Question

Ger wrote the following phone lattice for his CS 440 project. Before proceeding further, you will probably want to draw a picture of this state diagram.

states: 1,2,3,4,5,6,7
phones: b, m, d, c, k, o, a, r
start states: 3
end states: 1,7

transition function

(2,k): 7
(3,m): 5
(3,b): 5
(3,r): 6
(4,d): 1
(4,c): 2
(5,a): 4
(6,o): 4

Which of the following words does this NOT recognize?
Select one or more:
a. rod
b. mock
c. bad
d. rack

Answer 1

The word 'rod' does not have a transition from state 6 with 'o', and 'rack' does not have a transition from state 6 with 'a', making these words unrecognized by the provided state diagram. option a is the correct answer.

Step-by-step explanation:

When analyzing the phone lattice provided for Ger's CS 440 project, we must examine the transition function for each sequence of phones (characters) to determine if the word is recognized. The transition function tells us how to move from one state to another when a specific phone is encountered.

1. rod — Starting at state 3, r takes us to 6, but there's no transition defined for o from 6 in the present lattice; hence we cannot proceed further, making rod unrecognized.
2. mock — Starting at state 3, m takes us to 5, then o stays at 5 (since there's no transition defined, we assume the state doesn't change), followed by c which brings us to 2, and finally k which takes us to 7, an end state, making mock a recognized word.
3. bad — Starting at state 3, b takes us to 5, followed by a which takes us to 4, and d takes us from 4 to 1, an end state. So the word bad is recognized.
4. rack — Starting at state 3, r takes us to 6, and there is no transition for a from 6; therefore, the word rack is not recognized.

The words rod and rack are not recognized by the lattice as they cannot reach an end state through the defined transitions.