Mathematics High School

Show that the following language over Σ = {0, 1} is not context-free:
{w : w is a palindrome containing the same # of 0’s as 1’s}

Answers

Answer 1

In all cases, pumping the string w results in a string that is not in L, which contradicts the pumping lemma. And we can conclude that L is not a context-free language.

To prove that a language is not context-free, we can use the pumping lemma for context-free languages.

Assume that the language L = {w : w is a palindrome containing the same number of 0's and 1's} is context-free. Then, by the pumping lemma for context-free languages, there exists a constant p such that any string w in L with length |w| ≥ p can be written as w = uvxyz, where:

|vy| > 0|vxy| ≤ pFor all i ≥ 0, the string [tex]uv^ixy^iz[/tex] is also in L.

Let's choose the string w = [tex]0^p1^p0^p[/tex]. This string is in L because it is a palindrome and contains the same number of 0's and 1's. By the pumping lemma, we can write w = uvxyz, where |vxy| ≤ p and |vy| > 0.

There are three cases:

vxy contains only 0's. In this case, pumping up or down will break the palindrome property because the string will no longer be a palindrome.vxy contains only 1's. In this case, pumping up or down will break the property of having the same number of 0's and 1's.vxy contains both 0's and 1's. In this case, pumping up or down will break both the palindrome property and the property of having the same number of 0's and 1's.

Therefore, in all cases, pumping the string w results in a string that is not in L, which contradicts the pumping lemma. Hence, we can conclude that L is not a context-free language.

To know more about palindrome, refer to the link below:

https://brainly.com/question/14076732#

#SPJ11

Related Questions

Lucas and Mitchell were asked to add the numbers 3.54 and 12.09.


Lucas stated that he completed the addition problem by using the following method:

First, I broke the numbers apart. I broke 3.54 into 3.00+0.50+0.04 and 12.09 into 12.00+0.09.

Then, I combined 0.04 and 0.09 to get 0.13.

Next, I combined 0.13 and 0.50 to get 0.63.

Then, I combined 3.00+12.00 to get 15.00.

Finally, I added the decimal to get 15.63.

Mitchell stated that he completed the addition problem by using the following method:

First, I added the whole numbers to get 3.00+12.00=15.00.

Next, I added the numbers in the tenths place, 0.50+0.00=0.50.

Then, I added the numbers in the hundredths place, 0.04+0.09=0.013.

I then added 0.50 and 0.013 to get 0.513.

Lastly, I added the decimal to the whole number to get 15.513.

Determine if Lucas and/or Mitchell had a flaw in their method. If they did, correct the flaw(s) so that both the methods used are correct. PLZ ANSWER THE QUESTION!

Answers

Answer:

0.22

Step-by-step explanation:

Pls help me with this problem

Answers

Answer:

A is going to be 2.80

B is going to be 0.7

C points (1,0.70)

D he is buying four pounds of flour because you always put the x at the bottom and y at the top

E it will be 6.3

Step-by-step explanation:

Hope this Helped

AnswerA is going to be 2.80

B is going to be 0.7 this is all I know

Step-by-step explanation:

An 8th-grade class washed cars and pets to raise money for a children’s hospital. They charged $10 to wash a car and $5 to wash a pet. They raised $1,600 in one week, washing a total of 201 cars and pets. How much more money was raised washing cars than pets?
$1,399
$1,190
$780
$410

Answers

Answer:

780

Step-by-step explanation:

the answer is 780

Answer: 780

Step-by-step explanation:

WHATS THE ANSWER TO THIS PLS TIME IS RUNNING OUT

Answers

Answer:

ectangles, rhombuses (also called rhombi) and squares are all more specific versions of parallelograms, also called special parallelograms. A quadrilateral is a rectangle if and only if it has four right (congruent) angles.

Step-by-step explanation:

i hope it's right

Is 3x-22=-3x+8 no solution?

Answers

It has one solution which is X=5

Hope this helps

Have a great day/night

Feel free to ask any questions

write a active sentence then rewrite it as a passive​

Answers

What to do managers analyze to understand the behavior and attitude of other team members?

Hey there!

The answer is, for active, "Carla drove Emily to the theater," and, for passive, "Emily was driven to the theater by Carla."

Have a nice day :)

Somebody help me please

Answers

Answer:

The second one

Given the graph, what is in initial value of the function?

(5 points)

A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1. A straight line joins the ordered pair 0, 1 with the ordered pair 6, 7.


a
1

b
5

c
6

d
7

Answers

Answer:

6

Step-by-step explanation:

I have a big thick lookin brain

Im not completely sure so please dont get upset with me. : )

-12x = 3(y - 3)

y = ___

Answers

A a. AAnswer:

kid thanks

Step-by-step explanation:  kk k k

The measure of AOC is 90. Find the value of x.

Answers

Answer:

x = 10 degr

Step-by-step explanation:

3x + 46 + 14 = 90

3x + 60 = 90

3x + 60 - 60 = 90 - 60

3x = 30

x = 10 deg

Answer:

Step-by-step explanation:10

Anybody good in geometry?

Answers

Answer:

A) <6, 2>

Step-by-step explanation:

Moves along x-axis to the right six units. Moves along y-axis upward two units.

Answer:

which vector translated the triangle to its image?

A. < 6 , 2 >

Solve the system y = 3x + 2 and 3y = 9x + 6 by using graph paper or graphing technology. What is the solution to the system?
No solutions
Infinite solutions
(32)
(9,2)

Answers

Answer is -Infinite solution

What is (f + g)(x)?
f(x) = -4x
g(x) = -x^2 + 6x

Answers

-4x+-x^2+6x = -x^2 + 2x

f(x)=1/2x show steps please!!

find f(-3)

Answers

Answer:

x = -6f

Step-by-step explanation:

solve for x by simplifying both sides of the equation, then isolating the variable.

Work out, giving your answer in its simplest form:
4/7 divided by 2 1/3

Answers

Answer:

12/49  

Step-by-step explanation:

First write 2 1/3 as a improper fraction, to do that, first multiply the 2 by the denominator, then add it with the 1, which will result in 7/3

when doing division of fraction you have to remember this, KFG

KFG: Keep Flip Change

you keep the first number or fraction, which is 4/7

then you flip the sign, so you change division in to multiplication

after that, you change or write the reciprocal of the second number or fraction, so 7/3 will be 3/7

Now the equation is

4/7 times 3/7, which is 12/49  

WHERE ARE THE BLACK DOTS LOCATED?!?

Answers

Answer:

The first one (on the bottom) is (2, -3)

The second one (the top one) is (-1, 3)

Answer:

(-1, 3) and (2, -3)

Step-by-step explanation:

The x-value always goes first and the second is always the y-value.

HELPPP!!!! 50 points​

Answers

Answer:

5. 26

6. 11

7. 5, 3, 9, 5 (left to right)

Step-by-step explanation:

5. Plug in the numbers

6. 2x+9=31, 2x=22, x=11

7. Plug numbers in

Hope this helps and please give me Brainliest!

Answer:

5. 26

6. 11

7. 5, 3, 9, 5 (left to right)

Step-by-step explanation:

5. Plug in the numbers

6. 2x+9=31, 2x=22, x=11

7. Plug numbers in

Step-by-step explanation:

If the triangle are similar, write a similarity
statement and tell whether you would use
AA similarity, SAS similarity, or SSS
similarity. If not similar, explain why.
Explanation

Answers

Answer:

The triangles are similar due to AAA

Step-by-step explanation:

'The triangles ABC and DBE are similar because they have a common angle < B, and also angle < E is marked as congruent to angle < A. Then the third angle <C is going to be congruent to angle D as well due to the property of addition of internal angles of a triangle must add to 180 degrees.

Then the triangles are similar due to AAA

Use the relationship shown on this graph.

Answers

Answer:

B. y=50x

Step-by-step explanation:

We can see the y intercept is 0 because the line starts at 0.

To find the slope, we can look at the first point. It is at (1, 50).

Slope=rise/run or change in y/change in x=50/1=50.

I need to know what the answer to this problem is the right answer 4/8

Answers

I got 8/3 because 4/8 would simplify to 1/2 and the line would be flatter

M is the midpoint of AB. If A ( 4,0) and M (2, 1.5), then find the coordinates of B

Answers

Answer:

Step-by-step explanation:

(4 + x)/2 = 2

4 + x = 4

x = 0

(x + 0)/2 = 1.5

x + 0 = 3

x = 3

(0, 3)

answer is C

Write a polynomial in standard form that represents the area of the shaded region.

Answers

Answer:

Area of the smaller square is x * x, which is x^2

Area of the larger square is (x + 7)(x + 7), which is x^2 + 14x + 49

The area of the shaded area = Area of the larger square - Area of the smaller square

Area of the shaded region = x^2 + 14x + 49 - x^2

Area of the shaded region is 14x + 49.

Please help! Thank tou

Answers

Answer:

220mL

780mL

600mL

480mL

Step-by-step explanation:

500-280=220

500+280=780

280/8=35, so 35 mL is in one L, 35x5=175

875-175=600

750-280=480

Answer:

Step-by-step explanation:

2. Pierre works full time and is paid an hourly rate of $12.50 for 35 hours a week. He is paid for 52
weeks of the year. What are his total earnings for ONE YEAR?​

Answers

Answer:

$22,750

Step-by-step explanation:

First, find out how much Pierre is paid per week: $12.50 x 35 -> $437.5/week

Then, multiply to find how much he is paid the whole year: $437.5 x 52 -> $22,750

Which of these division problems have the same quotient as 12.3 divided by 0.4? Check all that apply.

A. 123 ÷ 4
B. 1.23 ÷ 0.4
C. 1,230 ÷ 40
D. 123 ÷ 0.04

Answers

Answer:

The answer is A and C

Step-by-step explanation:

The answer is A because 12.3 multiplied by 10 is 123, and 0.4 multiplied by 10 is 4.

12.3 * 10 = 123

0.4 * 10 = 4

So, this shows that this equation is the same as 12.3 divided by 0.4

The answer is C because 12.3 multiplied by 100 is equal to 1230, this is the same for 0.4

12.3 * 100 = 1230

0.4 * 100 = 40

So, the answer is both A and C.

Hope this helps! :)

Answer:

12.3 divided by 0.4 is 30.75

Step-by-step explanation:

You then go to letter A and 123/4 is also 30.75

but you go through the rest of the choices just in case.

B is 3.075 so that is incorrect

C is 307.5 so that is also incorrect

D is 3075 and that is incorrect and not 30.75.

Therefore your answer is A.

30.75 = 30.75.

Hope this helps :)

I need help with this​

Answers

Answer:

3.5

Step-by-step explanation:

the median is the dotted lines.

median of girls height: 65.5

median of boys height: 69

69-65.5=3.5

anlatarak cozmicekseniz cevaplamayin:) ​

Answers

Wish I could help! But maybe one day I can and hopefully there’s someone on here that and assist you!

Area of a room is 500m square. The cupboard takes 6% of the room’s area
a:what is the area of the cupboard
b:The table is 1/10 of the room. Calculate the area of the table.
c: bed has an area of 110m square. What is the percentage of the room is the bed?

Answers

Step-by-step explanation:

step 1. 500(.06) = 30m^2 (area of cupboard)

step 2. 500(1/10) = 50m^2 (area of table)

step 3. 110/500 = .22 = 22% (percentage of the bed area in the room).

Solve for x.
5/7x + 1/7= 63

Answers

Answer:

x=88

Step-by-step explanation:

Answer: x=88

Step-by-step explanation:

perrys bikes rents bikes for $18 plus $4 per hour. Lea paid $42 to rent a bike for how many hours did she rent the bike?

Answers

she rented the bike for 6 hours

Answer:

5 hours 30 min

Step-by-step explanation:

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