Symmetry and Autobisimulation

For event structures as a major branch of concurrent models, no one notices their symmetries. It is very likely that someone thinks that symmetry reduction over an event structure can be replaced by the (largest) autobisimulation reduction. We show that, given an event structure, there are some differences between the symmetric quotient model induced by symmetry reduction and the bisimilar quotient model induced by the (largest) autobisimulation. The former is ( interleaving ) bisimulation equivalent and pomset trace equivalent to the original event structure. However, though the latter is bisimulation equivalent to the original, it and its original event structure are not likely pomset trace equivalent.