Recursive definitions Give the recursive definition for the following languages: (a) L2a = {w = {0, 1}* |w has 00 as a substring} (b) L₁₁ = {w= {0,1}* |w all strings with alternating O's and 1's} (c) L2c = {w = {0, 1}* |w has a equal number of 0's and 1's}
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- java A time series is represented a list of time/value pairs Write a function that takes two time series and outputs a new series of the summation of themCan you edit the code and utilize these sample programs for timing and file reading: BinaryFileRead.cpp // BinaryFileRead.cpp : Defines the entry point for the console application. // #include "stdafx.h" #include <iostream> using namespace std; int main() { int *arrayToSort; char fileName[50]; int size,readVal; cout << "Enter a filename to sort => "; cin >> fileName; FILE *inFile; fopen_s(&inFile,fileName, "rb"); fread(&size, sizeof(size), 1, inFile); arrayToSort = new int[size]; for (int i = 0; i < size; i++) { fread(&readVal, sizeof(readVal), 1, inFile); arrayToSort[i] = readVal; } fclose(inFile); return 0; } Timing.cpp // Timing.cpp : Defines the entry point for the console application. // #include "stdafx.h" #include <iostream> #include <time.h> //ctime #include <sys/timeb.h> //_timeb _ftime_s using namespace std; int main() { struct _timeb timebuffer; char timeline[26]; _ftime_s(&timebuffer);…Instruction: Read Part 1: Chapter 1-4 of the book Automata, Computability and Complexity by Elaine Rich and answer the following Questions. 1 1. Let L₁ = {all string that ends in a} and L₂ = {all string that starts in b} for Σ = {a,b} Find the following language. a. L₂L1 b. ¬(L₂) (4₁) c. d. L₁ L₂ e. L₁ UL2 2. Let L {even numbers of a's and b's}. For each of the following strings, state whether it is an element of L. a. b. ababababaa aabbaabbaa aabbcc C. d. baabaabaabbb e. E 3. Let L = {up, down, right, left}. List the element of L² or LL in lexicographic order.