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#### Question 1 a) Construct the state transition table for the nondeterministic finite state machine with the state transition diagram shown below

###### Math

Question 1 a) Construct the state transition table for the nondeterministic finite state machine with the state transition diagram shown below.

Cs (5

\ Zz

b) Write the regular expression that can be accepted for the nondeterministic finite state machine above. (3 marks)

c) Find a deterministic finite state machine that recognizes the same language as the nondeterministic finite state machine in question | a). Show all the necessary steps in a state transition table.

Consider the finite state machine, M where the initial state is So, the input set is {0, 1} and the state transition diagram is shown below.

CONG

{> 0

| Loo

BY

a) Construct the state transition table of M. (4 marks)

b) Tabulate the word transition function fo110- (2 marks)

c) Find a partition of the state set corresponding to a machine congruence relation R with

as few classes as possible. (3 marks)

d) Construct the state transition table of the corresponding quotient machine. (2 marks)

Question 3 Construct the digraph of a Moore machine with five different states that has input elements a,

b, and accepts the input strings end with baba.

Question 4

Determine whether the binary operation on Z defined by x + y=x—3+y, Vx,yEZ

a) is closed, (2 marks)

b) is commutative, (3 marks)

c) is associative, (5 marks)

d) has an identity. (3 marks)

(Total: 13 marks]

Question 5

Determine whether the description of * is a valid definition of binary operation on the set.

a) On R*, where m +n = log,»n. (3 marks)

b) On Qt, where x + y = >: (3 marks)

(Total: 6 marks]

Question 6

Let G = (R*,x) be a group under the usual multiplication, x and Z* be the subset of R*. Determine whether Z* is a subgroup of R*. Show all the conditions to determine a subgroup and necessary steps to support your answer.