生命科学重写理论：CTMC语义学的统一理论
Rewriting Theory for the Life Sciences: A Unifying Theory of CTMC Semantics
摘要：
Kappa生物化学和MPERD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激烈的开发应用之一。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（根据经验发现蛋白质具有特定的位点特征，一个碳原子最多可以形成四个键，......）。在本文中，我们有助于这些类型的重写理论的理论基础的一些概念和技术的发展，允许实现一个通用的理论的连续时间马尔可夫链（CTMCs）的随机重写系统。我们的核心数学概念是一个新的规则代数结构的相关设置重写规则的条件，无论是在双和Sesqui-Pushout语义，增强了一个合适的随机力学形式主义扩展，允许获得动态演化方程的模式计数统计。
英文摘要：
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.
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