Define formally and provide state tables for the finite auto

Define formally and provide state tables for the finite automata that accept strings of zeros and ones which: Never contain three adjacent ones. Have a one as the next to last symbol. Contain an even number of zeros or an odd number of ones - not both!

Solution

I am assuming that you are asking for a deterministic finite state automata.

A formal definition would require using the tuple of (Q,,,q0,F)(Q,,,q0,F)
I will assume you can generate this on your own.

The idea for a DFSM that never accepts three adjacent ones would be a counter which after three consecutive ones would go to a non-accepting state which loops to itself on all input. Here are the states:

       0        1
q0| q0      q1
q1   q0      q2
q2   q0     q3
q3   q3     q3

All states except for q3 would be accepting.