Please solve both parts in 30 minute (b) Let h: {0, 1}* → {a,b}° be the function defined by h(e) = e, h(0) = aa and h(1) = b,and for words of length two or greater:h(a,a2... an) = h(a,)h(a2)...h(an)for n22 and a; E {0, 1}. For a language L C {0, 1}* we defineh(L) = {h(w)|w € L} C {a,b}°For cach of the following languages, give a regular expression over {a,b} thatcorresponds to h(L):(i) L = {0m1" |m,n > 0}.(ii) L = {w e {0, 1}° | w contains 010 as a subword}.

Given:- h : {0, 1}* --> { a, b }* h(e) = e h(0) = aa h(1) = b h(L) = {h(w) | w ∈ L }⊂= {a, b}*

(b) Let h : {0, 1}* → {a, b}° be the function defined by h(e) = e, h(0) = aa and h(1) = b, and for words of length two or greater: h(aja2...an) = h(a,)h(a2)...h(an) for n > 2 and a; E {0, 1}. For a language L C {0, 1}° we define h(L) = {h(w)|w € L} C {a,b}° For cach of the following languages, give a regular expression over {a,b} that corresponds to h(L): (i) L = {0"1"|m,n > 0}. (ii) L = {w e {0, 1}°| w contains 010 as a subword}.

(b) Let h : {0, 1}* → {a, b}° be the function defined by h(e) = e, h(0) = aa and h(1) = b, and for words of length two or greater: h(aja2...an) = h(a,)h(a2)...h(an) for n > 2 and a; E {0, 1}. For a language L C {0, 1}° we define h(L) = {h(w)|w € L} C {a,b}° For cach of the following languages, give a regular expression over {a,b} that corresponds to h(L): (i) L = {0"1"|m,n > 0}. (ii) L = {w e {0, 1}°| w contains 010 as a subword}.

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

Given the underneath fragment code that is written in C language, Write down the function with domain and codomain then prove that function is bijective (One to one and Onto) if codomain excludes {5}? Find the inverse of that function? SHOW ALL YOUR WORKS double fun(double n){ if ( (int)n!=2) return (5*n+1)/(n-2): }
Given g = {(1,c),(2,a),(3,d)}, a function from X = {1,2,3} to Y = {a,b,c,d}, and f = {(a,r),(b,p),(c,δ),(d,r)}, a function from Y to Z = {p, β, r, δ}, write f o g as a set of ordered pairs.
Let L = {01, 10} be a language over Σ = {0, 1}. TRUE or FALSE:(a) 1000 ∈ L*(b) 101001 ∈ L*
O Given the language L = {(ba)m, amb", aa: m,n 2 0}, find the regular expression r such that L(r) = L.
The finite state machine (FSM): B generates the regular language, L = {a"b" | a 2 1 and m > 2}. Implement the above FSM as a C++ function, int is abb(char str) /| C++ code here that returns al if the given string, str, is in L and returns a 0 if str is not in L. Assume the existence of a C++ function, int str len(char str), which returns the length of the given string, str. A. 9.
Giventhegrammar B-> BB | (B) | ε 1.Describe the language it generates 2.Show that it is ambiguous
Consider two strings A and B. Take string A as your First name and Last name without space in-between (eg:TEJINDERTHIND) and string B as the name of your home town (eg: JALANDHARCITY). Now find the LongestCommon Subsequence (LCS) common to strings A and B using Dynamic Programming. detailed explanation
The finite state machine (FSM): a B generates the regular language, L = {a*b" | a 2 1 and m 2 2}. Implement the above FSM as a C++ function, int is_abb(char * str ) { II C++ code here } that returns a 1 if the given string, str, is in L and returns a 0 if str is not in L. Assume the existence of a C++ function, int str_len(char * str), which returns the length of the given string, str. 9.
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.
2. Prove that the language L(G) is not regular where G is the following cfg: G= ({S,A,B}, {a,b,c}, {S→Abbb|B, A→aS, B c}, S). Note: You must first determine L(G).
For function f from {a, b, c, d} to {1, 2, 3, 4, 5}. f(a) = 4, f(b) = 5, f(c) = 1 and f(d) = 3, The set containing the domain has the following elements
Consider two strings A and B. Take string A as your First name and Last name without space in-between (eg: LUDHIANACITY) and string B as the name of your home town (eg: JALANDHARCITY). Now find the Longest Common Subsequence (LCS) common to strings A and B using Dynamic Programming.