Epsilon closure & automata

Question

I think I do not quite understand the concept of epsilon transitions when determining the language of a non-deterministic automata. For example in this automata:

automata-with-epsilon-transitions

The language is: 'A double sequence of a or a double sequence of b where there is a possibility of a baa sequence'.

But, the word a belongs to the automata too, doesn't it? (also the word b, and aaa and so on...)

You are right, `a,b,aaa,bbb,aa..` are acceptable strings for this automaton, probably the description is not fully correct. — Ilia Maskov, Dec 09 '18 at 18:05
What’s the source of the explanation of the automaton’s language? That looks incorrect to me. — templatetypedef, Dec 10 '18 at 03:24
As written, this NFA accepts (a|b)* -- also it is very unusual to combine epsilon transitions with normal transitions. I think those a,ε and b,ε transitions are probably mistakes. — Matt Timmermans, Dec 10 '18 at 03:39

score 1 · Accepted Answer · answered Dec 10 '18 at 03:33

1

An ε-transition is just a impromptu transition which doesn't consume any input.

When you are in a state which has outgoing ε-transitions it's like being in all of them until the automaton does something which is observable, from here the non determinism. The set of such states is the ε-closure of a state.

According to the layout you can have an arbitrary amount of baa prefixes followed by an arbitrary amount of of as or bs. So:

empty
baa
baabaa
a
aa
ba
abab
baabab
...

answered Dec 10 '18 at 03:33

Jack

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Thank you! i have another question if i may, regarding epsilon transitions- in this picture i sent, if i want to turn it to 'DFA' automata - is their any method that make it happend? – Shelly875 Dec 10 '18 at 15:49
It's always possible to convert a NFA to a DFA, there are multiple algorithms for this, [here](https://en.wikipedia.org/wiki/Powerset_construction)'s one – Jack Dec 10 '18 at 21:59

Epsilon closure & automata

1 Answers1