Prove that the language given by the CFG below is not regular. S → AA | B A → 0A| A0 | 1 B 0B00 | 1 Make sure that you give a formal proof with every step clearly erplained and justified with sentences (as seen in the tertbook), do not write just a sequence of mathematical erpressions. Attach File

Prove that the language given by the CFG below is not regular. S → AA | B A → 0A| A0 | 1 B 0B00 | 1 Make sure that you give a formal proof with every step clearly erplained and justified with sentences (as seen in the tertbook), do not write just a sequence of mathematical erpressions. Attach File

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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kindly give proper explanation and don't copy from any website, I will upvote you (Pumping lemma for regular languages) Let L be the language over the unary alphabet Σ = {1} consisting of all strings whose length is the square of an integer. Show that L is not regular
True or False Statements and provide proof with your answer. a. Suppose L is the empty language, then L only includes "epsilon", Furthermore, "epsilon" is the "identity" for concatenation since when concatenated with any string it yields the other string as a result. That is, for any string w, (epsilon)w = w(epsilon) = w. b. Suppose L us a regular language. Then, L is a set of stings satisfying a certain condition or conditions. So, L is unique. On the other hand, there can be more than one DFA (e,g,, two DFAs) accepting L. c. Consider finite antomata and regular expressions. The regular expression " 1{}*(0+1) " can be simplified to " 1(0+!) ". d. Consider the following language L, L = {ab, aabb, aaabbb, aaaabbbb, ......}. Note that L includes all strings of a's followed by the same number of b's. (Assume Sigma = {a,b}). Then, we can design the DFA for accepting L. e. If E and F are regular expressions, then E + F is a regular expression denoting the union of L(E) and L(F).…
3. show L = {0^n1^n0^n1^n | n >=0} is not context free language. Prove by stating that even though L follows condition 3 of pumping lemma , it will not follow condition 1, hence not context free?
Correct and detailed answer will be Upvoted. Thank you! Given a CFG G and a variable A, consider the problem of testing whether A is usable. We say A is usable if it appears in some derivation of some string w ∈ G. Formulate this problem as a language and show that it is decidable.
The quotient of two languages L_1/L_2 = { x | ∃y ∈ L_2 (xy ∈ L_1) } That is, the set of strings from which a string in L_1 could be created by appending a string in L_2. So, {aaa, aab, aba, abb} / {a, bb} = {aa, ab, a} Are regular languages closed with respect to quotient? What if L_1 is not regular but L_2 is? Is L_1/L_2 guaranteed to be regular? What if L_2 is not regular but L_1 is? Is L_1/L_2 guaranteed to be regular? Exhibit a nonregular language L1 and regular language L2 for which L1/L2 is nonregular.
dont copy from any existing answers I have previous answers SUrely dislike dont answer without any knowledge Let regular language L1 recognized by DFA (Q1,Σ,δ1,s1,F1) and regular language L2 recognized by DFA (Q2,Σ,δ2,s2,F2). We will construct a product DFA as the quintuple (Q,Σ,δ,s,F) where: •Q=Q1×Q2•For allx∈Σ and (q1,q2)∈Q1×Q2,δ((q1,q2),x) = (δ1(q1,x),δ2(q2,x))•s= (s1,s2) Suppose we have a DFA that recognizes concatenation of two languages L1 L2. Also suppose we have a DFA that recognizes L2. Using these two DFAs, can we construct a new DFA to recognize L1? If yes, construct it.If no, explain why. Let regular language L1 recognized by DFA (Q1,Σ,δ1,s1,F1) and regular language L2 recognized by DFA (Q2,Σ,δ2,s2,F2). We will construct a product DFA as the quintuple (Q,Σ,δ,s,F) where: •Q=Q1×Q2•For allx∈Σ and (q1,q2)∈Q1×Q2,δ((q1,q2),x) = (δ1(q1,x),δ2(q2,x))•s= (s1,s2) Suppose we have a DFA that recognizes concatenation of two languages L1 L2. Also suppose we have a DFA that recognizes L2.…
a)Prove that the following language is not regular. L = {w.w': w∈ {a, b}*| w' is obtained by replacing all a’s by aa’s and all b’s by bb’s}.
Consider the following languages over the alphabet Σ = {a, b}: 1. L1 = {xwx : x, w ∈ Σ∗}2. L2 = {xwx : x, w ∈ Σ∗, |w| = 1}3. L3 = {xwx : x, w ∈ Σ∗, |x| = 1} For each language, decide whether it is regular or not regular. Prove each of your claims. If you construct a FA or a regular expression, you do not need to prove the correctness of your construction.
dont post any existing answers directly dislike Let regular language L1 recognized by DFA (Q1,Σ,δ1,s1,F1) and regular language L2 recognized by DFA (Q2,Σ,δ2,s2,F2). We will construct a product DFA as the quintuple (Q,Σ,δ,s,F) where: •Q=Q1×Q2•For allx∈Σ and (q1,q2)∈Q1×Q2,δ((q1,q2),x) = (δ1(q1,x),δ2(q2,x))•s= (s1,s2) Suppose we have a DFA that recognizes concatenation of two languages L1 L2. Also suppose we have a DFA that recognizes L2. Using these two DFAs, can we construct a new DFA to recognize L1? If yes, construct it.If no, explain why. Let regular language L1 recognized by DFA (Q1,Σ,δ1,s1,F1) and regular language L2 recognized by DFA (Q2,Σ,δ2,s2,F2). We will construct a product DFA as the quintuple (Q,Σ,δ,s,F) where: •Q=Q1×Q2•For allx∈Σ and (q1,q2)∈Q1×Q2,δ((q1,q2),x) = (δ1(q1,x),δ2(q2,x))•s= (s1,s2) Suppose we have a DFA that recognizes concatenation of two languages L1 L2. Also suppose we have a DFA that recognizes L2. Using these two DFAs, can we construct a new DFA to recognize…
Dont post existing answers dislike if copied dont answer without knowledge Let regular language L1 recognized by DFA (Q1,Σ,δ1,s1,F1) and regular language L2 recognized by DFA (Q2,Σ,δ2,s2,F2). We will construct a product DFA as the quintuple (Q,Σ,δ,s,F) where: •Q=Q1×Q2•For allx∈Σ and (q1,q2)∈Q1×Q2,δ((q1,q2),x) = (δ1(q1,x),δ2(q2,x))•s= (s1,s2) Suppose we have a DFA that recognizes concatenation of two languages L1 L2. Also suppose we have a DFA that recognizes L2. Using these two DFAs, can we construct a new DFA to recognize L1? If yes, construct it.If no, explain why.
Question 3 Prove each language over {0,1} is undecidable using a reduction with A_TM = { < M, w > | w is an element of {0,1}*, M is a Turing machine, M accepts w }: a) L = { < M, k >, k > 2 | M visits at least k different states when given the empty string as input } b) L = { < M > | M halts on exactly 2 string inputs } Please solve all parts and Full explain this question and text typing work only thanks.
Prove or disprove the following: If L* is regular, then L must be regular. For any language L, L* must be regular If L1L2 is regular, then both L1 and L2 have to be regular. The union of finite number of regular languages is always regular. The union of infinite number of regular languages is always regular.