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Higher Study | Theory of Computation | Context Free Languages and Pushdown Automata

Consider L = L1 ∩ L2 Where L1 = {0m1m20n1n |m, n >= 0} L2 = {0m1n2k | m, n, k ≥ 0} Then, the language L is
Which of the following grammars is (are) ambiguous? (A) s → ss | asb | bsa | (B) s → asbs | bsas | λ (C) s → aAB A → bBb B →  A | λ where λ denotes empty string Choose the correct answer from the options given below:
Which of the following statements is/are TRUE? (a) The grammar S → SS | a is ambiguous. (Where S is the start symbol) (b) The grammar S → 0S1 | 01S |e is ambiguous. (The special symbol e represents the empty string) (Where S is the start symbol) (c) The grammar (Where S is the start symbol) S → T / U T → x S y | xy | ϵ U → yT generates a language consisting of the string yxxyy.
If G is a grammar with productions S → SaS | aSb | bSa | SS | ∈ Where S is the start variable. Then which one of the following strings in not generated by G?
Consider the following languages: I. \(?^? ?^??^??^?| ? + ? = ? + ?, where \text{ ?}, ?, ?, ? ≥ 0\) II. \({?^??^??^??^?| ? = ? \text{ and } ? = ?, where \text{ ?}, ?, ?, ? ≥ 0}\) III. \(?^??^??^??^?| ? = ? = ? \text{ and } ? ≠ ?, where \text{ ?}, ?, ?, ? ≥ 0\) IV. \(?^??^??^??^?| ?? = ? + ?, where \text{ ?}, ?, ?, ? ≥ 0\) Which of the languages above are context-free?
What is the number of steps required to derive the string ((() ()) ()) for the following grammar? S → SS S → (S) S → ϵ
What is the highest type number that can be assigned to this following grammar: S→Aa, A→Ba, B→abc
Which of the following statements in true?
Consider a grammar G with the following production rules: S → SS, S → λ, S → aSb, S → bSa Which one of the following languages is generated using the above rules?
Consider the following grammar. S → AB A → a A → BaB B → bbA Which of the following statement is FALSE?
Which of the following statements is true ?
Consider the following languages : L1 = {am bn | m ≠ n} L2 = {am bn | m = 2n + 1} L3 = {am bn | m ≠ 2n} Which one of the following statement is correct ? 
Consider the following languages over the alphabet Σ = {0,1, c}: L1 = {0n1n | n ≥ 0} L2 = {wcwr | w ϵ {0,1}*} L3 = {wwr | w ϵ {0,1}*} Here, w­r is the reverse of the string w. Which of these languages are deterministic Context-free languages?
Which of the following is/are correct? I. A language is context free if and only if it is accepted by PDA II. PDA is a finite automata with push down stack
The language which is generated by the grammar S → aSa | bSb | a | b over the alphabet {a, b} is the set of
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