LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

370 Sergey Verlan
2.3 Distributed Splicing Systems
A communicating distributed H system (CDH system) or a test tube system (TT
system) [1] is a construct
∆ =(V,T,(A1,R1,F1),...,(An,Rn,Fn)),
where V is an alphabet, T ⊆ V (terminal alphabet), Ai are finite languages over
V (axioms), Ri are finite sets of splicing rules over V ,andFi⊆V are finite sets
called filters or selectors, 1≤ i ≤ n.
Each triple (Ai,Ri,Fi), 1 ≤ i ≤ n, is called a component (or tube) of∆.
An n-tuple (L1,...,Ln), Li ⊆ V ∗ ,1≤ i ≤ n, is called a configuration of the
system; Li is also called the contents of ith component. For two configurations
(L1,...,Ln) and(L ′ 1 ,...,L′ n ) we define:
(L1,...,Ln) ⇒ (L ′ 1 ,...,L′ n )iff
L ′ i =
⎛
n�
⎝ σ ∗ j (Lj) ∩ F ∗
⎞ �
⎠ ∪ σ ∗ i (Li)
�
∩ V ∗ n�
��
− ,
L (k+1)
i
j=1
i
F
k=1
∗ k
where σi =(V,Ri) is the H scheme associated with the component i of the
system.
In words, the contents of each component is spliced according to the associated
set of rules like in the case of an H system (splicing step) and the result
is redistributed among the n components according to filters Fi; the part which
cannot be redistributed remains in the component (communication step). If a
string can be distributed over several components then each of them receives a
copy of the string.
We shall consider all computations between two communications as a macrostep,
so macro-steps are separated by communication.
The language generated by ∆ is:
L(∆) ={w ∈ T ∗ | w ∈ L1, ∃L1,...,Ln ⊆ V ∗ :(A1,...,An) ⇒ ∗ (L1,...,Ln)}.
A communicating distributed H system with m alternating filters (CDHF system
or TTF system) is a construct
Γ =(V,T,(A1,R1,F (1)
1 ,...,F (m)
1 ),...,(An,Rn,F (1)
n ,...,F (m)
n )),
where V , T , Ai and Ri are defined as in a communicating distributed H system.
Now instead of one filter Fi for each component i we have an m-tuple of filters
F (r)
i ,1≤ r ≤ m, where each filter F (r)
i is defined as in the above case. At
each macro-step k ≥ 1onlyfilterF (r)
i , r =(k− 1) (mod m) + 1, is active for
component i.
We define:
(L (1)
1 ,...,L(1) n )=(A1,...,An),
⎛
⎞
n�
� �
= ⎝
(r)∗
) ∩ F ⎠ ∪
V ∗ n�
��
−
,k ≥ 1,
j=1
σ ∗ j (L (k)
j
i
σ ∗ i (L (k)
i ) ∩
k=1
F (r)∗
k
where σi =(V,Ri) is the H scheme associated with component i of the system.