What does an NFA with epsilon transitions let us do?

Question

I have the following automaton. I am supposed to understand the use of empty transitions through it. NFA with empty transition

I think that the regular expression of this automaton is the following: 0* 1* 2*

I just want to know what this automaton lets us do? in other words what is the use of empty transitions in that case?

That's an epsilon, not a lambda. – Bergi Apr 02 '15 at 00:09 — Bergi, Apr 02 '15 at 00:09

score 4 · Answer 1 · answered Apr 01 '15 at 22:17

You're right, your automaton describes 0*1*2*. q₀ is where it handles a (possibly empty) series of 0s. q₁ is where it handles a (possibly empty) series of 1s. By having an empty transition from q₀ to q₁, no character is needed between the 0s and the 1s.

The empty transition does not let you describe any language that could not be described without it. However, just try reworking your automaton to not use empty transitions. It's possible, but it requires more transitions, it requires making every state a final state, and when you're done, you hopefully see that it makes it more difficult to tell what language is being described.

So the use of empty transitions is that they make your automaton easier to understand.

I am actually not intending to transform this automaton into a DFA, but rather trying to understand the features of a lambda transition. What is special about it, that is not possible to do using a DFA, in general, and specifically in this automaton (graph)? — user1680944, Apr 01 '15 at 22:49
I already answered that (or tried to, anyway): nothing. All regular languages can be described by a NFA with empty transitions, by a NFA without empty transitions, or by a DFA. Those are all equally capable. — , Apr 01 '15 at 22:57

score 3 · Accepted Answer · answered Apr 17 '15 at 06:10

i think u want to know about difference between this..

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and this

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difference is first first automaton accept string of 0,1 and 2 of anything... while second automaton accepts string of 0,1 and 2 of...0 followed by 1,1 followed by 2.... ex. it accepts 012,001122,0012,0112 etc. it won't accept 102,201,0121,0120,0011221.

so empty transitions make it nice and easy...

What does an NFA with epsilon transitions let us do?

2 Answers2