生命科学的重写理论: CTMC语义学的统一理论（CS LO）

Kappa 生物化学和MD有机化学框架是迄今为止在生命科学中重写理论方法的最为成熟的应用之一。这些类型的重写理论的一个典型特征是必须对要重写的对象实施某些结构约束(一个蛋白质被经验性地发现具有某些特定的位点，一个碳原子最多可以形成四个键，...)。 在本文中，我们为这些类型的重写理论的理论基础做出了贡献，许多概念和技术的发展使得连续时间马尔可夫链(CTMCs)的通用理论能够应用于随机重写。 我们的核心数学概念是一个新颖的规则代数结构，用于在双重和倍半推出语义学中相关的重写规则设置，并通过一个合适的随机力学形式扩展得到模式计数统计的动态演化方程。

原文题目：Rewriting Theory for the Life Sciences: A Unifying Theory of CTMC Semantics

The Kappa biochemistry and the MØD organo-chemistry frameworks are amongst the most intensely developed applications of rewriting theoretical methods in the life sciences to date. A typical feature of these types of rewriting theories is the necessity to implement certain structural constraints on the objects to be rewritten (a protein is empirically found to have a certain signature of sites, a carbon atom can form at most four bonds, ...). In this paper, we contribute to the theoretical foundations of these types of rewriting theory a number of conceptual and technical developments that permit to implement a universal theory of continuous-time Markov chains (CTMCs) for stochastic rewriting systems. Our core mathematical concepts are a novel rule algebra construction for the relevant setting of rewriting rules with conditions, both in Double- and in Sesqui-Pushout semantics, augmented by a suitable stochastic mechanics formalism extension that permits to derive dynamical evolution equations for pattern-counting statistics.

原文作者：Nicolas Behr

原文地址：https://arxiv.org/abs/2003.09395