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lfa:reg [2018/07/23 13:37] pdmatei |
lfa:reg [2018/07/23 14:47] (current) pdmatei |
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| $justtheorem | $justtheorem | ||
| - | Let $math[M] be a DFA. There exists a **regular expression** $math[E], such that $math[L(E)=L(A)]. | + | Let $math[M] be a DFA. There exists a **regular expression** $math[E], such that $math[L(E)=L(M)]. |
| $end | $end | ||
| Line 48: | Line 48: | ||
| If $math[i = j], then: | If $math[i = j], then: | ||
| - | * $math[R^{(0)}_{ii}] may contain **zero** transitions, hence $math[R^{(0)}_{ij} = \epsilon] | + | * $math[R^{(0)}_{ii}] may contain **zero** transitions, hence $math[R^{(0)}_{ij} = \epsilon] |
| - | * $math[R^{(0)}_{ii}] may contain one transition, and the construction follows the above rules, yielding some regular expression $math[E_0]. | + | * $math[R^{(0)}_{ii}] may contain one transition, and the construction follows the above rules, yielding some regular expression $math[E_0]. |
| We combine the two situations in a single one: $math[R^{(0)}_{ii} = \epsilon \cup E_0], where $math[E_0] is constructed as above. | We combine the two situations in a single one: $math[R^{(0)}_{ii} = \epsilon \cup E_0], where $math[E_0] is constructed as above. | ||