$\epsilon$-NFA can be illustrated using diagrams like it was the case for the DFA and the NFA.

Please note that the $\epsilon$-NFA are more general than NFA. Their definition include NFA as a special case. Of course, also the DFA are included as a special case.

The following example of an $\epsilon$-NFA accepts all strings over the alphabet $\{0,1\}$ with the following structure $$L=\{101\}^*\{0\}\{0\}^*\cup\{101\}^*\{1\}\cup \{01\}$$

The following example of an $\epsilon$-NFA accepts all strings over the alphabet $\{1,2,3\}$ with the following structure $$L=\{1^i2^j3^k\mid i,j,k\in\mathbb N\}$$

The empty word $\epsilon$ will be accepted, although $a$ is not one of the final states.

| | | | created: 2020-05-21 11:18:44 | modified: 2020-05-21 17:00:55 | by: *bookofproofs* | references: [1086], [7895]

[1086] **Erk, Katrin; Priese, Lutz**: “Theoretische Informatik”, Springer Verlag, 2000, 2. Auflage

[7895] **Hoffmann, Dirk**: “Theoretische Informatik, 3. Auflage”, Hanser, 2015