Question: 2. a) Use the Context-Free Pumping Lemma (Theorem 8.1) to prove that the language {a^i b^j a^i b^j : i, j } is not context-free.

2.

a) Use the Context-Free Pumping Lemma (Theorem 8.1) to prove that the language {a^i b^j a^i b^j : i, j } is not context-free.

b) . Use the previous result and closure of context-free languages under intersection with regular sets (Theorem 8.5) to prove that the language {ww : w {a, b}*} is not context-free.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Q:

For this exercise, we use JTRAIN.RAW to determine the effect of the job training grant on hours of job training per employee. The basic model for the three years is (i) Estimate the equation using...

Q:

Finite Languages & Automata a.) Use the Context-Free Pumping Lemma (Theorem 8.1) to prove that the language {a i b j a i b j : i, j } is not context-free. b.) Use the result from (a) and closure of...

Q:

Using the Pumping Lemma for Context-Free Languages, prove that L = {ai bj ai bj | i, j 0} is not a Context-Free Language.

Q:

The Basics of Financial Mathematics Spring 2003 Richard F. Bass Department of Mathematics University of Connecticut c These notes are 2003 by Richard Bass. They may be used for personal use or class...

Q:

Definitions Given a language L , we define the following two-player pumping games. In both games, the winner is the last player to make a legal move. So if they finish the game, N wins. Regular...

Q:

2. Regular languages are context-free Formally prove that every regular language is context-free. Use the following ingredients in your proof: the recursive definition of regular expressions; the...

Q:

Definitions Given a language L , we define the following two-player pumping games. In both games, the winner is the last player to make a legal move. So if they finish the game, N wins. Regular...

Q:

Definitions Given a language L , we define the following two-player pumping games. In both games, the winner is the last player to make a legal move. So if they finish the game, N wins. Regular...

Q:

Definitions Given a language L , we define the following two-player pumping games. In both games, the winner is the last player to make a legal move. So if they finish the game, N wins. Regular...

Q:

2. 15pt Use formal definition of context-free grammars to prove the following closure properties [5pt each: (a) Context-free languages are closed under union operation (b) Context-free languages are...

Q:

Hi I need some help with these I'm new to figure this out. Consider the following context-free grammar. X X+X | X*X |X| a What kind of terminal strings can this grammar generate? Determine whether...

Q:

Fatima Ahmad is evaluating a new project for her firm. She has determined that the after-tax cash flows for the project will be $25,000; $22,000; $32,000; $19,000; and $8,000, respectively, for each...

Q:

joan, an employee of great american market, was warned about her excessive absenteeism several times, both verbally and in writing. the written warning included notice that "further violations will...

Q:

Which of the following statements is true of a standard costing system? a. It can only be used in organizations where there are homogeneous work units. b. It establishes price and quantity standards...

Q:

CT Corp Comprehensive Question Canadian Tire Corporation, Limited (Canadian Tire) is a family of companies that includes a retail segment and a financial services division, among others. The retail...

Q:

Prepare a constructive performance appraisal.

Q:

Describe the purposes of visual aids in written and oral communication.

Q:

List the advantages of correct report formatting.