My first automaton
aabac
abaCa
cabac

Rollback automaton
abaCa
cabaCb
aabaC
ababaCc
abaabaC

Exercise 1: lock
abcabc
abababCababC
ababCbababC
cababCabc
abcababCabc

Execrise 2: three a before b
B
ab
aaaB
aaaab
aaaaaaaaaB

Exercise 3: three a before c
bbbbc
aaabbbC
abababC
aaaC
aabc
aaaabc

Exercise 4: (a|b)*c
Cab
aaabbbC
abababC
ababaaabbCabc

Exercise 5: ((a|b)*c)*
Cab
aaabbbC
abababC
ababaaabbCab
ababaaabbCabC
CCCCCCC

Exercise 6: abac or baca
abaCAAAAA
ababaC
babaC
bacA
bbbbaabaCAAABA
cabaC
cbacA

Exercise 7: vending machine
aaCcaCc
dcabC
cdacbC
adbcaC
baC
bbbC

Exercise 8: electric lock
ABcaaaaB
ABcaBBBcababB
ABAcabbA
ABABAcbA

Exercise 9: even numbers
bAAbAAAbAbbbbbAAA
AbA

Exercise 10: multiple of three
baaBAAAbabbbbbaaaB
AbabaBbaaB

Exercise 11: multiple of six
baabAAAbabbbbbaaabbbA

Exercise 12: 2A=B
ababbBbbbaaB