In the following Deterministic Finite Automaton (DFA) with the input alphabet {0,1}: S₁ 01 O empty string 0 What strings are accepted. Mark all correct answers. 00111111 0 110011100 011111 101010 S₂ 1
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- Design a deterministic finite state automaton (DFA) that accepts exactly the strings over the alphabet {A, B, ...,Z} that contain at least two R, at most one T, and where every E comes after some S (there may be other letters in between). For instance, your DFA should accept the strings: • MYSTICWARRIORS • MARSMATRIX • SHOCKTROOPERS • CONTRAHARDCORPS STRIDER but not the strings • CRAZYTAXI (it does not contain at least two Rs) LASTRESORT (it contains more than one T) AFTERBURNER (there are Es without a S somewhere before them) • BATTLECIRCUIT (all of these at the same time) Clearly indicate the meaning of each state. One way to do this is to number the states and have a numbered list of their meanings, but any readable method you use to label and explain your states is fine. Hint: there are three separate conditions accepted strings must meet; states will need to encode whether or not each one is met (or perhaps partially met). You can label an edge with the word “else" to indicate it…Create a Deterministic finite automaton that takes in binary strings and accepts them which has both an odd number of zeros and a sum that is divisible by 3 (but no others). For example, 0111 should be accepted, but not 011 or 111.Convert the following DFA to an equivalent regular expression: Deterministic finite automaton a 93 a b b b a q2 q1 b a 44 Grafstate® M 1. Create an initial GNFA GO that is equivalent to M. Here are suggested steps: a. Choose a state in Q. Modify GO to create an equivalent GNFA called G1 that contains all states in GO except for the state you chose. b. Choose another state in Q. Modify G1 to create an equivalent GNFA called G2 that contains all states in G1 except for the state you chose. c. Choose another state in Q. Modify G2 to create an equivalent GNFA called G3 that contains all states in G2 except for the state you chose. d. Choose another state in Q. Modify G3 to create an equivalent GNFA called G4 that contains all states in G3 except for the state you chose.
- You are given a N*N maze with a rat placed at maze[0][0]. Find whether any path exist that rat can follow to reach its destination i.e. maze[N-1][N-1]. Rat can move in any direction ( left, right, up and down).Value of every cell in the maze can either be 0 or 1. Cells with value 0 are blocked means rat cannot enter into those cells and those with value 1 are open.Input FormatLine 1: Integer NNext N Lines: Each line will contain ith row elements (separated by space)Output Format :The output line contains true if any path exists for the rat to reach its destination otherwise print false.Sample Input 1 :31 0 11 0 11 1 1Sample Output 1 :trueSample Input 2 :31 0 11 0 10 1 1Sample Output 2 : false Solution: //// public class Solution { public static boolean ratInAMaze(int maze[][]){ int n = maze.length; int path[][] = new int[n][n]; return solveMaze(maze, 0, 0, path); } public static boolean solveMaze(int[][] maze, int i, int j, int[][] path) {//…For which of the following is the set S equal to {(a, b)|a, b nonnegative integers }? Select one: O A. None of these. O B. (0,0) S; (x, y) = S → (x + y, y) = S and (x,x + y) = S O C. (0,0) = S; (x, y) = S→ (x + 1, y) = S and (x, y + 1) = S O D. (0,0) E S; (x, y) = S → (x + 1, y + 1) = SDraw a deterministic finite automaton (DFA) for the set of strings over the alphabet {a, b} whereeach string begins and ends with the same letter. For example, ababba and bbbab are strings thatshould be accepted by the DFA, but abbab and baaba should not be accepted.
- Consider the finite automaton M3 and answer the related questions. 91 1 0 0 1 92 93 1 94 0. 1 (a) For each of the following strings specify whether or not it is accepted/recognized by M3. i. 0100 ii. 1001 iii. 0101 iv. 1 v. 11111 vi. 0101011 (b) Describe in English the language that M3 accepts/recognizes.We wish to build the simplest possible automaton for L = {xcx: x is in (a+b)*}. Note there are two copies of x separated by a special center symbol 'c', e.g., "baacbaa". What is the simplest automaton for deciding L? A. We can decide L using only an NFA. B. We can decide L using a deterministic PDA. C. We need at least a nondeterministic PDA for deciding L. D. We need at least a Turing machine for deciding L.False For each language L over a given alphabet E, let 1(L, E) denote the language over E obtained from L by generating all permutations of its strings - that is, r(L, E) -{we E*: there is a string v in L such that w is a permutation of v ). Specify which one of the following statements is true. Choose None of the other statements is true. The language r((0b1)*, (0, b,1}) is decidable. The language n((Ob1)*, (0, b,1}) is regular. There is no regular language L over an alphabet E such that the language n(L, E) fails to be context-free. Consider alnhaber E-Lo and context-free grammar G over E with precisely one
- Draw a deterministic and non-deterministic finite automate which accept 00 and 11 at the end of a string containing 0, 1 in it, e.g., 01010100 but not 000111010.Q. Idempotency law isI. P Ú P = P.II. P Ù P = P.III. P + P = P.(a) Only (I) above(b) Only (II) above(c) Only (III) above(d) Both (I) and (II) aboveConsider the following Nondeterministic Finite Automaton (NFA). 1 Paragraph b b b b BI 3 a 4 b b (a) What are the possible states that this NFA could be in, after reading the input string bbb? (b) Prove, by induction on n, that for all positive integers n, the string (bbb)" is accepted by this NFA. (This string is obtained by n repetitions of bbb.) 20 30 a 2