a.dfa

#This DFA recognizes { x in {0,1}* | x does not end in 000 }

states:          lambda, # last bit was a 1 or non-existent
                 0,      # last two bits were 10
                 00,     # last three bits were 100
                 000     # last three bits were 000

input alphabet:  0,1

start state:     lambda  # no last bit when we start

accept states:   lambda,0,00 # accept as long as the last three bits weren't 000

delta:           # if we see a 1, reset
                 lambda,1 -> lambda
                 0,1      -> lambda
                 00,1     -> lambda
                 000,1    -> lambda

                 # if we see a 0, count one more 0 than before
                 lambda,0 -> 0
                 0,0      -> 00
                 00,0     -> 000

                 # until we get to three, and then just remember
                 000,0    -> 000