Computing via 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 \(\varOmega (\sqrt{n\log n})\) where n is the total initial population. We also present a fast protocol that correctly computes the Nand of two inputs with high probability. By combining Nand gates with the majority consensus protocol as an amplifier, it is possible to compute arbitrary Boolean functions. Finally, we extend the protocols to several biologically relevant settings. We simulate a plausible implementation of a noisy Nand gate with engineered bacteria. In the context of continuous cultures with a constant outflow and a constant inflow of fresh media, we demonstrate that majority consensus is achieved only if the flow is slower than the maximum growth rate. Simulations suggest that flow increases consensus time over a wide parameter range. The proposed protocols help set the stage for bio-engineered distributed computation that directly addresses continuous stochastic population growth.

通过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\(\varOmega (\sqrt{n\log n })\)其中 n是初始人口总数。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。通过将Nand门与多数共识协议作为放大器相结合，可以计算任意布尔函数。最后，我们将协议扩展到几个生物学相关的设置。我们模拟了嘈杂的Nand的合理实现与工程细菌的门。在具有恒定流出和恒定新鲜培养基流入的连续培养的背景下，我们证明只有当流量低于最大增长率时才能达成多数共识。模拟表明，流在广泛的参数范围内增加了共识时间。提议的协议有助于为直接解决连续随机人口增长的生物工程分布式计算奠定基础。