13th International Conference on Membrane Computing - MTA Sztaki

Time-varying sequential P systems
In the case of string grammars, from the results stated in [6], we obtain the
following, for α ∈ {λ, w}:
RE = L (CF -GC ac ) = L (CF -P ac ) = L (CF -MAT ac )
= L (CF -GC ut ) = L (CF -P ut )
= L (CF -αC (REG) ac
) = L (CF -αC (REG) ut
)
= L (CF -αT V ac ) = L (CF -αT V ut )
L (CF -GC) = L (CF -P ) = L (CF -MAT ) .
Remark 1. We would like to point out that we have not forbidden H C (∅) to
appear in a control word. Whereas in the case of unconditional transfer or in
the case of appearance checking, provided that H C (∅) ∈ F , this just means
that this derivation step is done without making any changes on the underlying
object, in the case of grammars with regular control and without appearance
checking, reaching H C (∅) means that the derivation has to have stopped with
the preceding derivation step.
3 P Systems
In this section we consider several variants of P systems with control languages
guiding the applicability of rules assigned to each membrane at a specific step
of a computation.
A (sequential) P system of type X with n membranes is a construct
Π = (G, µ, R, A, f)
where G = (O, O T , A ′ , P, =⇒ G ) is a grammar of type X and
– µ is the membrane (tree) structure of the system with n membranes (µ
usually is represented by a string containing correctly nested marked parentheses);
we assume the membranes, i.e., the nodes of the tree representing
µ, being uniquely labeled by labels from a set H;
– R is a set of rules of the form (h, r, tar) where h ∈ H, r ∈ P , and
tar, called the target indicator, is taken from the set {here, in, out} ∪
{in j | 1 ≤ j ≤ n}; the rules assigned to membrane h form the set R h =
{(r, tar) | (h, r, tar) ∈ R}, i.e., R can also be represented by the vector
(R h ) h∈H
; for the systems considered in this paper, we do not consider communication
with the environment, i.e., no objects may be sent out from the
skin membrane (the outermost membrane) or taken into the skin membrane
from the environment;
– A is the initial configuration specifying the objects from O assigned to each
membrane at the beginning of a computation, i.e., A = {(h, A h ) | h ∈ H};
– f is the final membrane where the terminal results are taken from at the end
of a computation.
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