马尔可夫链的分子计算
Molecular Computing for Markov Chains
摘要：
在本文中，它提出了一种方法来实现任意构造的时间齐次马尔可夫链与生化系统。不仅离散，而且连续时间马尔可夫链被允许计算。通过采用化学反应网络（CRN）作为可编程语言，分子浓度用于表示输入和输出值。每一个反应网络都是为每一个链精心设计的。物种浓度随时间的演化与目标连续时间马尔可夫链的瞬态解很好地匹配，而平衡浓度可以指示稳态概率。此外，二阶马尔可夫链被认为是实施，而一元的双分子反应。提出了一种将单分子系统编译为DNA链置换反应的新方案，以便于将来的物理实现。提供确定性、随机性和DNA模拟以增强正确性、有效性和可行性。
英文摘要：
In this paper, it is presented a methodology for implementing arbitrarily constructed time-homogenous Markov chains with biochemical systems. Not only discrete but also continuous-time Markov chains are allowed to be computed. By employing chemical reaction networks (CRNs) as a programmable language, molecular concentrations serve to denote both input and output values. One reaction network is elaborately designed for each chain. The evolution of species' concentrations over time well matches the transient solutions of the target continuous-time Markov chain, while equilibrium concentrations can indicate the steady state probabilities. Additionally, second-order Markov chains are considered for implementation, with bimolecular reactions rather that unary ones. An original scheme is put forward to compile unimolecular systems to DNA strand displacement reactions for the sake of future physical implementations. Deterministic, stochastic and DNA simulations are provided to enhance correctness, validity and feasibility.
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