I am looking for a Moore finite state machine that returns true if and only if the last 4 bits (the input is of bits) are 0011 or 0101, the FSM can return any value at the first 4 bits (yes, even at the 4th).
The issue is that I was asked for a 7 conditions (vertexes) limit, and despite my efforts could not create one, my questions are the following :
- Is there a FSM that solve this at 7 conditions (7 vertexes)? If there is than what is it and if not how can I prove there isn't?
- Is there any type of 'algorithm' to approach this? I can easily well define one if we can use as much conditions as we wish (16 for our case) but what way other than intuition can lead me to reducing to 7 conditions?