LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

Splicing Test Tube Systems 145
6. R1, ..., Rn are the sets of rules assigned to the membranes 1, ..., n which are
of the form
(or1,or2; r; tar)
for a splicing rule r over MW ∗ M; every splicing rule occurring in a rule in Ri
has to contain exactly one axiom from A as well as to involve another endmarked
string from MW ∗ M \ A; or1,or2 ∈{in, out} indicate the origins
of the objects involved in the application of the splicing rule r, whereas
tar ∈{in, out} indicates the target region the resulting object has to be sent
to, where in points to the region inside the membrane and out points to the
region outside the membrane. Observe that we do not assign rules to the
skin membrane labelled by 0.
A computation in Π starts with the initial configuration with the axioms from
Ak as well as the initial objects from Ik, 1 ≤ k ≤ n, being placed in region k.
We assume all objects occurring in Ak ∪ Ik, 1 ≤ k ≤ n, to be available in an
arbitrary (unbounded) number. A transition from one configuration to another
one is performed by applying a rule from Rk, 1 ≤ k ≤ n. The language generated
by Π is the set of all terminal objects w ∈ MT W ∗ T MT obtained in any of the
membrane regions by some computation in Π.
We should like to emphasize that we do not demand the axioms or initial
objects really to appear in an unbounded number in any computation of Π.
Instead we apply the more relaxed strategy to start with a limited but large
enough number of copies of these objects such that a desired terminal object
can be computed if it is computable by Π when applying the rules sequentially
in a multiset sense; we do not demand things to evolve in a maximally parallel
way. In that way we avoid target conflicts, i.e., the other copies of the strings
involved in the application of a rule (being consumed or generated) just remain
in their regions. This working mode of a P system with splicing rules assigned
to membranes also reflects the sequential way of computations considered in the
models of test tube systems defined above.
3 Splicing Test Tube Systems and Test Tube Systems
Communicating by Splicing Are Equivalent
In this section we show that the splicing test tube systems and the test tube
systems communicating by splicing newly introduced in this paper are equivalent
models for generating end-marked strings.
Theorem 1. For every HTTS we can construct an equivalent HTTCS.
Proof. Let
be an HTTS.
σ =(MW ∗ M,MT W ∗ T MT ,A1, ..., An,I1, ..., In,R1, ..., Rn,D)