search
Log In

Web Page

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

$$\small{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}&2&2&2&3&3&3&2&2.5&3
\\\hline\textbf{2 Marks Count}&3&3&5&3&3&3&3&3.3&5
\\\hline\textbf{Total Marks}&8&8&12&9&9&9&\bf{8}&\bf{9.2}&\bf{12}\\\hline
\end{array}}}$$

Recent questions in Theory of Computation

1 vote
1 answer
1
Consider the following languages: L1 ={a^nb^nc^m } U {a^nb^mc^m} n, m ≥ 0 L2={wwR|w {a,b}*} Where R represents reversible operation Which one of the following is (are) inherently ambiguous language(s)? 1) Only L1 (2) only L2 3) Both L1 and L2 (4) neither L1 nor L2
asked Dec 21, 2019 in Theory of Computation Sanjay Sharma 1.1k views
1 vote
2 answers
2
$\mathbf{Q57}$ Let $\mathrm{A={001,0011,11,101}}$ and $\mathrm{B={01,111,111,010}}$. Similarly , Let $\mathrm{C={00,001,1000}}$ and $\mathrm{B={0,11,011}}$. Which of the following pairs have a post correspondence solution? $\mathrm{1)\; Only \;pair \;(A,B) }$ $\mathrm{ 2) \;Only\; pair \;(C,D) }$ $\mathrm{ 3) \; Both (A,B)\; and (C,D) \; }$ $\mathrm{\; 4) \;Neither \;(A,B) \;nor\; (C,D) }$
asked Dec 20, 2019 in Theory of Computation Sanjay Sharma 1.3k views
3 votes
0 answers
3
1 vote
0 answers
4
Say that a variable $A$ in $CFG \:G$ is necessary if it appears in every derivation of some string $w \in G$. Let $NECESSARY_{CFG} = \{\langle G, A\rangle \mid \text{A is a necessary variable in G}\}$. Show that $NECESSARY_{CFG}$ is Turing-recognizable. Show that $NECESSARY_{CFG} $is undecidable.
asked Oct 20, 2019 in Theory of Computation Lakshman Patel RJIT 99 views
0 votes
1 answer
5
1 vote
1 answer
6
0 votes
0 answers
7
Prove that the following two languages are undecidable. $OVERLAP_{CFG} = \{\langle G, H\rangle \mid \text{G and H are CFGs where}\: L(G) \cap L(H) \neq \emptyset\}$. $PREFIX-FREE_{CFG} = \{\langle G \rangle \mid \text{G is a CFG where L(G) is prefix-free}\}$.
asked Oct 20, 2019 in Theory of Computation Lakshman Patel RJIT 134 views
0 votes
0 answers
8
Let $f(x)=\left\{\begin{matrix}3x+1 & \text{for odd}\: x& \\ \dfrac{x}{2} & \text{for even}\: x & \end{matrix}\right.$ for any natural number $x$. If you start with an integer $x$ and iterate $f$, you obtain a sequence, $x, f(x), f(f(x)), \dots$ ... problem. Suppose that $ATM$ were decidable by a $TM\: H$. Use $H$ to describe a $TM$ that is guaranteed to state the answer to the $3x + 1$ problem.
asked Oct 20, 2019 in Theory of Computation Lakshman Patel RJIT 82 views
1 vote
0 answers
9
Use Rice’s theorem, to prove the undecidability of each of the following languages. $INFINITE_{TM} = \{\langle M \rangle \mid \text{M is a TM and L(M) is an infinite language}\}$. $\{\langle M \rangle \mid \text{M is a TM and }\:1011 \in L(M)\}$. $ ALL_{TM} = \{\langle M \rangle \mid \text{ M is a TM and}\: L(M) = Σ^{\ast} \}$.
asked Oct 20, 2019 in Theory of Computation Lakshman Patel RJIT 110 views
0 votes
0 answers
10
Rice's theorem. Let $P$ be any nontrivial property of the language of a Turing machine. Prove that the problem of determining whether a given Turing machine's language has property $P$ is undecidable. In more formal terms, let $P$ be a language consisting of Turing ... any $TMs$. Prove that $P$ is an undecidable language. Show that both conditions are necessary for proving that $P$ is undecidable.
asked Oct 20, 2019 in Theory of Computation Lakshman Patel RJIT 58 views
0 votes
0 answers
11
Rice's theorem. Let $P$ be any nontrivial property of the language of a Turing machine. Prove that the problem of determining whether a given Turing machine's language has property $P$ is undecidable. In more formal terms, let $P$ ... $M_{1}$ and $M_{2}$ are any $TMs$. Prove that $P$ is an undecidable language.
asked Oct 20, 2019 in Theory of Computation Lakshman Patel RJIT 87 views
1 vote
0 answers
12
A two-dimensional finite automaton $(2DIM-DFA)$ is defined as follows. The input is an $m \times n$ rectangle, for any $m, n \geq 2$. The squares along the boundary of the rectangle contain the symbol $\#$ and the internal squares contain ... . Consider the problem of determining whether two of these machines are equivalent. Formulate this problem as a language and show that it is undecidable.
asked Oct 20, 2019 in Theory of Computation Lakshman Patel RJIT 163 views
0 votes
0 answers
13
Define a two-headed finite automaton $(2DFA)$ to be a deterministic finite automaton that has two read-only, bidirectional heads that start at the left-hand end of the input tape and can be independently controlled to move in either direction. The tape of a $2DFA$ is finite and is just large ... $E_{2DFA}$ is not decidable.
asked Oct 20, 2019 in Theory of Computation Lakshman Patel RJIT 91 views
0 votes
0 answers
15
0 votes
0 answers
18
...