Graphic lambda calculus and chemlambda (IV)

This post continues with chemlambda v2. For the last post in the series see here.

Instead of putting even more material here, I thought it is saner to make a clear page with all details about the nodes and rewrites of chemlambda v2. Down the page there are examples of conflicts.

Not included in that page is the extension of chemlambda v2 with nodes for Turing machines. The scripts have them, in the particular case of a busy beaver machine. You can find this extension explained in the article Turing machines, chemlambda style.

Turing machines appear here differently from the translation technique of Lafont (discussed here, see also these (1), (2) for other relations between interaction combinators and chemlambda). Recall that he proves  prove that interaction combinators are Turing universal by:

  • first proving a different kind of universality among interaction nets, to me much more interesting than Turing universality, because purely graph related
  • then proving that any Turning machine can be turned into an interaction nets graphical rewrite system.

In this extension of chemlambda v2 the nodes for Turing machines are not translated from chemlambda, i.e. they are not given as chemlambda graphs. However, what’s interesting is that the chemlambda and Turing realm can work harmoniously together, even if based on different nodes.

An example is given in the Chemlambda for the people slides, with the name Virus structure with Turing machines, builts itself


but mind that the source link is no longer available, since I deleted the chemlambda g+ collection. The loops you see are busy beaver Turing Machines, the structure from the middle is pure chemlambda.



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