LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

144 Franziska Freund, Rudolf Freund, and Marion Oswald
Example 1. The HTTCS (see Figure 1)
� {A, B, Z}{a, b} ∗ {A, B, Z} , {A, B}{a, b} ∗ {A, B} ,C,{AaZ, ZbB} , {AabB} , ∅ �
with the communication rules
1. (1,Aa#Z$A#a, 2) (using the axiom AaZ) and
2. (2,b#B$Z#bB, 1) (using the axiom ZbB)
generates the linear (but not regular) language
� Aa n+1 b n B,Aa n b n B | n ≥ 1 � .
✲ AabB ✲
✎ ☞
✲ ✲
✎ ☞
✍ ✌
✍ ✌
1 Aa#Z$A#a 2 b#B$Z#bB
Fig. 1. Example of an HTTCS.
2.5 P Systems with Splicing Rules Assigned to Membranes
A P system with splicing rules assigned to membranes (PSSRAM for short) is a
construct Π,
where
Π =(MW ∗ M,MT W ∗ T MT ,µ,A0, ..., An,I0, ..., In,R1, ..., Rn)
1. M is a set of markers, W is an alphabet with W ∩ M = ∅;
2. MT ⊆ M is the set of terminal markers and WT ⊆ W is the set of terminal
symbols;
3. µ is a membrane structure (with the membranes labelled by non-negaitive
integers 0, ..., n in a one-to-one manner);
4. A0, ..., An are the sets of axioms assigned to the membranes 0, ..., n, where
Ai ⊆ MW∗M, 0 ≤ i ≤ n; moreover, we define A := n�
Ai;
i=0
5. I0, ..., In are the sets of initial objects assigned to the membranes 0, ..., n,
where Ii ⊆ MW∗M, 0 ≤ i ≤ n; moreover, we define I := n�
Ii and claim
A ∩ I = ∅;
i=0