Consider alphabet Σ = {0,1,2,3} and language L = {w€Σ* : w = 0"1" 2" 3" for some positive m‚n €or disprove that L is context-free.Z}. Prove

Claim: The language L = {w ∈ Σ* : w = 0^m 1^n 2^m 3^n for some positive m, n ∈ Z} is not…

Answered: Consider alphabet Σ = {0,1,2,3} and…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

Consider alphabet Σ = {0,1,2,3} and language L = {w €Σ* : w=0'1" 2" 3" for some nonnegative l, m,n € Z}. Prove or disprove that L is context-free.
Consider the language L = {a'bck | i + j,j # k, i + k}; it is not a context- free language. Show that it nevertheless satisfies the conditions of the context-free pumping lemma, that i s, show that there exists an m so that for all strings w in L of length at least m, we can write w = uvxyz with |vxy| 1, such that Vi > 0 : uv'xy'z € L.
Consider alphabet Σ = {0,1} and language Lo₁ = {weΣ* : w=0"1" for some nonnegative n€ Z}. Prove or disprove that for each language L over Σ, if L n Lo₁ = 0 and L is regular, then L is finite.
Suppose L is a language over {a,b}, and there is a fixed integer k such that for every x ∈ Σ*, xz ∈ L for some string z with |z| ≤ k. Does it follow that there is an FA accepting L? Why or why not?
w W 2. Consider alphabet Σ = regular. {0,1} and language L = {wer : [w; # Σ Σ (1 - w;)). Prove or disprove that L is i=1 i=1
Suppose L is a non empty regular language, over Σ, such that every w E L satisfies |w] =k, for some ke N. Show that there cannot exist a DFA M = (E, Q, 8, q0, F), where |Q| = k.
Let E = {a, b, #} and L = {w |w can be written as t#s#t with s, t e {a, b}*}. Show that L is not regular. Show that L is context-free.
Please explain your answer for both questions. For the first part n is greater than or equal to zero
4. Consider alphabet Σ = {0,1} and language Lo₁ = {we*: w=0"1" for some nonnegative n€Z}. Prove or disprove that for each language Lover Σ, if Ln Lo₁ = 0 and L is regular, then L is finite.
If A is any language, let A 1/3 – 1/3 be the set of all strings in A with their middle thirds removed so that A 1/3 – 1/3 = {x z| for some y, |x| = |y = |z| and xyz ∈ A}. Show that, if A is regular, then A 1/3 – 1/3 is not necessarily regular.
2. Let RE be the set of regular expressions over alphabet E = {0, 1}, and for r E RE, let L(r) be the language denoted by r. Consider the claim: VL E P(E*),Vr1, r2 E RE, (|L(r1)| > 1 A L \ L(r2) = L(r1)) = L is regular Either prove this, or find L, rı and r2 that provide a counter-example.
For each question, build a deterministic FSM for the given language.

SEE MORE QUESTIONS

Recommended textbooks for you

Database System Concepts

Computer Science

ISBN:

9780078022159

Author:

Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:

McGraw-Hill Education

Starting Out with Python (4th Edition)

Computer Science

ISBN:

9780134444321

Author:

Tony Gaddis

Publisher:

PEARSON

Digital Fundamentals (11th Edition)

Computer Science

ISBN:

9780132737968

Author:

Thomas L. Floyd

Publisher:

PEARSON

Database System Concepts

Computer Science

ISBN:

9780078022159

Author:

Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:

McGraw-Hill Education

Starting Out with Python (4th Edition)

Computer Science

ISBN:

9780134444321

Author:

Tony Gaddis

Publisher:

PEARSON

Digital Fundamentals (11th Edition)

Computer Science

ISBN:

9780132737968

Author:

Thomas L. Floyd

Publisher:

PEARSON

C How to Program (8th Edition)

Computer Science

ISBN:

9780133976892

Author:

Paul J. Deitel, Harvey Deitel

Publisher:

PEARSON

Database Systems: Design, Implementation, & Manag…

Computer Science

ISBN:

9781337627900

Author:

Carlos Coronel, Steven Morris

Publisher:

Cengage Learning

Programmable Logic Controllers

Computer Science

ISBN:

9780073373843

Author:

Frank D. Petruzella

Publisher:

McGraw-Hill Education

SEE MORE TEXTBOOKS

Consider alphabet Σ = {0,1,2,3} and language L = {w€Σ* : w = 0"1" 2" 3" for some positive m‚n € or disprove that L is context-free. Z}. Prove