For each statement below, decide whether it is true or false. If it istrue, prove it. If it is not true, give a counterexample.All parts refer to languages over the alphabet {a, b}.(d) If neither L1 nor L2 can be accepted by an FA, then Lin L2 cannot.

d) let's assume a FA which accept all the string which starts from a L1 is bbabaaba so it's is not…

Answered: For each statement below, decide…

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

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For each of the following languages, determine whether or not it is context-free. You must justify youranswer. I understand this is a language accepting any a,b words as long as it is a palindrome, and have been using the pumping lemma, but am not sure how to approach it here.
For each statement below, decide whether it is true or false. If it is true, justify youranswer. If it is not true, give a counterexample. All parts refer to languages over {0,1}.a. If L1 ⊆ L2, and L1 cannot be recognized by a FSA, then L2 cannot.b. If L1 ⊆ L2, and L2 cannot be recognized by a FSA, then L1 cannot.c. If L1 cannot be recognized by a FSA, then L1c cannot. Note: L1c is the complement of L1.d. If neither L1 nor L2 can be recognized by a FSA, then L1 ∪ L2 cannot.e. If neither ?1 nor ?2 can be recognized by a FSA, then ?1 ∩ ?2 cannot.
PLease answer both question with clear explanastion. Thanks in advance 1. What is the regular expression for the language, over alphabet {a, b}, of strings that start and end with the substring ab and contain one or more repetition of the substring bab.2. Describe in English the language associated with the following regular expression: (a+b)*a(a+b)*a*(a+b)*a(a+b)*
Answer this please in 1 hr.:) -sorry for my grammar but i put some examples.
For each of the following statements about languages (i.e. sets of words), state whether they are true or false
For the alphabet Σ ={a, b}, construct an FA that accepts the following languages.(a) L = {all words with exactly one b}.(b) L = {all words with at least one a}.(c) L = {all words with no more than three b's}.(d) L = {all words with at least one a and exactly two b's}(e) L = {all words with b as the third letter}(f) L = {all words with the number of letters being divisible by 4}(g) L = {all words that do not have two a’s together or two b’s together}
Question 2 c) Give a regular expression for the following regular languages, assuming the alphabet is Σ := {0, 1}. I. The set of all strings, when viewed as binary representation of integers, that are divisible by 2. II. The set of all strings containing 00. III. Give a closed-form regular expression for the set of all string not containing consecutive 00.
For each of the following languages L, state whether L is regular, context-free but not regular, or not context-free and prove your answer. {xyx^R where x,y∈Σ^*} {xx^R yy^R{ where x,y∈Σ^*} {xx^R x{ where x∈Σ^*}
Find DFAs that accept the following languages. 1. L(ab(a + ab) ∗ (a + aa)) 2. L(ab∗a ∗ ) ∪ L((ab) ∗ ba)
Prove that the following language is not context free.
Show that the following pair of regular expressions define the same language over alphabet {a, b}: a(ba+a)*b and aa*b(aa*b)*
For each of the following languages L, state whether L is regular, context-free but not regular, or not context-free and prove your answer. {ww where w∈Σ^*} {a^n b^m where n≠m} {〖(ab)〗^n a^n b^n,n≥0}

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For each statement below, decide whether it is true or false. If it is true, prove it. If it is not true, give a counterexample. All parts refer to languages over the alphabet {a, b}. (d) If neither L1 nor L2 can be accepted by an FA, then Lin L2 cannot.