Let E = {a, b} and L = {ww|w e E and w is of length k}. Show that for each k, no DFA can recognize Lk with fewer than 2k states.
Q: Answer the following questions based on the e-NFA given above. 1. Which of the following states are…
A: ∈-closure of a state q is the set of states we can reach from q by taking zero or more ∈transitions.…
Q: Consider the region enclosed between the graph of f(x) = x³ + e* and the x-axis for 15 x< 3.5: Find…
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Q: [B'] We may rephrase [B] using the definition of GA to get the following state- ment. If A E P, and…
A: Answer :
Q: If a set of WFFS has no truth-value assig
A: We need to Solve the 2 given question.
Q: Consider a source x, e (A, B} are iid with probability mass vector (0.8,0.2}. Using binary Huffinan…
A: Here is the solution to given question:-
Q: From previous slide, if M hasn states, how many states does M' have by this construction? (а) 2n (b)…
A: According to the information given:- We have to choose the correct option to satisfy the statement.
Q: Let M be an NFA with n states. Show that if |L(M)| > 1 then 3w E L(M) with w| < n. You may use…
A: In this question we have to proof the fact that δ*(q0 , xy) = U p€δ*(qo,x) δ* (p,y) by…
Q: If we know P(X1=1) =P(X1=2) =1/4, find P(X1=3, X2=2,X3=1)
A: The state transition diagram of the given problem is mentioned below.
Q: How many states are there in minimal DFA that accepts the following regular expression?…
A: Introduction :
Q: Find a denial (or the negation) for "(3!x)P(x)".
A: Find a denial (or the negation) for ” (!)P(x)". We first look at the negation of a statement…
Q: Using the law of total probabilty Suppose we have a sample space S and two events A and B such that…
A: Law of Total Probability-Let B1,B2------Bn be a set of mutually exclusive events of sample space S.…
Q: Use A algorithm to find the solution path for the following graph where the h(n) for the states are…
A: check further steps for the answer :
Q: Consider the Markov chain with three states,S={1,2,3}, that has the following transition matrix…
A: I have given solution in step2
Q: Question 4: Assume that there is a problem in your computer and the random number generator…
A: Answer
Q: Q. 4 For the following DFA, find the minimal DFA (minimal number of states (Arrow represent the…
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Q: For a Turing machine M(.) with an input w, let M(w) be the output on the output tape if it stops in…
A: TMs model a general purpose computer's computational capacity, which can be defined informally…
Q: Let M ({qo, q1, q2, q3, q4, qs}, {a, b, c}, qo, fs, {q1,q3, qs}) be the Deterministic Finite %3D…
A: Q = { q0, q1, q2, q3, q4, q5 } ∑= { a, b, c } q0 = q0 T = fs F = { q1, q3, q5 }
Q: Minimize the DFA M1 given by its transition table below into a minimal DFA M2 using the DFA…
A: We are given DFA M1 and we are going to minimize the DFA to M2. Minimization in DFA is done to make…
Q: For which sets of states is there a cloning operator? If the set has a cloning operator, give the…
A: There is a cloning operator and the operator is {|->}.
Q: Construct an ε-NFA using 10 states, three of which are final states and at least two are ε…
A: Let NFA be as given below that accepts expression (a|b)(b|ab|abb), where 1 is the starting stateand…
Q: (3) Show that if n 2 4 is even, then any pairwise stable network in the co-author model [JW(1996)]…
A: Answer: I have given answered in the handwritten format
Q: Information entropy for classification of m tuples in D is calculated as follows: m I(D) =2 P, log2…
A: so your question is information entropy for classification of m tuples in D is calculated as I(D) =…
Q: Consider now the case of a BA model with m = 1 and starting from the following network Find the…
A: 9) Solution Baraba`si - Albert Model (BA model or Scale free model) Which is a model used to…
Q: þ Minimize the following DFA and identify the distinguishable and indistinguishable states. Also…
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Q: Consider the state machine whose states are triples of non-negative integers (r, s, a). The initial…
A: The solution for the above-given question is given below:
Q: Consider the Markov chain with three states, S={1,2,3}, that has the following transition matrix ½ 4…
A: I have given answer in step2
Q: Let G be a PRG with (n) = 2n. Assume this is true for all values of n. Let H: {0,1}" {0,1}2" be as…
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Q: Use the Subset construction, as defined in the lecture notes, to construct DFA from the NFA produced…
A: We may use Thompson Construction to obtain a Finite Automaton from Regular Expression. We will…
Q: Consider the following Deterministic Finite Automaton (DFA) with the 5-tuple of (Q,E,90,F,6): 91 q3…
A: A string is said to be accepted when we end at one of the final states from the initial state q0.…
Q: Consider a DFA over E = {a, b} accepting all %3D strings which have number of a's divisible by 6 and…
A: Introduction :We have asked for the numbers of states in the DFA which will accept the string which…
Q: 1. Let M = ({qo, q1, q2, q3, q4, q5}, {a, b, c, d}, qo, fs, {q4, q5}) be the Deterministic Finite…
A: Given DFA contains, Set of states= {q0, q1, q2, q3, q4, q5} Input alphabets= {a, b, c, d} Start…
Q: A E 10 В D F 5. Consider the MDP above, with states represented as nodes and transitions as edges…
A: Solution : As the graph is given here, Answer a) max horizon length =15, then the optimal action…
Q: Q/ Given a sequence x(n), n from 0 to 3, where x(0)=-2, x(1)=4, x(2)=0 and х(3)--5 Evalute its DFT…
A: There are two ways to answer the above questions 1. Find the inverse fourier transform then…
Q: Let the Deterministic Finite Automaton (DFA) M be given by the following transition diagram: b. a 92…
A: I have given an answer in step 2.
Q: Let M be a FSM with n states. Let p and q be distinguishable states of M and let x be a shortest…
A: A finite deterministic automation M (transducer, Mealy machine, n M (transducer, Mealy machine,…
Q: Find an nfa with four states for L={an :n≥1}∪{bm ak :m≥0, k≥0}
A: The nfa with four states for for L={an :n≥1}∪{bm ak :m≥0, k≥0} will be
Q: Draw a non-deterministic PDA that recognizes the following: ‒‒‒‒‒‒ a. {wOwR | w€ {0,1}* } R is for…
A: Non-deterministic PDA (NPDA): It require multiple computation to check acceptance of string .…
Q: c) ( ) Consider now the case of a BA model with m = 1 and starting from the following network A Find…
A: The Answer start from step-2.
Q: Prove that for any m ∈ N, there exist an NFA with m states such that the equivalent DFA has at least…
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Q: Let A %3D (с, n, b), В%3 (х, у) and C %3 (0, 1). Find a) AXBXC b) СХВХА с) ВХСХ
A: The cartesian product of 3 sets produces another set such that, the new set has tuples of 3 elements…
Q: Solving using DFS on the below graph A come before Z
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Q: an NFA with m states
A: Given :- The NFA having m states and DFA is mention in the above given question Need to prove that…
Q: For the following decision problem, show that the problem is undecidable. Given a TM T and a…
A: Here, we have to write a solution for the above question.
Q: Prove that gcd(a + b, a – b) = gcd(2a, a – b) = gcd(a + b, 2b). Show your work! Justify each step.
A: Given that, Prove gcd(a+b, a-b) = gcd(2a, a-b) = gcd(a+b, 2b) Suppose d divides a+b and a-b.Then d…
Q: Consider the following E-NFA. (a) Compute E-closure of each state (b ) Convert the automaton to DFA…
A: Given ∈ - NFA: ∈ a b c p θ {p} {q} {r} q {p} {q} {r} θ *r {q} {r} θ {p}
Q: Let M = ({go. 91.q2. 93. 94. gs}, {a, b, c, d}, go. fe {q4. qs})be the Deterministic Finite…
A: q0, q1, q2, q3, q4, q5 are the states in DFA. q0 is the initial state. q4,q5 are final states. There…
Q: Consider a discrete random variable X with 2n+1 symbols xi, i = 1, 2, ..., 2n+1. Determine the upper…
A: Entropy can be find out by using the below formula :-
Q: find the associated guarantee:
A: Solution :- The game matrix is mention in the above given question Need to compute the associated…
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- Prove that for any m ∈ N, there exist an NFA with m states such that the equivalentDFA has at least 2^m−1 statesPlease do a formal proof! Prove that for any m ∈N, there exist an NFA with m states such that the equivalentDFA has at least 2m−1 states.Let M be a FSM with n states. Let p and q be distinguishable states of M and let x be a shortest string distinguishing p and q. How long can the string x be as a function of n?
- Given the complement of a graph G is a graph G' which contains all the vertices of G, but for each unweighted edge that exists in G, it is not in G', and for each possible edge not in G, it is in G'. What logical operation and operand(s) can be applied to the adjacency matrix of G to produce G'? AND G's adjacency matrix with 0 to produce G' XOR G's adjacency matrix with 0 to produce G' XOR G's adjacency matrix with 1 to produce G' AND G's adjacency matrix with 1 to produce G'Let R=ABCDEGHK and F= {ABK→C, A→DG, B→K, K→ADH, H→GE} . Is it in BCNF? Prove your answer.Consider a state of the 8-queens problem with the state representation (2, 2, 2, 2, 2, 2, 2, 2) (i.e., the positions are represented as a 8-tuple where the i-th element is the row number of the queen in column i). Let the successors/neighbors of a state be those states generated by moving only one queen in its column. Which of the following states represents a neighbor/successor of this specific state? (There could be multiple correct answers; pick all.)Group of answer choices (3, 2, 2, 2, 2, 2, 2, 2) (2, 2, 2, 2, 2, 2, 2, 2) (3, 3, 3, 3, 3, 3, 3, 3) (2, 2, 2, 2, 2, 2, 2, 3)
- Show that for one-dimensional cellular automata, CA-Predecessor is in P. Hint:think about using recursion on a one-bit-shorter prefix of the input configuration.Suppose that the CA follows the rule that the configuration shrinks by 2 cells on each update, sincethe leftmost cell has no left neighbor and the rightmost cell has no right neighbor. Therefore, oninput a configuration of length n, we are asking whether there is a predecessor configuration oflength n + 2.Show that for one-dimensional cellular automata, CA-Predecessor is in P. Hint:think about using recursion on a one-bit-shorter prefix of the input configuration.Suppose that the CA follows the rule that the configuration shrinks by 2 cells on each update, sincethe leftmost cell has no left neighbor and the rightmost cell has no right neighbor. Therefore, oninput a configuration of length n, we are asking whether there is a predecessor configuration oflength n + 2. PROVIDE A STEP BY STEP EXPLAINATION SHOWING TIME COMPLEXITYShow that for one-dimensional cellular automata, CA-Predecessor is in P. Hint:think about using recursion on a one-bit-shorter prefix of the input configuration.Suppose that the CA follows the rule that the configuration shrinks by 2 cells on each update, sincethe leftmost cell has no left neighbor and the rightmost cell has no right neighbor. Therefore, oninput a configuration of length n, we are asking whether there is a predecessor configuration oflength n + 2. By the way 2^n is not polynomial at all.
- Show that for one-dimensional cellular automata, CA-Predecessor is in P. Hint:think about using recursion on a one-bit-shorter prefix of the input configuration.Suppose that the CA follows the rule that the configuration shrinks by 2 cells on each update, sincethe leftmost cell has no left neighbor and the rightmost cell has no right neighbor. Therefore, oninput a configuration of length n, we are asking whether there is a predecessor configuration oflength n + 2. By the way 2^n is not polynomial at all. Also,show how your algorithm works for input =010011 which follows rule 111 110 101 100 011 010 001 000 0 0 0 1 1 1 1 0Show that for one-dimensional cellular automata, CA-Predecessor is in P. Hint:think about using recursion on a one-bit-shorter prefix of the input configuration.Suppose that the CA follows the rule that the configuration shrinks by 2 cells on each update, sincethe leftmost cell has no left neighbor and the rightmost cell has no right neighbor. Therefore, oninput a configuration of length n, we are asking whether there is a predecessor configuration oflength n + 2. Use the information from :https://core.ac.uk/download/pdf/82054937.pdfShow that for one-dimensional cellular automata, CA-Predecessor is in P. Hint:think about using recursion on a one-bit-shorter prefix of the input configuration.Suppose that the CA follows the rule that the configuration shrinks by 2 cells on each update, sincethe leftmost cell has no left neighbor and the rightmost cell has no right neighbor. Therefore, oninput a configuration of length n, we are asking whether there is a predecessor configuration oflength n + 2. Show the solution step by step and use the link below Use the information from :https://core.ac.uk/download/pdf/82054937.pdf