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7. Consider the following NFA 2 a, 7 Assume we convert this NFA to an equivalent...
4. (5 points) Conversion form NFA to equivalent DFA Convert the following NFA into an equivalent...
4. (5 points) Conversion form NFA to equivalent DFA Convert the following NFA into an equivalent DFA by using the Powerset-Construction. Write the transition table and draw the final DFA. start — 9o
Consider an NFA defined by the following transition table q a b λ 1 {1} &nbs
Consider an NFA defined by the following transition table
q
a
b λ
1 {1}
Ф {2,4}
2 {3}
{5} Ф
3
Ф
{2} Ф
4 {5}
{4} Ф
5
Ф
Ф Ф
Convert this table to the corresponding table for the NFA
without λ transitions
Convert the resulting NFA into DFA.\
Consider an NFA defined by the following transition table 4 а ь 2 1 {1} {2,4} 2 {3} {5} 3 0 {2} 4 {5} {4} 5 ¢ (a)...
Consider the following E-NFA. {9,r} Sols 19 a. Compute the E-closure of each state. b. Convert...
Consider the following E-NFA. {9,r} Sols 19 a. Compute the E-closure of each state. b. Convert the automaton to DFA using subset construction method.
Consider the following relation R on the set A = {1,2,3,4,5}. R= {(1, 1), (2, 2),...
Consider the following relation R on the set A = {1,2,3,4,5}. R= {(1, 1), (2, 2), (2, 3), (3, 2), (3, 3), (4,4), (4,5), (5,4), (5,5)} Given that R is an equivalence relation on A, which of the following is the partition of A into equivalence classes? Select the correct response. A. P = {{1}, {1, 2}, {3}, {3,4}, {4},{5}} B. P ={{1,2,3,4,5}} C. P ={{1,2},{3,4}, {5}} D. P = {{1}, {2,3}, {4,5}} E. P ={{1,2,3}, {1,5}} F. P= {{1},...
Consider the following FSM state transition diagram: 7. Let's see if there is an equivalent state machine with fewe...
Consider the following FSM state transition diagram: 7. Let's see if there is an equivalent state machine with fewer states by checking to see if any states in the diagram above are equivalent. Two states are equivalent if (1) they have identical outputs and (2) for each possible combination of inputs they transition to equivalent states. A. Start by filling in a "compatibility table" like the one shown below. Place an "X" in square (SISI) if SI produces a different...
Provide complete definitions for the following: 7 marks] Choosing a universe and predicates. (a) Consider the...
Provide complete definitions for the following:
7 marks] Choosing a universe and predicates. (a) Consider the following statement: Vz E N, P(x,165) -> P(x, 1) Provide one definition of a binary predicate P over N x N that makes the above statement True, and another definition of P that makes the statement False. Briefly justify your answers, but no formal proofs are necessary. b) Consider the following statement: Provide one definition of a non-empty set U, and predicates P, Q,...
9. Prove that the following kogical expressions aro logically equivalent by applying the law of logic...
9. Prove that the following kogical expressions aro logically equivalent by applying the law of logic 10. Give a logical expression with variables p, q, and r that's true only if p and q are false and r is true. 11. Predicates P and Q are defined below. The domain of discourse is the set of all positive integers. P(x): x is prime Qlx): x is a perfect square Are the following logical expressions propositions? If the answer is yes,...
4. [7 marks] Choosing a universe and predicates. (a) Consider the following statement: Vx EN, P(r,...
4. [7 marks] Choosing a universe and predicates. (a) Consider the following statement: Vx EN, P(r, 165)P(x,1) Provide one definition of a binary predicate P over Nx N that makes the above statement True, and another definition of P that makes the statement False. Briefly justify your answers, but no formal proofs are necessary b) Consider the following statement: Provide one definition of a non-empty set U, and predicates P, Q, and R over U, that makes the above statement...
discrete math Need 7c 9ab 10 15 16 17 (7) Consider the following matrices. Compute the...
discrete math
Need 7c 9ab 10 15 16 17
(7) Consider the following matrices. Compute the following matrices A=[ ]B=[ 1 c-[! (a) CA (b) BAA (c) AOC (9) Determine if the following statements are True or False. If the statement is False, explain why. (a) Consider A={1,2,3,4,5). Do A1 = {1,3,5}, A2 = {2,4}. (i) Show that P ={A1, A2} forms a partition of A. (ii) Construct the matrix of the relation R corresponding to P (b) Consider A...
Problem 2. For the following statements, write down whether true or false (No justification needed, and...
Problem 2. For the following statements, write down whether true or false (No justification needed, and for ease of grading, please make it clear what is) (1) (a) xE (b) х€ {{x}} (c) x}€{{x}} (d) } E (2) (a) C 1,2,3 (b) E {1,2,3 (c)E P({1,2,3} (d) n0 (3) (a) 1,2,3 (b) {1,2,3} с {1, 2, 3} (c) An0 (d) AU A (4) a) ZnZ = Z (b) ZUZ 22 your answer Problem 3. List the elements of the following...
4. (5 points) Conversion form NFA to equivalent DFA Convert the following NFA into an equivalent DFA by using the Powerset-Construction. Write the transition table and draw the final DFA. start — 9o
Consider an NFA defined by the following transition table
q
a
b λ
1 {1}
Ф {2,4}
2 {3}
{5} Ф
3
Ф
{2} Ф
4 {5}
{4} Ф
5
Ф
Ф Ф
Convert this table to the corresponding table for the NFA
without λ transitions
Convert the resulting NFA into DFA.\
Consider an NFA defined by the following transition table 4 а ь 2 1 {1} {2,4} 2 {3} {5} 3 0 {2} 4 {5} {4} 5 ¢ (a)...
Consider the following E-NFA. {9,r} Sols 19 a. Compute the E-closure of each state. b. Convert the automaton to DFA using subset construction method.
Consider the following relation R on the set A = {1,2,3,4,5}. R= {(1, 1), (2, 2), (2, 3), (3, 2), (3, 3), (4,4), (4,5), (5,4), (5,5)} Given that R is an equivalence relation on A, which of the following is the partition of A into equivalence classes? Select the correct response. A. P = {{1}, {1, 2}, {3}, {3,4}, {4},{5}} B. P ={{1,2,3,4,5}} C. P ={{1,2},{3,4}, {5}} D. P = {{1}, {2,3}, {4,5}} E. P ={{1,2,3}, {1,5}} F. P= {{1},...
Consider the following FSM state transition diagram: 7. Let's see if there is an equivalent state machine with fewer states by checking to see if any states in the diagram above are equivalent. Two states are equivalent if (1) they have identical outputs and (2) for each possible combination of inputs they transition to equivalent states. A. Start by filling in a "compatibility table" like the one shown below. Place an "X" in square (SISI) if SI produces a different...
Provide complete definitions for the following:
7 marks] Choosing a universe and predicates. (a) Consider the following statement: Vz E N, P(x,165) -> P(x, 1) Provide one definition of a binary predicate P over N x N that makes the above statement True, and another definition of P that makes the statement False. Briefly justify your answers, but no formal proofs are necessary. b) Consider the following statement: Provide one definition of a non-empty set U, and predicates P, Q,...
9. Prove that the following kogical expressions aro logically equivalent by applying the law of logic 10. Give a logical expression with variables p, q, and r that's true only if p and q are false and r is true. 11. Predicates P and Q are defined below. The domain of discourse is the set of all positive integers. P(x): x is prime Qlx): x is a perfect square Are the following logical expressions propositions? If the answer is yes,...
4. [7 marks] Choosing a universe and predicates. (a) Consider the following statement: Vx EN, P(r, 165)P(x,1) Provide one definition of a binary predicate P over Nx N that makes the above statement True, and another definition of P that makes the statement False. Briefly justify your answers, but no formal proofs are necessary b) Consider the following statement: Provide one definition of a non-empty set U, and predicates P, Q, and R over U, that makes the above statement...
discrete math
Need 7c 9ab 10 15 16 17
(7) Consider the following matrices. Compute the following matrices A=[ ]B=[ 1 c-[! (a) CA (b) BAA (c) AOC (9) Determine if the following statements are True or False. If the statement is False, explain why. (a) Consider A={1,2,3,4,5). Do A1 = {1,3,5}, A2 = {2,4}. (i) Show that P ={A1, A2} forms a partition of A. (ii) Construct the matrix of the relation R corresponding to P (b) Consider A...
Problem 2. For the following statements, write down whether true or false (No justification needed, and for ease of grading, please make it clear what is) (1) (a) xE (b) х€ {{x}} (c) x}€{{x}} (d) } E (2) (a) C 1,2,3 (b) E {1,2,3 (c)E P({1,2,3} (d) n0 (3) (a) 1,2,3 (b) {1,2,3} с {1, 2, 3} (c) An0 (d) AU A (4) a) ZnZ = Z (b) ZUZ 22 your answer Problem 3. List the elements of the following...
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