A Formal Framework for Static (Tissue) P Systems

Transition and Halting Modes in (Tissue) P Systems

“…In this section we consider membrane systems as a collection of interacting cells containing multisets of objects like in [5] and [12]. …”

“…The set of all multisets of rules applicable to C is denoted by Appl (Π, C) (a procedural algorithm how to obtain Appl (Π, C) is described in [12]). …”

“…In [12], further restricting conditions on the four basic modes defined above, especially interesting for the minimally parallel transition mode, were considered. The following variant all aset min requires that from all applicable partition at least one rule has to be applied: Definition 6.…”

“…In the original model of membrane systems, the maximally parallel transition mode was used, yet later on also other new transition modes for P systems and tissue P systems have been introduced and investigated, for example, the sequential and the asynchronous transition mode as well as the minimally parallel transition mode (see [6]). In [12], a formal framework for (tissue) P systems capturing the formal features of these transition modes was developed, based on a general model of membrane systems as a collection of interacting cells containing multisets of objects (compare with the models of networks of cells as discussed in [5] and networks of language processors as considered in [7]). Continuing the formal approach started in [12], the k-bounded minimally parallel transition mode (see [13]) was introduced, where at most k rules can be taken from each of the sets of the partitioning of the set of rules used in the minimally parallel transition mode.…”

“…The main parts of notions, definitions, and results presented in the following are taken from [12] and [13] as well as from [3] and [10]. For an introduction to the area of membrane computing we refer the interested reader to the monograph [17], the actual state of the art can be seen in the web [22].…”