As a preparation for the Turing computation properties of the chemical concrete machine, in this post I shall explain what multipliers and co-multipliers are.
Basically, multipliers and co-multipliers are molecules which self-multiply. More precisely, in the next figure we see the definition of those:
Here and are molecules from the formalism of the chemical concrete machine and and are labels. The blue arrow means any chemical reaction which is allowed.
Question: by close examination of the previous posts on graphic lambda calculus, can you identify any multiplier? or co-multiplier?
If not, then be patient, because in a future post I shall give plenty examples of those, especially connected with logic.
Further, we shall see that zippers, introduced in Chemical concret machine, detailed (III) , multiply in a very graphic way, kind of like what happens with the DNA of a cell when it divides. Let’s see.
We want to know if a zipper can be a multiplier. In the following figure we see what happens in the presence of DIST enzymes:
The reaction continues:
Now, the zipper multiplied into two zippers, but they are still connected. We need more information about and . Remark that:
In conclusion: if are multipliers and are co-multipliers, then the zipper is a multiplier!