![]() ![]() $$q_6$$ has transition to $$q_7$$, from there are four ε-transitions to other states, itself included. There are no transition from $$q_0$$ and $$q_1$$, thus both machines die. Anyway, let's look at first input symbolĪ. Therefore, if we would give an empty string, it would accept it. What is more interesting, that one of those states $$q_0$$ is anĪccept state. ![]() Input any symbol and yet ε-NFA is already in 4 states. This is interesting, because we haven't even So, the second level of the tree shows all current states of the machine. That there is an extra ε-transition from state to itself, even state diagrams don't show it. IMPORTANT: When discussing about a set of all possible ε-transitions from the state, it's convenient to think Lastly, to indicate that $$q_0$$ is included in a set of current states, From $$q_1$$ there are two more transitions: one to $$q_2$$, another to $$q_6$$, We create new branch node with a leaf of $$q_1$$. Image 1.0.7: Shows how ε-NFA accepts $$ab$$ string.įirst of all, computation begins at the start state $$q_0$$ (root node). Or we can think of it as 4 parallel machines computing simultaneously. So actually, at the beginning of computationĪutomaton is in 4 states. How should we interpret all those transitions? Let's say automaton's current state is $$q_0$$, then withoutĪny input it transitions to $$q_1$$, from there to $$q_2$$ and $$q_6$$. We can see bunch of ε-transitions: from $$q_0$$ to $$q_1$$, then from $$q_1$$ to both $$q_2$$ and $$q_6$$ and so on. The start state $$q_0$$ is also an accept state. Image 1.0.6: State diagram of ε-NFA recognising language of $$(ab ∪ a)^*$$. Shows a state diagram of ε-NFA which recognises language of $$(ab ∪ a)^*$$. In other words,Ī transition when there are no input symbol at all. Similarly, ε-transition means a state's transition to the next state when input symbol is an empty string. It was used in the base case of $$δ^∗$$įunction $$δ^∗(q, ε) = q$$ to indicate the end of the string. One element of $$Σ^*$$ is an empty string, denoted by $$ε$$. Mentioned Kleene closure $$Σ^*$$, which denotes all the strings over alphabet $$Σ$$. We have already encountered something similar. Thus, NFA can be seen as a special kind of ε-NFA without ε-transitions. I say may have because some ε-NFA don't have, in that case we will call it simply NFA. (Nondeterministic Finite Automaton) which may or may not have ε(read as "epsilon")-transitions.Īs you may guessed, the main difference between NFA and ε-NFA is ε-transitions. ![]()
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