Boolean automata networks (aka Boolean networks) are space-time discrete dynamical systems, studied as a model of computation and as a representative model of natural phenomena. A collection of simple entities (the automata) update their 0-1 states according to local rules. The dynamics of the network is highly sensitive to update modes, i.e., to the schedule according to which the automata apply their local rule. A new family of update modes appeared recently, called block-parallel, which is dual to the well studied block-sequential. Although basic, it embeds the rich feature of update repetitions among a temporal updating period, allowing for atypical asymptotic behaviors. In this paper, we prove that it is able to breed complex computations, squashing almost all decision problems on the dynamics to the traditionally highest (for reachability questions) class PSPACE. Despite obtaining these complexity bounds for a broad set of local and global properties, we also highlight a surprising gap: bijectivity is still coNP.

翻译：布尔自动机网络（亦称布尔网络）是时空离散动力系统，既作为计算模型被研究，也被视为自然现象的典型表征。这些简单实体（自动机）根据局部规则更新其0-1状态。网络的动力学对更新模式高度敏感，即自动机施加局部规则的时间调度。近期出现了一类新型更新模式——块并行模式，它与已被深入研究的块序列模式构成对偶关系。尽管基础，该模式嵌入了时间更新周期中重复更新的丰富特性，使得非典型渐近行为成为可能。本文证明，该模式能够孕育复杂计算，将动力学上几乎所有决策问题（针对可达性问题）的系统复杂度压缩至传统最高复杂度类PSPACE。在获得这些局部与全局性质的复杂度边界的同时，我们还揭示了一个令人惊讶的鸿沟：双射性仍属于coNP复杂度类。