Show all work (1) State the pumping lemma with all its conditions and indicate how you go aboutproving that a language is not regular.(II) If the languages are regular, give an automaton. Otherwise, show it is notregular by using pumping lemma.L= {b²anbma³ | m, n ≥ 0}.L= {b²anbma³ | m = n}.L == {ww | w is any string over {a.b}}L = {a³b4}L = {anbn+1}L= {ambamn | m,n≥ 0 }

(I) Pumping Lemma for Regular Languages:The pumping lemma for regular languages states that for any…

Answered: (1) State the pumping lemma with all…

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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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?
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.…
(I) State the pumping lemma with all its conditions and indicate how you go about proving that a language is not regular. (II) If the languages are regular, give an automaton. Otherwise, show it is not regular by using pumping lemma.
Question 1 a) Based of your study for automata and theory of computer science, explain push down automata and give examples for each. b) State the Pumping Lemma for regular languages. Is every language that satisfies the pumping lemma property a regular language?
Hello, Using the constructions described in the proof of Kleene’s theorem, find nondeterministic finite-state automata that recognize this set: (0 ∪ 11)* Please show each step to get the automaton. ALSO each step needs to have the finite state machine DRAWN BY HAND
Dont copy the answer otherwise will surely 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…
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.
Think about the concept of extended transition functions δ* and ∆* of Deterministic Finite Automata and Nondeterministic Finite Automata respectively. Prove the following facts about those functions using mathematical induction. 1. Given a DFA M = (Q, Σ, δ, s0, F) and strings x, y ∈ Σ*, we have δ*(q, xy) = δ*(δ*(q, x), y). 2. Given a NFA N = (Q, Σ, ∆, S0, F), subsets A ⊆ Q, B ⊆ Q and a string x ∈ Σ∗, we have ∆* (A ∪ B, x) = ∆*(A, x) ∪ ∆*(B, x).
Please prove or disprove: If a language L ⊆ Σ∗ is recognized by a FA, then there is an NFA M = (K,Σ,δ,s0,F) with |F|= 1 such that L = L(M).
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.
Check whether the following Finite Automata’s are for regular language or not? Use pumpinglemma for detailed answers. Note: 1-n should be greater than 1. 2-At least make 3 different words for each FA and run a pumping lemma to prove your answer.
Prove that the following language A is decidable (e.g., give a TM that decides A). A = {⟨M⟩ | M is an NFA and L(M) = B}, B = {w | w ∈ {0,1}∗ and w contains 001 as a substring}. Observe that B is a regular language. Recall that the language EQ_DFA is decidable.

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