Reactive systems \`a la Leifer and Milner, an abstract categorical framework for rewriting, provide a suitable framework for deriving bisimulation congruences. This is done by synthesizing interactions with the environment in order to obtain a compositional semantics. We enrich the notion of reactive systems by conditions on two levels: first, as in earlier work, we consider rules enriched with application conditions and second, we investigate the notion of conditional bisimilarity. Conditional bisimilarity allows us to say that two system states are bisimilar provided that the environment satisfies a given condition. We present several equivalent definitions of conditional bisimilarity, including one that is useful for concrete proofs and that employs an up-to-context technique, and we compare with related behavioural equivalences. We consider examples based on DPO graph rewriting, an instantiation of reactive systems.

翻译： ⁇ a la Leifer 和 Milner 是一个抽象的、绝对的重写框架,它为产生闪烁性和谐提供了一个合适的框架。 这是通过综合与环境的相互作用来实现的。 我们通过两个层次的条件来丰富反应系统的概念: 首先,和先前的工作一样,我们认为规则因应用条件而丰富; 其次,我们调查有条件的两样概念。 有条件的两样性允许我们说两个系统国家是两样的,只要环境满足一个特定条件。 我们提出了几个有条件的两样性等同的定义, 包括一个对具体证据有用的定义, 一种是采用上到正文的方法, 并且我们比较相关的行为等同。 我们考虑基于 DPO 图形重写的例子, 即反应系统的即即时化。