Rule-based and object-based event structures for membrane systems

We introduce two event structures for basic membrane systems with one membrane. In the rule-based structure an event is given by a single rule application, while in the object-based structure an event is given by the occurrence of a type of resource (in a certain quantity). Both event structures are introduced without the use of fresh names to distinguish between similar events. We discuss causality by using the order relation on the object-based event structure as well as a dependence relation on the rules of the membrane system.