The paper begins by highlighting the limitations of current semiconductor-based information technology, such as power inefficiency and environmental sensitivity. It then introduces the concept of molecular computing as a potential alternative, emphasizing its advantages in terms of space and energy efficiency. The authors review existing molecular computing methods, including those based on reaction-diffusion processes (e.g., Belousov-Zhabotinsky reaction) and DNA computing, pointing out their respective limitations, such as complex spatio-temporal signals and temperature sensitivity. The paper then proposes a new approach using acid-base chemistry, arguing that its simplicity, ubiquity, and inherent complementarity make it suitable for encoding binary information (acids representing '0' and bases representing '1'). The core concept is that the majority function, combined with inversion, forms a functionally complete set, allowing for the implementation of any Boolean function. The challenge of realizing a simple chemical inversion operation is addressed by employing a dual-rail encoding scheme, representing data values as complementary pairs (e.g., (acid, base) for '1' and (base, acid) for '0'). This approach simplifies inversion by exchanging the roles of the complementary rails.

The paper reviews existing molecular computing paradigms, highlighting the advantages and disadvantages of each. Reaction-diffusion systems, while offering unique capabilities, suffer from challenges related to spatiotemporal control and sensitivity to environmental factors. DNA computing, despite being widely studied, presents issues concerning temperature sensitivity, computational speed, and the need for complex reagent preparation. The authors note that previous work has explored complementary solutions with different concentrations to represent bits, but this work extends the dual-rail concept to acid-base chemistry, offering a simpler and more universally applicable method.

The proposed methodology centers on the use of strong acids (HX) and strong bases (YOH) that, when mixed, reach an equilibrium governed by three reactions: HX + H₂O → H₃O⁺ + X⁻, YOH → Y⁺ + OH⁻, and H₃O⁺ + OH⁻ → 2H₂O. The neutralization reaction (3) forms the basis of the majority function. The dual-rail encoding scheme represents each bit as a pair of solutions. (Acid, Base) signifies '1', (Base, Acid) signifies '0'. The robotic fluid handler (Echo 550, Beckman Coulter) acts as the system's 'wiring', precisely mixing solutions and transferring them between wells. The methodology includes procedures for encoding data, performing logic operations (AND, OR, NOT, NAND, NOR), and implementing digital circuits like decoders. To avoid neutral pH outputs, a biasing input is added to ensure an odd number of inputs for each gate. Dilution effects from cascaded gates are acknowledged, with manual replacement of intermediate solutions proposed as a simple solution. Future strategies involving pH-sensitive materials are suggested for automated solution renewal. For the neural network implementation, the authors focus on the inference phase using pre-trained binary weights. Images are encoded as sequences of (Acid, Base) or (Base, Acid) pairs, corresponding to pixel values. The weighted sum is computed by mixing the solutions. A pH indicator is used to determine the final output ('1' or '0') based on the resultant pH.

The paper presents experimental results validating the proposed acid-base computing system. A significant finding is the successful implementation of a neural network classifier for MNIST digits (0 and 1). The experimental results using the robotic fluid handler show a near-perfect match (approximately 99% similarity) with the *in silico* simulation. The authors demonstrate the feasibility of their method across various image sizes (8x8, 12x12, 16x16, 28x28) and encoding schemes (binary and 3-bit grayscale). Tables are provided showing high matching accuracy between the experimental acid-base network and the digital simulations across various experimental parameters. The methodology for implementing fundamental digital logic gates (AND, OR, NOT, NAND, NOR) is also demonstrated and visualized using diagrams. A complete 2-bit decoder circuit is implemented, showing the efficacy of cascading the acid-base logic blocks. The runtime of the experiments is analyzed and presented, with detailed breakdown for image encoding and output pooling.

The results demonstrate the potential of acid-base chemistry as a viable approach for implementing both digital circuits and neural networks. The simplicity and speed of acid-base reactions, coupled with the precision of robotic fluid handling, offer a compelling alternative to traditional semiconductor-based methods. The dual-rail encoding elegantly handles the challenge of negation, and the use of readily available materials makes the approach cost-effective and accessible. The high accuracy achieved in both the digital circuit and neural network implementations validates the feasibility of the approach. The authors highlight the potential of incorporating weaker acids and bases to introduce non-linearity and improve the capabilities of the system for supporting more complex computations, such as deep neural networks.

This work successfully demonstrates the use of acid-base chemistry for universal computation, using a robotic fluid handler to perform the complex series of reactions. The dual-rail encoding method effectively solves the problem of negation in chemical computation. Both digital logic circuits and neural network classifiers are successfully implemented with high accuracy. Future research directions involve exploring non-linear chemistries (weaker acids and bases), automated solution renewal mechanisms, and optimization of digital logic design. The proposed encoding and computational methodology could potentially be adapted for use with other binary systems.

The authors acknowledge that the dilution effect in cascaded logic gates is a limitation of the current approach. While a manual replacement of solutions is proposed as a simple solution, future work needs to focus on automating this process. The use of a pH indicator for reading the output introduces a source of error; a more precise method could further improve the accuracy of the results. Finally, the experiments are limited to relatively simple neural network architectures. Extending this to more complex networks with numerous layers remains a challenge.