II. Pushdown Automata. Draw a PDA that recognizes the following languages. All machines should be deterministic (each transition from each state has a unique transition symbol), non-deterministic machines will not be considered: d. L = {w & akb'gc | k > 0, f is 2 times the value of k, and c =k+f}
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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…construct a deterministic finite automaton that describes R=ab*a*The following four statements describe differences between Finite Automata and Pushdown Automata. Three of them are correct. Which one is incorrect? Finite Automata can only have a finite number of states while Pushdown Automata can have an infinite number of states. Pushdown Automaton = Finite Automaton + a stack Finite Automata cannot count while Pushdown Automata can. In Finite Automata, a transition is represented by 3-tuple, but in Pushdown Automata, a transition is represented by 5-tuple.
- The Harvard robotics club has organized a Robothon. n robots are placed alongthe edge of a circular area at the middle of the OAT(open air theatre). Each robot will move along arbitrary tracksinside the circle while leaving behind a heat signature along its trail. However, they have beenprogrammed not to cross their own trail or the trail of another robot, neither will they ever moveout of the circle. In case a pair of robots i and j meet at any point, they are removed from the sceneand the club will pay a reward sum of M[i, j] to the owners of these robots. Note that some robotscan keep moving infinitely without ever meeting another one. Given the reward matrix M whereM[i, j] = M[j, i], design a polynomial time algorithm that determines the maximum money theclub might potentially end up spending. For this particular problem, give a very brief justificationof the recurrence. Give pseudo-code for a dynamic program which solves the recurrence efficiently Youdo not need to prove…b) Given a state table as below, where S = {o0, 01, 02, 03}, I = {a, b, c} and F = {o0, 02}. %3D f b I a S σι 02 σι 02 02 03 σι σι σι i. Draw the transition diagram of the finite-state automaton (S, I, f, 00, F). Determine whether the following strings are accepted by the Deterministic Finite Automata (DFA) or not. • abaabbc • abbccbab1. Turing machines may also be used to compute functions. Give a state-transition diagram for a Turing machine that takes as input a binary string w, increments w, and enters the accepting state. For example, on input w = 100111, the Turing machine begins like this: 90 1|0|0|11|1|-|-|-|-|-|- The Turing machine should halt with 101000 on the tape: Jaccept 101000
- 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.Correct answer will be upvoted else downvoted. Computer science. in case there are two planes and a molecule is shot with rot age 3 (towards the right), the cycle is as per the following: (here, D(x) alludes to a solitary molecule with rot age x) the primary plane delivers a D(2) to the left and lets D(3) progress forward to the right; the subsequent plane delivers a D(2) to the left and lets D(3) progress forward to the right; the primary plane lets D(2) forge ahead to the left and creates a D(1) to the right; the subsequent plane lets D(1) progress forward to one side (D(1) can't create any duplicates). Altogether, the last multiset S of particles is {D(3),D(2),D(2),D(1)}. (See notes for visual clarification of this experiment.) Gaurang can't adapt up to the intricacy of the present circumstance when the number of planes is excessively huge. Help Gaurang find the size of the multiset S, given n and k. Since the size of the multiset can be extremely huge, you…C-F languages (or see the following figure). In particular..it points out that the language {am,a"b" | m,n = N} is a deterministic C-F language, but not LL(k) for any k Palindromes over {a, b} Non-deterministic C-F {am,a"b" | m.ne N}; Deterministic C-F -LL(K) {ab❘n EN}- Regular To show the language is not LL(k) for any k, note that a grammar for this language is SAB A→ B -> 10 or S-A|B A→ B (you only need to answer one case here, either one). The language contains A as an element. Now consider the case k = 1 and consider the input string ab. When the first symbol is scanned, we get an 'a'. This information alone is not enough for us to make a proper choice. So we don't even know what to do with the first step in | the parsing process. For k = 2, if we consider the input string aabb, we face the same problem. For any k > 2, the input string ab would cause exactly the same problem. So this grammar is not LL(k) for any k. On the other hand, by putting proper instructions into the blanks…
- Question: For each of the below three problems, draw the state diagram of a pushdown automaton. (a) {ww starts and ends with same symbol } (b) {w the length of w is odd } (c) {w\w = WR, i.e., w is a palindrome }. For instance the word noon is a palindrome because reversing the letters results in the same word.21 Given a Mealy automaton, which is described in the following table. 8/A so 54/1 S1/0 S1 52/1 sO/1 S2 53/1 S1/0 S3 S4 /0 s0 /1 54 S0/1 $1/0 Reduce the machine using Ginsburg /Huffmann method .Hint: Tables/input fields that are not required can be left empty. AK A A A A A A A A A A A A A A A ÄK 8/A B B B B B B B B. AK 6/A 1 8/A 1 S'O I.S S2 S'3 S'A produce dealer has a warehouse that stores a variety of fruits. He wants a machine capable of sorting the fruit according to the type. There is a conveyor belt on which the fruit is loaded. It is then passed through a set of sensors which measure 3 properties of the fruit: shape, texture, and weight. The sensor system is somehow rather primitive: • Shape sensor : -1 if the fruit is round and 1 if it is more elliptical• Texture sensor : -1 if the surface is smooth, 1 if it is rough• Weight sensor : -1 if the fruit is > 500g, 1 if is < 500g The sensor output will then be input to a Neural Networks based classifying system. As an AI Engineer you are supposed to design (draw the architecture and determine the optimal weight W and bias b) a simple neural network (could be a single perceptron) that can be used to recognize the fruit so that it can be directed to the correct storage bin. As a startup case, the simple network will only be used for two type of fruit i.e. banana and…