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## Example: Examples of $\epsilon$-NFA

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

### Example 1 – Every NFA is an example of an $\epsilon$-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.

### Example 2

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

### Example 3

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]