LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

142 Franziska Freund, Rudolf Freund, and Marion Oswald
are objects of the form mwn, where m, n ∈ M, M a set of markers, and w ∈ W ∗
for an alphabet W with W ∩ M = ∅.
A splicing scheme (over end-marked strings) is a pair σ, σ =(MW ∗ M,R) ,
where M is a set of markers, W is an alphabet with W ∩ M = ∅, and
R ⊆ (M ∪{λ}) W ∗ #W ∗ (M ∪{λ})$(M ∪{λ}) W ∗ #W ∗ (M ∪{λ});
#, $ are special symbols not in M ∪W ; R is the set of splicing rules. Forx, y, z ∈
MW ∗ M and a splicing rule r = u1#u2$u3#u4 in R we define (x, y) =⇒r z if and
only if x = x1u1u2x2, y= y1u3u4y2, and z = x1u1u4y2 for some x1,y1 ∈ MW ∗ ∪
{λ} ,x2,y2 ∈ W ∗ M ∪{λ} . By this definition, we obtain the derivation relation
=⇒σ for the splicing scheme σ in the sense of a molecular scheme as defined
above. An extended H-system (or extended splicing system) γ is an extended
molecular system of the form γ =(MW ∗ M,MT W ∗ T MT ,R,A) , where MT ⊆ M
is the set of terminal markers, VT ⊆ V is the set of terminal symbols, and A is
the set of axioms.
2.3 Splicing Test Tube Systems
A splicing test tube system (HTTS for short) with n test tubes is a construct σ,
where
σ =(MW ∗ M,MT W ∗ T MT ,A1, ..., An,I1, ..., In,R1, ..., Rn,D)
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. A1, ..., An are the sets of axioms assigned to the test tubes 1, ..., n, where
Ai ⊆ MW∗M, 1 ≤ i ≤ n; moreover, we define A := n�
Ai;
i=1
4. I1, ..., In are the sets of initial objects assigned to the test tubes 1, ..., n,
where Ii ⊆ MW∗M, 1 ≤ i ≤ n; moreover, we define I := n�
Ii and claim
A ∩ I = ∅;
5. R1, ..., Rn are the sets of splicing rules over MW∗M assigned to the test
tubes 1, ..., n, 1 ≤ i ≤ n; moreover, we define R := n�
Ri; every splicing rule
in Ri has to contain exactly one axiom from Ai (which, for better readability,
will be underlined in the following) as well as to involve another end-marked
string from MW ∗ M \ A;
6. D is a (finite) set of communication relations between the test tubes in σ of
the form (i, F, j) , where 1 ≤ i ≤ n, 1 ≤ j ≤ n, and F is a filter of the form
{A} W ∗ {B} with A, B ∈ M (for any i, j, there may be any finite number of
such communication relations).
In the interpretation used in this section, a computation step in the system
σ run as follows: In one of the n test tubes, a splicing rule from Ri is applied
i=1
i=1