13th International Conference on Membrane Computing - MTA Sztaki

2D P colonies
5. when there are three live neighbouring automata - fifty-six eight possible
〈 ⎡ ⎤
S S S
〉
programs for dead as well as live automata ⎣ D e D ⎦ → ⇑; Z → O and
D D D
other fifty-five combinations.
6. when there are four live neighbouring automata - eight possible programs
〈 ⎡ ⎤
S S S
〉
for dead as well as live automata ⎣ S e D ⎦ → ⇑; Z → M and other
D D D
sixty-nine combinations.
7. when there are at least five live neighbouring automata - fifty- eight possible
〈 ⎡
programs for dead as well as live automata ⎣ S S S ⎤
〉
S e S ⎦ → ⇑; Z → M and
∗ ∗ ∗
other fifty-five combinations.
After the execution of one of the above programs, all agents move one step
forward and rewrite one of their objects e to object M (automaton will be dead)
or to object O (automaton will be live). The following programs are for downward
movement and for refreshing the state of an automaton - i.e., the replacement
of the object in the cell for an object in the agent to change the state of the
automaton.
〈 ⎡ ⎣ ∗ ∗ ∗
⎤
〉 〈 ⎡
∗ e ∗ ⎦ → ⇓; O → S ; ⎣ ∗ ∗ ∗
⎤
〉
∗ e ∗ ⎦ → ⇓; M → D ;
∗ ∗ ∗
∗ ∗ ∗
〈e → L; S ↔ S〉 ; 〈e → N; D ↔ S〉 ; 〈S → e; L → e〉 ; 〈S → e; N → e〉 ;
〈e → L; S ↔ D〉 ; 〈e → N; D ↔ D〉 ; 〈D → e; L → e〉 ; 〈D → e; N → e〉 .
It is easy to see that in such a way we can simulate every classical cellular
automaton.
In the third example we discuss the problem of ants.
Example 3. The aim is to construct a 2D P colony that will simulate the movement
of ants in searching for food. The agents - ants - are placed in the home
cell from which they are looking for food. Their search is nondeterministic until
they encounter food or a track. If they find food, they take one piece (one object)
and return by the shortest route to the home cell. They mark this route using a
specific object. If they find the track, they follow it.
Agents in this 2D P colony have so many programs that to list and describe them
takes more than a single sheet of paper. One agent has fifty-seven programs.
We have compiled an agent-ant that was using fifty-seven programs. An agent
explores the environment. If it finds food, it carries one object of food to the
home cell. On the way back it places the object-tag into each cell on the path.
Then, after returning to the food source, the agent carries it to the home cell
again. The configuration with four agents and two paths is shown on the figure
3. When the food source is exhausted, the agent stops If we added an agent
program which would enable it to return to the home cell, follow its marks and
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