# اثبات مستقل از متن بودن یک زبان

```Context Free Languages
and
Pushdown Automata
)PDA(‫اثبات مستقل از متن بودن یک زبان‬
Prove that the class of Context-Free Languages is closed under
MissingMiddle, where, assuming L is over the alphabet Σ,
Suppose that A and B are regular languages. Prove that the
following language is context free:
‫اثبات مستقل از متن بودن یک زبان(‪)CFG‬‬
‫اثبات مستقل از متن بودن یک زبان‬
‫اثبات مستقل از متن نبودن یک زبان‬
The language of all palindromes over {0, 1} that contain the
same number of 0s and 1s.
L = { 1n^2 | n a positive integer }
L = {ap bq c max(p,q)}
L = {ww | w in {0,1}*}
‫اثبات مستقل از متن نبودن یک زبان‬
• The set of all strings with the unary alphabet {#} with length a perfect
square.
• The set of all strings with the unary alphabet {#} with length a prime
number.
‫مسائل گوناگون‬
Let L be some regular set in which all strings happen to have length
equal to a multiple of three. Let Twist3(L) be the set of all strings in L
where every three symbols are reversed. For example if L = {aag,
cttgta, ttggagagc, ...} then Twist3(L) = {gaa, ttcatg, gttgagcga, ...}.
Explain why Twist3(L) is a CFL.
‫مسائل گوناگون‬
‫مسائل گوناگون‬
```

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