13th International Conference on Membrane Computing - MTA Sztaki

T. Mihálydeák, Z. Csajbók
3 P Systems with Neighborhoods
In this section we focus on hierarchical P systems with communication rules.
3.1 P Systems with Communication (Symport, Antiport) Rules
Definition 5. A membrane structure µ of degree m (m ≥ 1) is a rooted tree
with m nodes identified with the integers 1, . . . , m.
Remark 7. If µ is a membrane structure of degree m, then µ can be represented
by the set R µ , R µ ⊆ {1, . . . , m} × {1, . . . , m}. 〈i, j〉 ∈ R µ means, that there is
an edge from i (parent) to j (child) of tree µ (parent(j) = i).
Definition 6. Let µ be a membrane structure with m nodes and V be a finite
alphabet. The tuple
is a P system if
Π = 〈V, µ, w 0 1, w 0 2, . . . , w 0 m, R 1 , R 2 , . . . , R m 〉
1. w 0 i ∈ MS