Computing with synthetically engineered bacteria is a vibrant and active field with numerous applications in bio-production, bio-sensing, and medicine. Motivated by the lack of robustness and by resource limitation inside single cells, distributed approaches with communication among bacteria have recently gained in interest. In this paper, we focus on the problem of population growth happening concurrently, and possibly interfering, with the desired bio-computation. Specifically, we present a fast protocol in systems with continuous population growth for the majority consensus problem and prove that it correctly identifies the initial majority among two inputs with high probability if the initial difference is $\Omega(\sqrt{n\log n})$ where $n$ is the total initial population. We also present a fast protocol that correctly computes the NAND of two inputs with high probability. We demonstrate that combining the NAND gate protocol with the continuous-growth majority consensus protocol, using the latter as an amplifier, it is possible to implement circuits computing arbitrary Boolean functions.

中文翻译：

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人口持续增长的分布式计算

用合成工程细菌进行计算是一个充满活力和活跃的领域，在生物生产、生物传感和医学方面有许多应用。由于缺乏鲁棒性和单个细胞内的资源限制，细菌之间通信的分布式方法最近引起了人们的兴趣。在本文中，我们关注人口增长同时发生的问题，并可能干扰所需的生物计算。具体来说，我们在人口持续增长的系统中为多数共识问题提出了一个快速协议，并证明如果初始差异为 $\Omega(\sqrt{n\log n} )$ 其中 $n$ 是总初始种群。我们还提出了一种快速协议，可以高概率正确计算两个输入的 NAND。我们证明了将 NAND 门协议与连续增长多数共识协议相结合，使用后者作为放大器，可以实现计算任意布尔函数的电路。