LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

Splicing Test Tube Systems 143
to an object in the test tube (which is not an axiom in A) together with an
axiom from Ai. If the resulting object can pass a filter F for some (i, F, j) ∈ D,
then this object may either move from test tube i to test tube j or else remain
in test tube i, otherwise it has to remain in test tube i. The final result of the
computations in σ consists of all terminal objects from MT W ∗ T MT that can be
extracted from any of the n tubes of σ.
We should like to emphasize that for a specific computation we assume all
axioms and all initial objects not to be available in an infinite number of copies,
but only in a number of copies sufficiently large for obtaining the desired result.
2.4 Test Tube Systems Communicating by Splicing
A test tube system communicating by splicing (HTTCS for short) with n test
tubesisaconstructσ,
where
σ =(MW ∗ M,MT W ∗ T MT ,A,I1, ..., In,C)
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. A is a (finite) set of axioms, A ⊆ MW∗M; 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. C is a (finite) set of communication rules of the form (i, r, j) , where 1 ≤ i ≤
n, 1 ≤ j ≤ n, and r is a splicing rule over MW∗M which has to contain
exactly one axiom from A as well as to involve another end-marked string
from MW∗M \ A; moreover, we define R := �
{r} .
(i,r,j)∈C
In the model defined above, no rules are applied in the test tubes themselves;
an end-marked string in test tube i is only affected when being communicated
to another tube j if the splicing rule r in a communication rule (i, r, j) canbe
applied to it; the result of the application of the splicing rule r to the end-marked
string together with the axiom from A which occurs in r is communicated to
tube j. The final result of the computations in σ consists of all terminal objects
from MT W ∗ T MT that can be extracted from any of the n tubes of σ.
We should like to point out that again we avoid (target) conflicts by assuming
all initial objects to be available in a sufficiently large number of copies,
and, moreover, we then assume only one copy of an object to be affected by a
communication rule, whereas the other copies remain in the original test tube.
Obviously, we assume the axioms used in the communication rules to be available
in a sufficiently large number.
i=1