cannot be accepted for publication in Electronics since it needs a major revision.

Author Response

I have read manuscript entitled “Chemical wave computing from labware to electrical systems” in a fairly detailed fashion. This paper deals with the mathematical simulation of the reaction-diffusion rules that govern the chemical computers and in order to enable a simpler and faster investigation of new logic architectures. Further, memristor-based wave propagating circuits have been designed that mimic the dynamics of the chemical computers. In general, the topic of this manuscript is academically and technologically relevant. However, there exist some points that need to be clarified.

We thank the Reviewer for his/her kind comments and in the following we have tried to address the corresponding comments adequately.

Figure 10 shows the specific values of a modified transmission line circuit model including a memristor (R = 0.01Ω, L = 1mH, C = 10mF ). The values for L and C are not even close to the values that are present in modern transmission lines realised in integrated technologies such as microstrip. Why these values? It is completely unclear in the text of the paper whether these values or some others were used in numerical simulations.

In reply to the Reviewer’s comment, we would like to clarify that the objective of this work was not in the first place to propose a circuit favourable in terms of area and power efficiency, but to design a circuit equivalent to the chemical medium, capable of propagating waves that interact with each other in order to emulate the behaviour of chemical computers. Even with these figures of metrics, the proposed hardware implementation surpasses the real processes in a number of figures enabling us to reproduce in a much faster way the corresponding phenomena while taking advantage of the inherent computation abilities of the studied chemical systems. On the other hand, there is no denying that an optimisation of these values is necessary which is already under investigation and will be integrated in a future, enhanced version of the proposed M-RLC circuit. Nevertheless, and in order to comply with the Reviewer’s  comment, we have added properly the following text in the manuscript (page 21, lines 509-513): “The challenges foreseen towards this path include the effect of memristors’ variability to the system’s performance and functionality along with the sizes of the capacitors and inductors, which need further optimisations in order  for the proposed systems to be able to compete in terms of speed with current state of the art classical computing systems.”

Also, nothing has been said about the nature of memristors used in numerical simulations. It is completely unexplained how and why logical gates was realised on a 111 × 50 M-RLC grid with two output channels of 5 × 50 M-RLC units each.

Taking under consideration the Reviewer’s comment regarding the utilized memristor dynamics in the M-RLC, more details have been added respectively to the manuscript (page 11, lines 279-287):

“The utilised memristor model is a behavioural model of a voltage-controlled, threshold-type switching bipolar memristive device implemented in circuit-level [80]. The versatility of this generalised memristor model provides to circuit designers, a powerful tool able to qualitatively reproduce the behaviour of filamentary-based resistance switching, accurately fitting the response of the model to experimental data [81]. The following equations describe the aforementioned memristor’s dynamics:

\textcolor{red}{\begin{equation}
 \dot{r}=\begin{cases}
     a_{Rst}\cdot \frac{V_{Mem}+V_{Rst}}{c+|V_{Mem}+V_{Rst}|} & \text{,} V_{Mem} < V_{Rst}\\
     \beta \cdot V_{Mem} & \text{,} V_{Rst} \leq V_{Mem} \leq V_{Set}\\
     a_{Set} \cdot \frac{V_{Mem}-V_{Set}}{c+|V_{Mem}-V_{Set}|} & \text{,} V_{Mem}>V_{Set}
   \end{cases} \label{eq:r}
\end{equation}
\begin{equation}
 x=x_0\cdot \left(1-\frac{m}{r}\right) \label{eq:state}
\end{equation}
\begin{equation}
 R(x)=\frac{1}{G(x)}=f_0\cdot \frac{e^{2x}}{x} \label{eq:memristance}
\end{equation}}

Further details regarding the model and their parameter selection can be examined in [80].”

Regarding the selection of Boolean logic computation in the proposed M-RLC grid, it should be noticed that Boolean gates have been demonstrated in the chemical examples to showcase the computational capabilities of the chemical medium through the BZ-reaction process. In order to mimic this behaviour and to demonstrate the resemblance in terms of functionality of the proposed circuit to the chemical equivalent, Boolean logic has been selected. Concerning the size of the grid (111 x 50) as well as the current values of RLC (R = 0.01Ω, L = 1mH, C = 10µF), they have been selected this way so as the M-RLC grid to be capable of propagating a sinusoidal wave, as well as for the illustration of the propagating wave to be apparent and distinct during simulation of the medium. Concerning the two output channels (5 x 50), the time difference between the incoming waves in the output channels defines the logical output of the gate, in correspondence to the chemical gates’ output mechanism. The output is true or false depending on whether the propagating waves exit synchronously or asynchronously from the two output channels located on the right of the grid. The  size of the output channels has been set to 5 x 50 in order for the time difference (phase) to be visually clear in the figures of the manuscript. To comply with the Reviewer’s comment, a brief explanation has been added to the manuscript that better explain the functionality of the proposed Boolean gates (page 12, lines 297-301):

“The time difference between the incoming waves in the output channels is remaining constant and defines the logical output of the gate, in correspondence to the chemical gates’ output mechanism. The output is true or false depending on whether the propagating waves exit synchronously or asynchronously from the two output channels located on the right of the grid.”

Further, Figure 14 is not mentioned anywhere in the text of the paper.

In order to comply with the Reviewer’s comment, the corresponding reference to Figure 14 has been added in the main text coloured in red (page 14, line 351).

Generally, the paper is very interesting, but also a little confusingly written to be understandable to the general scientific community, especially to scientists in the field of electronics. Based on the above, I think that manuscript in this version cannot be accepted for publication in Electronics since it needs a major revision.

We thank the Reviewer for her/his comment and for his understanding on the resulting complexity of the manuscript aiming to describe the adaption of chemical wave computing to electrical systems. This attempt requires the review of both labware setups of chemical systems as well as the equivalent implementations in electronic systems and can be considered as a cross-disciplinary topic with unique properties. Following the Reviewers’ comments, we are confident that the current version of this review manuscript has addressed sufficiently the aforementioned issues.

Reviewer 3 Report

The authors presented a comprehensive review of research for the design and simulation of chemical wave computing circuits. Specifically, the authors discuss several classes of circuits with the integration of memristor and consequent wave propagation. Overall, the review delivers a clear summary of trendy chemical wave computing circuit designs, and the structure is well organized. This review will be of broader interest to readers and can be published if the authors can elaborate on the future research directions of chemical wave computing, such as the challenges of implementation in the real world and possible approaches to overcome these challenges.

Author Response

The authors presented a comprehensive review of research for the design and simulation of chemical wave computing circuits. Specifically, the authors discuss several classes of circuits with the integration of memristor and consequent wave propagation. Overall, the review delivers a clear summary of trendy chemical wave computing circuit designs, and the structure is well organised.

We thank the Reviewer for his/her thoughtful remarks on our manuscript.

This review will be of broader interest to readers and can be published if the authors can elaborate on the future research directions of chemical wave computing, such as the challenges of implementation in the real world and possible approaches to overcome these challenges.

Following Reviewer's suggestion, the following paragraphs have been included on discussion section coloured in red, focusing on future perspectives and challenges of chemical wave computing and its electronic analogue (pages 20-21, lines 496-516):
``The potential of chemical systems to perform computations was observed in nature a priori. Even human brains communicate through the diffusion of mediators and neuromodulators. Since the brain's computing capability is exerted by chemical agents, it can be considered as an electrochemical computing system rather than an electrical one. Combining the high speed of modern nanoelectronic chips with the inherent processing power of chemical computing can result in a novel approach to artificial intelligence. Consequently, future research of the wave propagating and oscillating circuits revolves around performing neuromorphic calculations, in order to take advantage of the principles of distributed, parallel, and event-driven operations inherently found in such computational systems. Through the wave propagating behaviour of memristive oscillators, the design of a hardware equivalent to biological nervous system will be thoroughly investigated.

Following the present research results, and from hardware implementation point of view, the fabrication of the suggested MRLC and MRC systems is seen as critical for the next step in electronic-based chemical computing circuits. The challenges foreseen towards this path include the effect of memristors' variability to the system's performance and functionality along with the sizes of the capacitors and inductors, which need further optimisations in order for the proposed systems to be able to compete in terms of speed with current state of the art classical computing systems. Nevertheless these drawbacks are offseted by the distributed and simultaneous operations of these systems which provide fault tolerance and speedup through parallel processing of information. Further modifications to the proposed systems may be needed in order to deal with and overcome the mentioned demands."

All in all, we do appreciate the constructive criticism provided by the handling Editor(s) as well as by the anonymous Reviewers, which allowed us to improve the quality and presentation of our work. We do hope that the revised manuscript meets adequately with the publication criteria of MDPI Electronics journal.

Round 2

Reviewer 2 Report

I suggest accepting the manuscript in present form for publication in Electronics.