Robust Real-Time Computing with Chemical Reaction Networks
Robust Real-Time Computing with Chemical Reaction Networks
复制标题
化学反应网络的鲁棒实时计算
DOI：
10.1007/978-3-030-87993-8_3
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Rayman, Matthew
中科院分区：
文献类型：
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作者：
Fletcher, Willem;Klinge, Titus H.;Lathrop, James I.;Nye, Dawn A.;Rayman, Matthew
最近对模拟计算的研究引入了计算真实的数的新概念。Huang、Klinge、Lathrop、Li和Lutz定义了用化学反应网络（CRN）实时计算真实的数的概念，引入了类（所有Lyapunov CRN可计算的真实的数的类）和（所有实时CRN可计算的数的类）。在他们的论文中，他们展示了包含的真实的代数数，但留下开放的地方，包括是适当的。在本文中，我们解决了这个开放的问题，并显示。然而，他们对实时计算的定义是脆弱的，因为它对初始条件的扰动很敏感。为了解决这个缺陷，我们进一步要求CRN能够承受这些扰动。这样，我们就得到了一个离散的记忆模型。这种方法有几个好处。首先，有界CRN可以近似地在有限时间内计算值。第二，CRN可以容忍其物种浓度的小扰动。第三，测量CRN的状态只需要与这些近似的精确度成比例的精度。最后，如果CRN只需要有限的内存，这个模型和图灵机在实时仿真下是等价的。
Recent research into analog computing has introduced new notions of computing real numbers. Huang, Klinge, Lathrop, Li, and Lutz defined a notion of computing real numbers in real-time with chemical reaction networks (CRNs), introducing the classes(the class of all Lyapunov CRN-computable real numbers) and(the class of all real-time CRN-computable numbers). In their paper, they show the inclusion of the real algebraic numbersand thatbut leave open where the inclusion is proper. In this paper, we resolve this open problem and show. However, their definition of real-time computation is fragile in the sense that it is sensitive to perturbations in initial conditions. To resolve this flaw, we further require a CRN to withstand these perturbations. In doing so, we arrive at a discrete model of memory. This approach has several benefits. First, a bounded CRN may compute values approximately in finite time. Second, a CRN can tolerate small perturbations of its species’ concentrations. Third, taking a measurement of a CRN’s state only requires precision proportional to the exactness of these approximations. Lastly, if a CRN requires only finite memory, this model and Turing machines are equivalent under real-time simulations.