Boolean networks (BNs) are widely used to model the qualitative dynamics of biological systems. Besides the logical rules determining the evolution of each component with respect to the state of its regulators, the scheduling of component updates can have a dramatic impact on the predicted behaviours. In this paper, we explore the use of Read (contextual) Petri Nets (RPNs) to study dynamics of BNs from a concurrency theory perspective. After showing bi-directional translations between RPNs and BNs and analogies between results on synchronism sensitivity, we illustrate that usual updating modes for BNs can miss plausible behaviours, i.e., incorrectly conclude on the absence/impossibility of reaching specific configurations. We propose an encoding of BNs capitalizing on the RPN semantics enabling more behaviour than the generalized asynchronous updating mode. The proposed encoding ensures a correct abstraction of any multivalued refinement, as one may expect to achieve when modelling biological systems with no assumption on its time features.

中文翻译：

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布尔网络中的并发

布尔网络（BN）被广泛用于对生物系统的定性动力学建模。除了确定每个组件相对于其调节器状态的演变的逻辑规则之外，组件更新的计划还可能对预测的行为产生重大影响。在本文中，我们从并发理论的角度探讨了使用Read（上下文）Petri网（RPN）来研究BN的动力学。在显示了RPN和BN之间的双向转换以及关于同步敏感性的结果之间的相似性之后，我们说明了BN的常规更新模式可能会遗漏合理的行为，即，错误地推断出是否缺乏达到特定配置的可能性。我们建议利用RPN语义对BN进行编码，从而实现比广义异步更新模式更多的行为。拟议的编码可确保对任何多值精化进行正确的抽象，正如在不对生物系统的时间特征进行任何假设的情况下对生物系统进行建模所期望的。