CS402 - Theory of Automata

CS 402 GDB 1 SOLUTION FALL 2020 FINITE AUTOMATA (FA): Finite Automata = PDA with finite stack. = TM with finite tape. = TM with unidirectional tape. = TM with read only tape. PUSH DOWN AUTOMATA (PDA): PDA = Finite Automata with Stack TURING MACHINE ™: Turing Machine = PDA with additional stack. = FA with 2 stacks. The Applications of these Automata are given as follows: Finite Automata (FA) – • For the designing of lexical analysis of a compiler. • For recognizing the pattern using regular expressions. • For the designing of the combination and sequential circuits using Mealy and Moore Machines. • Used in text editors. • For the implementation of spell checkers. Push Down Automata (PDA) – • For designing the parsing phase of a compiler (Syntax Analysis). • For implementation of stack applications. • For evaluating the arithmetic expressions. • For solving the Tower of Hanoi Problem. Linear Bounded Automata (LBA) – • For implementation of genetic programming. • For constructing syntactic parse trees for semantic analysis of the compiler. Turing Machine ™ – • For solving any recursively enumerable problem. • For understanding complexity theory. • For implementation of neural networks. • For implementation of Robotics Applications. • For implementation of artificial intelligence.

@zaasmi said in CS402 Assignment 1 Solution and Discussion: Re: CS402 Assignment 1 Solution and Discussion Please share CS402 Assignment 1 Fall 2020 Theory of Automata (CS402) Assignment # 01 Fall 2020 Total marks = 20 30th November, 2020 Please carefully read the following instructions before attempting assignment. RULES FOR MARKING It should be clear that your assignment would not get any credit if: The assignment is submitted after the due date. The submitted assignment does not open or file is corrupt. Strict action will be taken if submitted solution is copied from any other student or from the internet. You should concern the recommended books to clarify your concepts as handouts are not sufficient. You are supposed to submit your assignment in .doc or docx format. Any other formats like scan images, PDF, zip, rar, ppt and bmp etc will not be accepted. Topic Covered: Objective of this assignment is to assess the understanding of students about: · The concept of languages · Regular Expressions · Finite automata. NOTE No assignment will be accepted after the due date via email in any case (whether it is the case of load shedding or internet malfunctioning etc.). Hence refrain from uploading assignment in the last hour of deadline. It is recommended to upload solution file at least two days before its closing date. If you people find any mistake or confusion in assignment (Question statement), please consult with your instructor before the deadline. After the deadline no queries will be entertained in this regard. For any query, feel free to email at: CS402@vu.edu.pk Questions No 01 Marks (10) Construct a FA which recognizes the set of all strings defined over ∑= {0, 1} ending with the suffix ‘10’. Also draw transition table for that language. Questions No 02 Marks (10) Identify the language L accepted by the following regular expression abab(a + b)*. Also define the recursive definition of that language. Which of the following string(s) is/are part of language L defined as above? baaba aabaa abbbab babaa

Solution: [image: Q6aVBO6.png] [image: PB7zJDO.png] [image: XnCOX5j.png] [image: KG4WE2y.png] [image: kagU2d1.png] [image: FdZJjgG.png] [image: GgAlx12.png] [image: JkCiwJs.png] [image: oyMNZdX.png] [image: Te4WVHR.png]

Develop a program that calculates Loan in C++. Your program should satisfy the following requirement: User Input: 1 User is asked to enter name. 2 User is asked to enter number of dependent with range (0-5). 3 User is asked to enter status i.e. (Permanent or Probation). 4 User is asked to enter Salary. 5 User is asked to enter Duration at Job (in years): o <1 o 1-2 o 2-4 o 4-7 o >7 6 User is asked how much loan is required. Criteria:  Loan can be given if and only if a person is on Permanent job for more than 1 years.  Minimum salary from which a loan can be given is 35,000 per month for a person having no dependent. Minimum salary requirement increases by 20,000 per dependent.  If years of services is from 1 to 2 years, then max loan amount can be up to 6 salaries.  If years of services is from 2 to 4 years, then max loan amount can be up to 8 salaries.  If years of services is from 4 to 7 years, then max loan amount can be up to 10 salaries.  If years of services is from 7 to 10 years, then max loan amount can be up to 12 salaries.  If years of services is more than 10 years, then max loan amount can be up to 24 salaries.  Add 13% interest on the approved loan amount. This amount will be payable within 8 years’ time i.e. 96 months.  If the money to lend is more than the lend amount, then calculate the difference and show it properly.  For unsuccessful Loan Application: Show Message: “CUSTOMER NAME, your lend application has not been successful this time”.  For Successful Loan Application: Show Message: “Congratulations CUSTOMER NAME, your lend application is successful this time. Your monthly installment will be ______ Amount Payable for 96 months”.

Q1. Show that the following pairs of regular expressions define the same language over the alphabet L = {p, q}. (i) (pq)p and p(qp) (ii) (p* + q)* and (p + q)* (iii) (p* + q*)* and (p + q)* [15 marks = 5*3] https://youtu.be/6OJ6PEp-3w8 Solution: (i) (pq)p and p(qp) represents same language. Both will never generate pp’s and both are starting and ending with p (ii) (p* +q)* (p+q)* (p*)+ q p* + q* p* + q* p* + q* Both are all strings possible in L = {p,q} (iii) (p* +q*)* (p+q)* (p*)* + (q*)* p* + q* (p + q)* Language with all strings Q2. Write a regular expression for the following language over the alphabet L = {x, y} such that it accepts all strings in which the letter y is never tripled. This means that no word contains the substring yyy. [5 marks] Solution: The required R.E will be (˄ + y + yy) (x + xy + xyy)*

Idea Solution: [image: DTgY5qn.png]

@zareen thanks for sharing

CS402_Assignment#01_Solution_cyberian.pk.docx [image: 1573729827421-e9b034a6-5143-46d8-a96c-bfbeda3e1b82-image.png]