1. Suppose that a bank only permits passwords that are strings from the alphabets = {a,b.c, d, 1, 2, 3, 4). The passwords follow the rules (a) The length can be 5 or more. (b) The first alphabet must be from {a, b, c, d}. (c) The last two alphabets must be from {1,2,3,4} Give a regular expression for this language.
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- Let A = {a, b, c}, B = {x, y}, and C = {0, 1}.8. Consider the following: An online trading company wants to offer discounts to new customers. The company has recently emailed discount code to the customers. New customer must have a discount code to be eligible but returning customer are not eligible for a discount. Let A = Returning Customer B = Discount Code (a) Draw a truth table to represent when a customer has a discount. (b) From your truth table in (a) produce a Boolean expression to represent discounted customer (Q) for the trading company.5. Let A = {(G, a) | G is a CFG, a is a terminal symbol, and L(G) na' # Ø.} Show that A is decidable.
- Q3. Let E = {a, b}. Let BDFA = {(M)| M is a DFA that accepts some string containing an equal number of as and bs). Show that BDFA is decidable. (Hint: remember the different results/theorems about CFLs, provide a semi-formal discussion/argument)8. Let E = {0, 1}. Compute the language of the given regular expression. (a) L(10) (b) L(ɛ +0*)Answer this in C++ Asap Alice and Bob play a game. At first, there is only one tree with roots. The players take turns, Alice begins. At one point, Alice has to pick up any empty underground tree roots (or shrubs) and remove them. Bob, on the other hand, has to pick out any part of the empty leaves and remove them from the tree (or trees). (Please note that Bob always takes some depth from the leaves of the first tree.) It is not allowed to skip the turn. The game ends when the player is unable to take a chance. Alice's goal is to reduce the number of turns made by both players, while Bob wants the number to be greater. Considering that they both played very well, how many turns did they make last? Input 1 2 12 Output 2
- Q. No. 2: Let Σ = {a, b, c}. a. Draw a DFSA that rejects all words for which the last two letters match. b. Draw a DFSA that rejects all words for which the first two letters match.An argument is expressed in English below. The domain is the set of people attending a party. Every person who was late to the party left the party early. There is a person who was late to the party and was not happy. .. There is a person who left the party early and was not happy. The form of the argument is: x (P(x) → Q(x)) 3X (P(x) ^ ¬R(x)) .: 3x (Q(x) ^ ¬R(x)) Select the definitions for predicates P, Q, and R. P(x): Pick Q(x): Pick R(x): PickYou are the chief commander of US Army; you have been deployed in an ongoing war training of defusing the mine. Mines are placed on the ground which can be considered as a gird of size N*M. Each block (i, j) has a mine in it if and only if the summation of the block coordinates is divisible by 2. Your task is to move from the first row to the last row. The mines will not blow if the given rules are followed: • If you are on even row you can move to any cell that is in the neighborhood • If you are on odd row, you can only go the odd row that has mine on that and same with the unmined row. You have to develop a python program to calculate the number of ways to reach row number N starting from row number 1. Test Cases: 4 8 Output: 10
- True or False 1. Matrices are often represented by single small letters a, b, c... etc.2. Two m x n matrices A and B are equal if aij=bij for each i & j. (i.e., the two matrices havesame size, and all the corresponding elements are equal).3. Matrices A & B are said to be conformable in the order AB if, and only if, the number ofrows in A is equal to the number of columns in B.4. Suppose Matrix A is having 4 rows and 3 columns, and Matrix B is having 3 rows and 2columns. The product size of AB is a 4 x 2 matrix.5. Suppose B is the matrix obtained from an n x n matrix A by multiplying the entries in arow/column by a non-zero constant and adding the result to the corresponding entries inanother row/column. Then, det(B) = det(A).Question 2: Encoding Cryptography is the study of trying to create secure information by obscuring the original message. One simple encryption method is to substitute letters from the original message with other letters. To make it harder to decrypt the hidden message, we may also remove clues such as the length of the words in the message and any punctuation or capitalization. Write a function encode that consumes a string message. The function produces a string which is encrypted according the following procedure: • Only the letters from the original message will be encrypted. Other characters such as spaces, punctuation, numeric digits, etc. are not included in the encrypted message at all. • The encrypted message will only contain uppercase letters. • Each letter will be replaced by the uppercase letter at the opposite end of the English alphabet. In other words, A or a will become z, B or b will become Y, C or c will become x, .., z or z will become A. • The encrypted message will…Let p = "Paris is called the City of Lights" and let q = "The Eiffel Tower is locatedin Paris". Write the English statements corresponding to each of the following:(i) ∼p V q(ii) p → q(iii) p V q(iv) ∼p ʌ∼q(v) ∼(p V q).