Mutual Mobile Membranes Systems with Surface Objects

In this paper we introduce mutual mobile membranes with surface objects, systems which have biological motivation. In P systems with mobile membranes with surface objects, a membrane may enter or exit another membrane. The second membrane just undergoes the action, meaning that it has no control on when the movement takes place. This kind of movement illustrates the lack of an agreement (synchronization) similar to an asynchronous evolution. In mutual mobile membranes with surface objects this aspect is adjusted: any movement takes place only if both participants agree by synchronizing their evolution. In membranes two kinds of competition can occur: resource competition and location competition. Resource competition refers to rules which request the same resources, and the available resources can only be allocated to some of the rules. Location competition refers to the movement of a membrane in the hierarchical structure of the membrane systems under the request of some conflict rules. We use the two variants of membrane systems in order to describe and explain these kinds of competition, and introduce synchronizing objects in mutual mobile membranes which will help to solve the resource and location competitions.