Graphs have nodes connected together by edges, for example (not directed, not in

Question

Graphs have nodes connected together by edges, for example (not directed, not including connecting nodes to themselves, or multiple connections between the same two nodes) 2 graphs exist with 3 nodes, but this number increases acceleratingly with more nodes.

Both programs and graphs can be enumerated using natural numbers (positive integers).

However, what languages or ideas most naturally combine the two?

For example enumerating programs using graphs instead of natural numbers.

Or executing graphs, in other words code described by a graphs shape, instead of by text, and not just a tree shaped graphs, that can for example calculate and return numeric values.

Explanation / Answer

We can summarize your original findings as follows: there is an effective enumeration for programs and graphs. An effective enumeration of a countable set S is a computable bijection between the natural numbers and S, that is, a program P(n) such that S={P(n):n?0} and P(n)?P(m) for n?m.

There are many countable sets which can be effectively enumerated

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.