Arithmetical Metabolic P Systems - Foundations on Natural and Artificial Computation - page 287

Table 1. Graphical notations

Symbol Description

In substances

Out substances

In-Out substances

Start substance

· Halt substance

↓

open system input rule λ → a

↓

open system output rule a → λ

substance

membrane

y

s x

y

h

Fig. 2. Limited Subtraction. Note that x contains part of the input and the output.

y . If there is not enough of both molecular species the rule blocks and the input
will be left untouched. Otherwise a proper subtraction x

− y will be left in x .

Note that the rules are unlinked from the Start / Halt signalling substances,

that is, the system needs the In substances to be fed at the same time with

the Start substance. Moreover, after the system has provided the result, the

substances ( x , y ) are likely to be left in state which does not allow to
safely start another computation.
The definition of the MP-Limited-Subtraction is:

In / Out

S = { x, y, s, h }

R Φ

In = { y }

ϕ 1 =1

In / Out = { x }

r 1 : s → h

Start = s

r 2 : xy →∅ ϕ 2 = y

Halt = h

Conditional Construct. The Conditional construct is implemented addressing
the notes mentioned above: the whole network is linked to the sig-

nalling substances and there are clean-up reactions making the system slightly
more complicated but also reusable . Given two alternative biological MP net-
works, one must be chosen depending on the value of a guard. The idea is
therefore to produce two alternative substances used to

Start / Halt

Start the correspond-

ing system (see Fig. 3). Encoding the truth values { true , false } as { 1, 0 } we are

defining the function: