3.4 KiB
3.4 KiB
Př. 1: Vytvořte gramatiku, která bude nad abecedou \{0, 1\}
generovat řetězec obsahující lichý počet 0 a sudý počet 1.
\{0, 1\} \quad w \dots \text{lichý počet } 0 \text{, sudý počet } 1
- 4 stavy
Př. 2:
S \to abA \mid bS \mid aa \mid A
A \to abA
B \to aS \mid baA \mid a
a) Najděte G'
typu G3R takovou, že L(G') = L(G)
.
S \to bS | aS_{1} | aS_{2} \mid aS | bB_{1} | aB_{2} \mid aA_{1}
A \to aA_{1} \mid aS | bB_{1} | aB_{2}
B \to aS | bB_{1} | aB_{2}
S_{1} \to bA
B_{1} \to aA
A_{1} \to bA
S_{2} \to aS_{3}
S_{3} \to e
B_{2} \to e
b) Vytvořte tabulku popisující nedeterministický konečný automat A takový, že platí L(A) = L(G') = L(G)
.
a | b | |
---|---|---|
\to S |
\{S, S_{1}, S_{2}, A_{1}, B_{2}\} |
\{S, B_{1}\} |
S_{1} |
- | \{A\} |
S_{2} |
\{S_{3}\} |
- |
\leftarrow S_{3} |
- | - |
A |
\{S, A_{1}, B_{2}\} |
\{B_{1}\} |
A_{1} |
- | \{A\} |
B |
\{S, B_{2}\} |
\{B_{1}\} |
B_{1} |
\{A\} |
- |
\leftarrow B_{2} |
- | - |
c) Vytvořte tabulku popisující deterministický konečný automat A' takový, že platí L(A') = L(G') = L(G)
.
a | b | |
---|---|---|
\to S (0) |
\{S, S_{1}, S_{2}, A_{1}, B_{2}\} (1) |
\{S, B_{1}\} (2) |
\leftarrow \{S, S_{1}, S_{2}, A_{1}, B_{2}\} (1) |
\{S, S_{1}, S_{2}, S_{3}, A_{1}, B_{2}\} (3) |
\{S, A, B_{1}\} (4) |
\{S, B_{1}\} (2) |
\{S, S_{1}, S_{2}, A, A_{1}, B_{2}\} (5) |
\{S, B_{1}\} (2) |
\leftarrow\{S, S_{1}, S_{2}, S_{3}, A_{1}, B_{2}\} (3) |
\{S, S_{1}, S_{2}, S_{3}, A_{1}, B_{2}\} (3) |
\{S, A, B_{1}\} (4) |
\{S, A, B_{1}\} (4) |
\{S, S_{1}, S_{2}, A, A_{1}, B_{2}\} (5) |
\{S, B_{1}\} (2) |
\leftarrow\{S, S_{1}, S_{2}, A, A_{1}, B_{2}\} (5) |
\{S, S_{1}, S_{2}, S_{3}, A_{1}, B_{2}\} (3) |
\{S, A, B_{1}\} (4) |
Př. 3: Sestrojte NKA A
, kde platí L(A) = L(G_{1})^R \cup L(G_{2})
.
G_{1}
S \to aS | bbA
A \to aaA | B
B \to bbB | e
G_{2}
S \to Aba | Ab | B
A \to Aaa | B
B \to Bbb | e
- G3L -> reverze -> G3P -> NKA -> reverze -> NKA
Plán
A_{1} \qquad L(A_{1}) = L(G_{1})
A_{1}^R \qquad L(A_{1}^R) = L(A_{1})^R = L(G_{1})^R
G_{2}^R \qquad L(G_{2}^R) = L(G_{2})^R
A_{2}^R \qquad L(A_{2}^R) = L(G_{2}^R) = L(G_{2})^R
A_{2} \qquad A_{2} = (A_{2}^R)^R \quad L(A_{2}) = \dots = L(G_{2})
A \qquad L(A) = L(A_{1}^R) \cup L(A_{2}) = L(G_{1})^R \cup L(G_{2})
G_{2}^R
S \to abA | bA | B
A \to aaA | B
B \to bbB | e