AI 中文总结
本文针对反应网络，提出因果连续语义与微分符号语义，基于抽象解释生成的布尔迁移图，细化了现有粗糙的定性抽象，可更准确捕捉反应网络的连续时间动态。
AI 中文摘要
反应网络用于建模有限物种集合之间的反应，根据分析类型和所研究的现象，这些网络可关联不同的语义。标准连续语义由基于反应动力学表达式的微分方程组给出，要在该语义下模拟网络，需完全掌握每个反应的动力学定律及每个物种的初始浓度。由于在实验场景中，反应的定量信息可能部分或全部未知，因此面临的挑战是引入仍可应用的新语义。在该方向上，现有技术中针对反应网络的最新方法提出了一种定性抽象，但该抽象过于粗糙，无法正确捕捉随时间变化的连续行为。基于该方法的思路，本文首先为反应网络引入因果连续语义，以捕捉其连续时间动态，同时保留每个迁移内部隐藏的因果关系；随后引入微分符号语义，对因果连续语义下系统的行为进行定性抽象。研究表明，本文基于抽象解释的新方法可生成合适的布尔迁移图，该图对先前方法提供的迁移图进行了细化。
英文摘要
Reaction networks model reactions between a finite set of species. These networks can be associated with different semantics, depending on the type of analysis and the phenomena under study. The standard continuous semantics is given by a system of differential equations based on the kinetic expressions of the reactions. To simulate a network under this semantics, the full knowledge of the kinetic laws of each reaction and the initial concentrations of each species is necessary. Since in empirical settings the quantitative information about the reactions can be partially or totally unknown, the challenge is to introduce new semantics that can still be applied. In this direction, a recent approach in the state of the art concerning Reaction Networks proposes a qualitative abstraction that is too coarse to properly capture the time-course continuous behaviour. Starting from the ideas of this approach, in this paper we first introduce the causal continuous semantics for Reaction Networks to capture their continuous-time dynamics, preserving the causality hidden inside each transition. Later, we introduce the differential sign semantics to abstract in a qualitative way the behaviour of a system under the causal continuous semantics. We show that our new method, based on abstract interpretation, yields appropriate Boolean transition graphs that refine those provided by the previous approach.
