3. Give regular expressions for each of the following languages over Σ = = {0,1}. (a) All strings that begin with 1 and end with 00. (b) All strings that have both 00 and 01 as substrings. Note that the substrings in either order and possibly overlap. 4. Describe the language L over Σ = {0,1} defined by each of the following equatio your answers as fully as you can. (a) L = 0+1L

3. Give regular expressions for each of the following languages over Σ = = {0,1}. (a) All strings that begin with 1 and end with 00. (b) All strings that have both 00 and 01 as substrings. Note that the substrings in either order and possibly overlap. 4. Describe the language L over Σ = {0,1} defined by each of the following equatio your answers as fully as you can. (a) L = 0+1L

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.
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
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.
Let Cbe the language over {a, b,c, d, e, f} accepting all strings so that: 1.There are precisely two b’s in the string. 2.Every a is immediately followed by an odd number of e’s. 3.Every d is immediately followed by an even number of f’s. 4.e’s and f’s don’t occur except as provided in rules 2 and 3. 5.All a’s occur after the first b. 6.All d’s occur before the second b. 7.In between the two b’s there are exactly twice as many a’s as d’s.HINT: Don’t be intimidated by the number of rules. The way they interact actually helps you simplify the number of cases you have to deal with while constructing this grammar. a. Construct a context-free grammar generating C.Explain how your construction accounts for each rule. b. We could eliminate one rule from Cand make it regular. Which rule would that be, and why would it work? You do not need a formal proof, but you do need an explanation.
Question 2. Find a regular expression that describes the given language:(2.a) Language of strings over Σ = {a, b, c} in which every character c is followed by the character a.(2.b) Language of strings over Σ = {a, b} which contain both substrings abb and bab. Note that thesubstrings can occur in any order and can overlap, so for example the string babb is in this language.(2.c) Let Σ = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, −, .}. The language L contains all strings that form a properdecimal representation of some number.Some examples of strings in the language: 42, -999, 0, 12.333, -0.14, 5.000.Some examples of strings that are not in the language: 028 (leading zero), 75. (decimal point but nodecimal part), -.5 (no integer part), -0 (there is no negative zero), 4..2-6 (malformed nonsense).You can use the shorthand [0−9] to stand for (0 + 1 + 2 + ···+ 9).
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)*
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…
Can you please help me with this problem I am struggling and I don't know how to solve this problem, can you do something visual for me to understand it better or show calculations and can you explain it step by step very thoroughly. question that I need help with: 1.42 For languages A and B, let the shuffle of A and B be the language {w| w = a1b1 · · · akbk, where a1 · · · ak ∈ A and b1 · · · bk ∈ B, each ai, bi ∈ Σ ∗ }. Show that the class of regular languages is closed under shuffle.
use the language operations (repetition, union, and concatenation). construct an NFA that realizes the language L over the alphabet {a, b, c} that consists of all strings that are either abc repeated any number of times, or an even length string with no as and ending in bc
1. For each of the following regular expressions find a language (i.e., a set of strings) over A = {a,b,c} that can be represented/described by that expression. a. ??∗ + ?∗?? b. ?∗????∗
Please dont copy or use chegg answeres. Please! Also explain Let Σ = {a, b, c} and define the finite languages L1 = {, aa, ab, ca, bab, bba, ccc} L2 = {a, c, ca, ccc} L3 = {c, ba, bab, bba, abc}. 1. (L1 ∪ L3) \ (L1 ∩ L2) 2. (L2 ∩ L3)L1
1) Given the alphabet as {0, 1}, write a DFA for the following three regular languages.(Give the complete description of the DFA with transition function as a table and also as a transition graph) (i) L = {w | w is a string of even length} (ii) L = {w | |w| mod 3 = 0} (iii) L = {w | w contains the string 001 as a substring} 2)Describe the extended transition function on a string recursively using transitions one symbol at a time for the three automata of the above problem. (i) A string (of length >=4) that belongs to the language (II) A string (of length >=4) that does not belong to the language