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

Factors, Question Suppose that f(x) has (x - 2) 2 and (x + 1) as its on...

Question Suppose that f(x) has (x - 2) 2 and (x + 1) as its only factors. Sketch the graph of f. State all the zeros of f.

Example of cartesian coordinate graph, Example of Cartesian coordinate Grap...

Example of Cartesian coordinate Graph: Example:   The temperature of water flowing in a high pressure line was measured at regular intervals.  Plot the subsequent recorded da

Common graphs, Common Graphs : In this section we introduce common graph o...

Common Graphs : In this section we introduce common graph of many of the basic functions. They all are given below as a form of example Example   Graph y = - 2/5 x + 3 .

Rules of integration, Rules of Integration 1. If ...

Rules of Integration 1. If 'k' is a constant then ∫Kdx =  kx + c 2. In

Rational Number Application, in the horizontal bar event the u.s.a scored 2...

in the horizontal bar event the u.s.a scored 28.636,gremany scroed 28.7,romnia scored 27.962,and chain scored 28.537 points.which list shows these scored in descending order

Matrix, how to solve for x

how to solve for x

Area between two curves, Area between Two Curves We'll start with the ...

Area between Two Curves We'll start with the formula for finding the area among y = f(x) and y = g(x) on the interval [a,b].  We will also suppose that f(x) ≥ g(x) on [a,b].

Find the initial number of balls, Balls are arranged in rows to form an equ...

Balls are arranged in rows to form an equilateral triangle .The first row consists of one ball, the second two balls and so on.   If 669 more balls are added, then all the balls ca

Area in polar cordinates, find the area of the region within the cardioid r...

find the area of the region within the cardioid r=1-cos

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