Consider the finite state diagram of Fig. 1. Here 50 is the initial state and 52

Question

Consider the finite state diagram of Fig. 1. Here 50 is the initial state and 52 is the final state. Final states (also referred to as accepting states) are those at which the machine reports that the input string, as processed so far, is a member of the language it accepts. [Ref: wikipedia] According to this figure find out whether the following input is valid or not. A valid input means, the input which is possible according to the diagram and the input which ends at the final state. For example, 00, 11, 10 is a valid input sequence. However, 11, 11, 10 is not a valid input because in initial state there is the only one input possible and it is 00. Another invalid input example is 00, 01. Because it ends at state 50 which is not an accepting or final state. Also justify your answer. 00, 11, 11, 11, 10, 11, 10 00, 11, 10, 11, 01 00, 10, 11, 10 00, 11, 10, 10, 10 00, 11, 11, 10, 11, 10, 01

Explanation / Answer

a) 00, 11 , 11, 11, 10, 11, 10- valid input

it ends at state s2 .

b) 00,11,10,11,01- not valid

it ends at state s0.

c)00, 10,11,10- valid input

it ends at state s2 .

d) 00,11,10,10,10 - not valid

because in iinitiaal state there is the only one input possible and it is 00

e) 00, 11, 11, 10, 11, 10, 01 -not valid

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