Question 1: Provide state diagram of DFAs recognizing the subsequent languages (the alphabet is {0,1}):
a) L1 = the set of all strings that start with 0 and have odd length
b) L2 = the set of all strings that start with 1 and have even length
c) L3 = the set of all strings that end with 1 and have even number of 1s
d) L1 U L2
e) L1 U L3
f) The set of all strings such that every occurrence of 0 is followed by at least two 1s, e.g.,
0111, 01101111011111, 1110111 are in this language, but 0101 is not.
g) The set of all strings that does not contain substring 101.
Question 2: Give nondeterministic finite automata accepting the set of strings of 0's and 1's such that there are two 0's separated by a number of positions that is a multiple of 3. (Note: 0 is an allowable multiple of 3). Try to take advantage of non determinism as much as possible.
I'm not sure how to solve these questions. Can anyone help me?