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How do you determine how many different Transition Graphs are over a particular alphabet? For example How many TG's are over the alphabet {x, y}. I am taking a class with a similar question from Daniel I. A. Cohen's book, "Introduction to computer theory." There are plenty of examples of how to create a TG but nothing to determine how many can be created per language. I'm assuming I'm looking for finite amount of TG's? Thank You very much!

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cross-posted on cstheory: mathoverflow.net/questions/71158/transition-graph-per-alphabet –  Kaveh Jul 24 '11 at 23:19
I'm not convinced that this is a question of interest to research mathematicians, as per the faq, which see. Voting to close. –  Gerry Myerson Jul 25 '11 at 5:53

1 Answer 1

Adding a post because I lack the rep to comment.

There is at least one graph per language (assuming a language is a finite or countably infinite set of finite-length words). There will in fact be infinitely many graphs per language. You need to restrict the question further to have interesting answers. Your first question is about the graphs over a given alphabet whereas the comment later is about graphs per language. There are markedly different.

These pages may help (the latter two based on your tags).

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OK sorry my terminology was sloppy. EXAMPLE: How many TG in {x,y}? Or something to that effect. –  trentonknight Jul 25 '11 at 4:54
Many. Or something to that effect. –  Vijay D Jul 25 '11 at 11:10

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