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For the following questions answer them individually
For $$\sum = \left\{a, b\right\}$$ the regular expression $$r = (aa) * (bb) * b$$ denotes
Consider the grammar with productions
$$S \rightarrow aSb \mid SS \mid ε$$
This grammar is
Identify the language generated by the following grammar
$$S \rightarrow AB$$
$$A \rightarrow aAb \mid ε$$
$$B \rightarrow bB \mid b$$
Let $$L_1$$ be regular language, $$L_2$$ be a deterministic context free language and $$L_3$$ a recursively enumerable language, but not recursive. Which one of the following statements is false?
Let $$L = \left\{a^p \mid p is a prime \right\}$$. Then which of the following is true
Which of the following are context free?
$$A = \left\{a^nb^n a^mb^m \mid m, n \geq 0\right\}$$
$$B = \left\{a^mb^n a^mb^n \mid m, n \geq 0\right\}$$
$$C = \left\{a^mb^n\mid m \neq 2n, m, n \geq 0\right\}$$
Let S be an NP-complete problem. Q and R are other two problems not known to be NP. Q is polynomial time reducible to S and S is polynomial time reducible to R. Which of the
following statements is true?
The number of structurally different possible binary trees with 4 nodes is
Using public key cryptography, X adds a digital signature σ to a message M, encrypts $$\langle M, \sigma \rangle$$ and sends it to Y, where it is decrypted. Which one of the following sequence of keys is used for operations?
Which of the following are used to generate a message digest by the network security protocols?
(P) SHA-256
(Q) AES
(R) DES
(S) MD5
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