LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

328 Gheorghe Păun
For the reader convenience, the initial configuration of the system, including
the metarules different from (r, here) from the two regions, is pictorially
represented in Figure 1.
1✬
cX1X2 ...Xs
r4,h : h ′′ → h ′′′
r6,h : h ′′′ → α
r7,h : h → Ah ′′
r8,h : cA → cx ′
rX : X → XX
r
2
✬
′ X : X → λ
cXA
r1,h : X → h
r2,h : h → h ′
r3,h : h ′ → h ′′
✫
✫
r4,h : h ′′ → h ′′′
r5,h : ch ′′′ → c#
rB : B ′ → B
r ′ B : B → B
r∞ :#→ #
(r1,h,in)
(r6,h,in)
(r8,h,in)
(r1,h,out)
(r6,h,out)
(r8,h,out)
✩
✩
✪
✪
Figure 1: The P systems with migrating rules from Theorem 1.
The skin region contains the rules X → XX and X → λ for each X ∈ N1;
they can produce any necessary copy of symbols from N1 and can also remove
all such symbols in the end of a computation. The inner region contains a rule
B → B for each B ∈ N2, hence the computation will continue as long as any
symbol from N2 is present.
Assume that we start with a multiset cXw, X ∈ N1,w ∈ (N2 ∪ T ) ∗ in region
2–initially,wehaveherecXA, forXA introduced by the initial matrix of G.
The only possibility (besides rules r ′ B : B → B which we will ignore from now
on)istousearuleoftheformr1,h for some matrix h :(X → α, A → x). We
obtain the object h in region 2, and the rule r1,h goes to region 1.
Assume that in region 1 we have available a copy of X, moreover,weuseit
for applying the rule r1,h; thus,theruler1,h returns to the inner region. At the
same time, in region 2 we use the rule r2,h : h → h ′ .Nowwehavehinregion 1andh ′ in region 2; no nonterminal from N1 is available in region 2, so no rule
of type r1,g,g ∈ H, can be used. Simultaneously, we use now r3,h : h ′ → h ′′ in