On the Origin of Events: Branching Cells as Stubborn Sets

In prime event structures with binary conflicts (pes-bc)3 a branching cell [1] is a subset of events closed under downward causality and immediate conflict relations. This means that no event outside the branching cell can be in conflict with or enable any event inside the branching cell. It bears a strong resemblance to stubborn sets, a partial order reduction method on transition systems. A stubborn set (at a given state) is a subset of actions such that no execution consisting entirely of actions outside the stubborn set can be in conflict with or enable actions that are inside the stubborn set. A rigorous study of the relationship between the two ideas, however, is not straightforward due to the facts that 1) stubborn sets utilise sophisticated causality and conflict relations that invalidate the stability and coherence of event structures [18], 2) without stability it becomes very difficult to define concepts like prefixes and branching cells, which prerequire a clear notio...

• Type: Journal
• Year: 2011
• Where: APN
• Authors: Henri Hansen, Xu Wang
• Keywords: APN 2011, Artificial Intelligence, Prime Event, Proper Subsets, Stubborn Sets