Register

Recent questions tagged cmi2021

0 votes
0 answers
4
CMI2021-B: 4
For a language $\text{L}$ over an alphabet $\Sigma$, define $\text{SW(L)}:= \left \{ y \in \Sigma^{\ast} \mid \exists x \in \Sigma^{\ast}\; \text{s.t.}\; xyx \in \text{L} \right \}$ Prove that if $\text{L}$ is regular, $\text{SW(L)}$ is also regular.
For a language $\text{L}$ over an alphabet $\Sigma$, define$$\text{SW(L)}:= \left \{ y \in \Sigma^{\ast} \mid \exists x \in \Sigma^{\ast}\; \text{s.t.}\; xyx \in \text{L}...
User Avatar
0 votes
0 answers
7
CMI2021-B: 7
Consider the function $\textsf{foo}$ and $\textsf{bar}$ described in pseudocode below, where $/ /$ denotes quotient (integer division) and $\%$ denotes remainder. int foo (int n) { int i = 1; while (bar (i) < n){ i = 2* i; } return (i); } ... $\textsf{bar}$ and made in computation of $\textsf{foo(100)}?$
Consider the function $\textsf{foo}$ and $\textsf{bar}$ described in pseudocode below, where $/ /$ denotes quotient (integer division) and $\%$ denotes remainder.int foo ...
User Avatar
0 votes
0 answers
10
CMI2021-A: 3
Which of the following regular expressions represents binary strings that are multiples of $3?$ Note that we consider the leftmost bit to be the most significant. $((11)0^{\ast})^{\ast}$ $(10^{\ast})^{\ast}$ $1(01^{\ast})^{\ast}$ $(11+101^{\ast}01+0)^{\ast}$
Which of the following regular expressions represents binary strings that are multiples of $3?$ Note that we consider the leftmost bit to be the most significant.$((11)0^...
User Avatar
0 votes
0 answers
14
CMI2021-A: 7
You are given a sequence of letters $x_{1}, x_{2} \dots x_{n}$ where each $x_{i} \in \left \{ a, b, c, d, e, f, g, h \right \}$. You can form a new sequence from the given sequence as follows. Start with $x_{1}$. ... $becgdfg?$ $ggebcdf$ $ggfedcb$ $ggecbdf$ $ggfebcd$
You are given a sequence of letters $x_{1}, x_{2} \dots x_{n}$ where each $x_{i} \in \left \{ a, b, c, d, e, f, g, h \right \}$. You can form a new sequence from the give...
User Avatar
0 votes
0 answers
15
CMI2021-A: 8
There is a basket full of apples, oranges, mangoes, pears and pomegranates. You want to pick three fruits from the basket. Multiple pieces of the same fruit can be picked. However, if you pick mangoes, you cannot pick apples. In how many ways can you pick three fruits satisfying this condition? $14$ $40$ $28$ $20$
There is a basket full of apples, oranges, mangoes, pears and pomegranates. You want to pick three fruits from the basket. Multiple pieces of the same fruit can be picked...
User Avatar
To see more, click for the full list of questions or popular tags.