生命科學的重寫理論: CTMC語義學的統一理論（CS LO）
- 2020 年 3 月 26 日
- 筆記
Kappa 生物化學和MD有機化學框架是迄今為止在生命科學中重寫理論方法的最為成熟的應用之一。這些類型的重寫理論的一個典型特徵是必須對要重寫的對象實施某些結構約束(一個蛋白質被經驗性地發現具有某些特定的位點，一個碳原子最多可以形成四個鍵，…)。 在本文中，我們為這些類型的重寫理論的理論基礎做出了貢獻，許多概念和技術的發展使得連續時間馬爾可夫鏈(CTMCs)的通用理論能夠應用於隨機重寫。 我們的核心數學概念是一個新穎的規則代數結構，用於在雙重和倍半推出語義學中相關的重寫規則設置，並通過一個合適的隨機力學形式擴展得到模式計數統計的動態演化方程。
原文題目：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
