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Regular expressions and finite automata, Context-free grammars and push-down automata, Regular and context-free languages, Pumping lemma, Turing machines and undecidability.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1} & \textbf{2024-2} & \textbf{2023} & \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &1&1&3& 2 &2&3& 1&2&3
\\\hline\textbf{2 Marks Count} &2&3&3& 3 &3&4& 2&3&4
\\\hline\textbf{Total Marks} &5&7&9& 8 &8&11&\bf{5}&\bf{8}&\bf{11}\\\hline
\end{array}}}$$

Recent questions in Theory of Computation

#122
250
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Let h : {0, 1}∗ → {a, b}∗ be the function defined by h(e) = e, h(0) = aa and h(1) = b,and for words of length two or greater:h(a1a2 . . . an) = h(a1)h(a2) . . . h(a...
#123
265
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1 answers
0 votes
What is the regular expression that accept following string aaaabbbb ؟a) a+ b+b) a* b*c) (a+b)* (a+b)*d) (a+b)*e) abab
#124
249
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0 answers
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If G is a CFG then L(G) = (Sigma)* is Decidable or Undecidable?The reference where I solved this question says this is an Undecidable problem! But I think it's Decidable ...
#125
153
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0 answers
0 votes
Let Σ and ∆ be any two alphabets. In this question, we consider maps h : Σ∗ → ∆∗ that satisfy the following properties: (I) h(e) = e, (II) h(uv) = h(u)h(v) fo...
#126
171
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0 votes
Construct pushdown automata that accept each of the following languages :-(i) {a^nu ∈ {a, b}∗| |u| = n, n ≥ 0} ⊆ {a, b}∗
#127
275
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1 answers
0 votes
Convert this language to Push Down Automata – {a^n u | u ∈ {a, b}*, |u| = n, n ≥ 0}
#128
562
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2 answers
1 votes
Convert DFA to regular expression
#129
79
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0 answers
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Construct a PDA for { a^nu E { a, b }* | |u| = n, n >=0 }
#131
251
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1 answers
0 votes
Regular expression for having atleast 2 a's(1). (a + b)* a (a + b)* a (a + b)*(2). (a + b)* a b* a (a + b)*(3). b* a (a + b)* a (a + b)*(4). (a + b) * a (a + b) * a b*(...
#132
120
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0 answers
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How to design a Mealy machine for binary subtraction?
#135
268
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1 answers
1 votes
#136
636
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3 answers
0 votes
Which of the following pairs of regular expression are equivalent?(a) 1(01)* and (10)*1(b) x(xx)* and (xx)*x(c) x* and x*x(d) All of the above
#137
91
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0 answers
0 votes
#139
283
views
2 answers
0 votes
#140
401
views
1 answers
1 votes
In a DFA, does every state have to have a transition for each of the symbols?