13th International Conference on Membrane Computing - MTA Sztaki

D. Sburlan
hence one can gather useful data regarding the proteins interactions in one single
experiment. For example, by shining UV light on the sample, one can visualize
the fine detail of the interior of cells, reflecting the position and the amount of
particular tagged proteins.
Having as inspiration the way by which the behavior of glowing proteins in
a living cell can be externally watched, here we propose a computational model
composed by two independent systems: a standard P system with symbol objects
and multiset rewriting rules (which corresponds to a mathematical model
for the living cell) and a finite state machine with output that observes (changes
its state) and interprets (produces an output action) the computation of the P
system. A related model was introduced in [2] and since then a similar idea was
applied for many types of abstract machines (see [4], [1], and [3]). However, here
the observation is performed from a different perspective. Firstly, we assume that
given a nano-computing bio-device, which operates at the level of bio-reactions,
it will be very difficult to count the number of objects in a given configuration.
Consequently, the original method for collecting the results of a successful
computation will be hard to be implemented. Instead, we believe that it will
be much easier to detect the increasing/decreasing of the number of objects in
consecutive configurations. More precisely, we are interested by the changes that
appear between consecutive configurations (and not by the apparition of certain
symbols as in the cases studied in the existing literature).
2 Background
We presume the reader to be aware of the basic knowledge from formal language
theory, theory of computation, and membrane computing field (see [6], [7] for
the classical theory of formal languages and [5], [9], and [10] for the theory of
membrane computing). Here we will only recall several concepts and results
which are related strictly to what will be further presented.
We denote by F IN, REG, CF , CS, and RE the families of finite, regular,
context-free, context-sensitive, and recursively enumerable languages, respectively.
The Chomsky hierarchy states that F IN ⊂ REG ⊂ CF ⊂ CS ⊂ RE.
If F L is a family of languages then we denote by NF L the family of length
sets of languages in F L. In terms of length sets, the Chomsky hierarchy is
NF IN ⊂ NREG = NCF ⊂ NCS ⊂ NRE.
Generalized Sequential Machines
The family of regular languages REG is equal with the family of languages
accepted by finite state machines.
Generalized sequential machines (GSM) are finite state machines with output.
More formally, a GSM is a tuple M = (Q, Σ, ∆, δ, q 0 , F ) where Q is the state
set, Σ is the input alphabet, ∆ is the output alphabet, δ : Q × Σ → P(Q × ∆ ∗ )
is the transition function, q 0 ∈ Q is the initial state, and F ⊆ Q is the set of
final states. In order to describe the functioning of M, the transition function δ
can be extended to a function on Q × Σ ∗ as follows:
408