Solution for Section 7.2 Question 4

4. The transition diagram for Question 2 was:

a) i)  The string 01 would leave the automaton in the state t₂.
ii) The string 0010 would leave the automaton in the state t₁.
iii) The string 11000 would leave the automaton in the state t₃.
iv) The string 111 would leave the automaton in the state t₂.

b) From part a), the strings 01 and 111 send the automaton to an accepting state.

c) You are looking for all the strings which will cause you to finish in the state t₂. If we examine which input values will send the automaton to the state t₂ for each of the three states, we see that in each case the input symbol 1 sends the automaton to the state t₂ (or keeps it in state t₂ if it was already there). Hence the language accepted by this automaton consists of all strings (of length at least one) of 0's and 1's which end in a 1.

Back to Section 7.2