Compute the regular expression, Mathematics

Assignment Help:

1. Consider the following context free grammar G with start symbol S (we write E for the empty string, epsilon):

S ---> bB | aSS

A ---> aB | bAA

B ---> E | bA | aS

a. Describe L(G), i.e. complete the following definition: L(G) = { w ∈ {a, b}* | ...

b. Show that G is ambiguous.

2. Give a context free grammar for regular expressions over the alphabet Σ = {0, 1}.

Use the definition of a regular expression given on page 64 of the text.

3. Let L1 and L2 be regular languages and let L = {xy | x ∈ L1 and y ∈ L2 and |x| = |y|}.

a. Is L regular? Answer clearly YES or NO and justify/prove your answer.

b. Is L context free? Answer clearly YES or NO and justify/prove your answer.

4. Let L = {w ∈ {0, 1}* | (the number of 0's in w) mod 3 = 2}. Give a state diagram in the style of the text for a TM that recognizes, but does not decide, L.

5. Turing machines can be considered computers of functions and not just accepters of strings. The function parameter or input is what is written on the tape when the TM starts and its value or output is what is written on the tape when it halts. If it does not halt, the function it computes is not defined for that particular parameter.

Consider the function f(n) = 8n + 5. Assume that n is written on the tape in binary (just 0's and 1's, perhaps with leading 0's) and that the value computed is also written in binary. We don't care whether the value computed has unnecessary leading 0's or not. All numbers are considered unsigned.

Describe at a high level a TM to compute this function.

6. Let L = { | R is a regular expression describing a language that contains at least one string with the substring 111}.

Show that L is decidable.

Questions are shown in the order received.

1. Q: Should here be a * after the {0, 1} in question 2?

A: No. S is an alphabet, not a language. When we speak of a string over S that is the same as saying a string in S*

2. Q: In question 3, does "the number of 0's in w mod 3 = 2" mean you count the 0's in the string and mod that number by 3?

A: Yes. I've now put parentheses around part of it to make it clear; as in: (the number of 0's in w) mod 3


Related Discussions:- Compute the regular expression

ADDING AND SUBTRACTING EQUATION, GUESS THE NUMBER THAT WHEN YOU SUBTRACT 6 ...

GUESS THE NUMBER THAT WHEN YOU SUBTRACT 6 AND THEN SUBTRACT 0 IS-14

Pre-algebra, How do you solve a table to get the function rule?

How do you solve a table to get the function rule?

Find out a series solution for differential equation, Find out a series sol...

Find out a series solution for the following differential equation about x 0 = 0 y′′ + y = 0.   Solution Note that in this case p(x)=1 and therefore every point is an or

Recognize the intervals for function h ( x ) = 3x5 - 5x3 + 3, For the given...

For the given function recognize the intervals where the function is increasing and decreasing and the intervals where the function is concave up & concave down. Utilizes this info

The sum of the clock, how many times In a 12 hour period will he numbers ad...

how many times In a 12 hour period will he numbers add up to 6? (hint 3:00 is one answer0

g ( x ) = 3sec ( x ) -10 cot ( x ) -differentiate , Differentiate followin...

Differentiate following functions.                   g ( x ) = 3sec ( x ) -10 cot ( x ) Solution : There actually isn't a whole lot to this problem.  We'll just differentia

Number system, NATURAL NUMBERS The numbers 1, 2, 3, 4.... Are called as...

NATURAL NUMBERS The numbers 1, 2, 3, 4.... Are called as natural numbers, their set is shown by N. Hence N = {1, 2, 3, 4, 5....} WHOLE NUMBERS The numbers 0, 1, 2, 3, 4

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd