What's wrong with the following "proof" of Proposition 2? Consider any DFA D. Since D is also an NFA, there exists an equivalent NFA N with only one accept state, by Proposition 1. Since we proved in class that every NFA can be converted to an equivalent DFA, there exists a DFA D' that's equivalent to N (and hence equivalent to D) and has only one accept state.
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- Consider a robot that is capable of picking objects from a shelf and placing them on the table. Suppose that the robot’s arm works perfectly, and the environment is fully-observable. (i) Define a STRIPS operator that could be used for planning the actions of this robot. (ii) Give an example of a state S of the world at which this STRIPS operator is applicable. (iii) Describe the operation of this STRIPS operator at this state S, to show the next state S0 of the world.Explain what is wrong with the following proposed definition of the set membershippredicate ∈ :∀ x, s x∈{x|s}∀ x, s x∈ s ⇒ ∀y x∈{y|s} .Let P(x) and Q(x) be predicates and suppose D is the domain of x. For the statement forms in the given pair, determine whether they have the same truth value for every choice of P(x), Q(x), and D, or whether there is a choice of P(x), Q(x), and D for which they have opposite truth values. ∃x ∈ D, (P(x) ∧ Q(x)) and (∃x ∈ D, P(x)) ∧ (∃x ∈ D, Q(x))
- Please answer part 3 of this question.Let Σ = {0, 1} and consider the following language L = {w ∈ Σ∗ : w contains the substring 10 or 01}. 1. Give a minimal deterministic finite automaton M accepting L. 2. Provide a “proof sketch” which shows the correctness of your automaton. To do this: a. Make a claim about your machine’s extended transition function δ∗. You do not need to prove your claim. b. Show, using your claim, that L(M) = L. 3. Show that your automaton is minimal by showing that no determistic finite automaton, N, can exist such that L(N) = L and N has fewer states than M.Suppose a biking environment consists of n ≥ 3 landmarks,which are linked by bike route in a cyclical manner. That is, thereis a bike route between landmark 1 and 2, between landmark 2 and 3,and so on until we link landmark n back to landmark 1. In the centerof these is a mountain which has a bike route to every single landmark.Besides these, there are no other bike routes in the biking environment.You can think of the landmarks and the single mountain as nodes, andthe bike routes as edges, which altogether form a graph G. A path is asequence of bike routes.What is the number of paths of length 2 in the graph in termsof n?What is the number of cycles of length 3 in the graph in termsof n?What is the number of cycles in the graph in terms of n?Correct answer will be upvoted else downvoted. Computer science. lamp can be coordinated to enlighten either a few lights to the left or a few lamps to the right. In the event that the I-th lamp is gone to one side, it enlightens all such lights j that j∈[i−pi,i−1]. Also, in case it is gone to one side, it enlightens all such lamps j that j∈[i+1,i+pi]. You will probably pick a course for every light so every lamp is enlightened by undoubtedly another lamp, or report that it is incomprehensible. Input The primary line contains one integer t (1≤t≤10000) — the number of experiments. Each experiment comprises of two lines. The primary line contains one integer n (2≤n≤3⋅105) — the number of lamps. The subsequent line contains n integers p1,p2,… ,pn (0≤pi≤n) — the force of the I-th lamp. The amount of n over all experiments doesn't surpass 3⋅105. Output For each experiment, print the appropriate response as follows: In case it is feasible to coordinate all lamps…
- Use the standard process we saw in class to derive an NFA from the RE ((a∗bc)∗)∗, and then use the subset algorithm to give an equivalent DFA. Either formalizing the DFA/NFA or diagramming them clearly will be sufficient. The final DFA should be labled with sets of NFA states.In this question, we will explore the seman- tic properties of propositional Horn clauses. For any set of clauses S, define Is to be the interpretation that satisfies an atom p if and only if S = p. • Show that if S is a set of positive Horn clauses, then Is = S. • Give an example of a set of clauses S where Is S. ● Suppose that S is a set of positive Horn clauses and that c is a negative Horn clause. Show that if Is c then SU{c} is unsatisfiable. Suppose that S is a set of positive Horn clauses and that T is a set of negative ones. Using part (c), show that if SU{c} is satisfiable for every c E T, then SUT is satisfiable also. • In the propositional case, the normal Prolog interpreter can be thought of as taking a set of positive Horn clauses S (the program) and a single negative clause c (the query) and determining whether or not SU{c} is satisfiable. Use part (d) to conclude that Prolog can be used to test the satisfiability of an arbitrary set of Horn Clauses.For all sets A and B, (A − B) ∩ B = ∅. Complete the proof begun below in which the given statement is derived algebraically from the properties on the attached sheet. Be sure to give a reason for every step that exactly justifies what was done in the step: Proof: Let A and B be any sets. (A − B) ∩ B = (A ∩ Bc ) ∩ B by the _______ law _____ = ______by the ______ law _____ = ______by the ______ law _____ = ______by the ______ law _____ = ______by the ______ law The number of lines in the outline shown above are just meant to be suggestive. To complete the proof you may need more or less. Use however many lines that you need
- Use a direct proof technique to prove the following theorems: For all integers x and y, x2 + y2 − 3 is not divisible by 4. The sets A, B, and C are arbitrary subsets of some universal set U. Prove that (C − A) ∪ (C − B) = C − (A ∩ B).Correct answer will be upvoted else Multiple Downvoted. Computer science. Utkarsh is compelled to play one more one of Ashish's games. The game advances turn by turn and obviously, Ashish moves first. Think about the 2D plane. There is a symbolic which is at first at (0,0). In one maneuver a player should increment either the x facilitate or the y arrange of the token by precisely k. In doing as such, the player should guarantee that the symbolic stays inside a (Euclidean) distance d from (0,0). As such, in the event that after a move the directions of the token are (p,q), p2+q2≤d2 should hold. The game finishes when a player can't take action. It tends to be shown that the game will end in a limited number of moves. In the event that the two players play ideally, figure out who will win. Input The main line contains a solitary integer t (1≤t≤100) — the number of experiments. The main line of each experiment contains two space isolated integers d (1≤d≤105) and k…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…