In a brewery the beer bottles are standing on a conveyer and passing a detector based on the "two light rays principle". The sequence 00, 10, 11, 01, 00 causes an increment of a bottle counter. One day the mafia plans to steal 1/4 of that days production and they want that their theft should pass unnoticed on the counter. The production each day is fairly stable.

The mafia constructs a sequential circuit such that when three bottles have passed through the detector, the counter has been incremented four times!

Specify the input and output sets, I and Z, draw a state-transition graph that models the described behavior, and specify the starting state.

So we have input set I={L1,L2} for the two light rays, and output set Z={0,1} which gives 0 if there is no bottle and 1 when a bottle is detected (counted). I understand how a state transition graph can be made for how the detector would usually behave (without the involvement of the mafia), see the attached image. But after that, how would you reason when making the state transition graph after the mafia have had their way?

 

It's a little unclear. Are you supposed to be designing something to go between the counter and the sensor, attaches onto the sensor, or replaces the sensor?

This doesn't sound like the kind of mafia I have always heard of...

 

The mafia constructs a sequential circuit such that when three bottles have passed through the detector, the counter has been incremented four times!

How many cannoli's are consumed in the construction of said sequential circuit?

 

You need a two bit internally generated signal, N{1,0} to use with your original 4 states to create 12 states (4 states each bottle). N increments on every transition of 01 -> 00. I counts 0, 1, 2, 0, etc.

 

It's a little unclear. Are you supposed to be designing something to go between the counter and the sensor, attaches onto the sensor, or replaces the sensor?

This doesn't sound like the kind of mafia I have always heard of...

I wonder that also. Maybe someone who thinks it's more clear what it's being asked for could explain this?
Brownout?

You need a two bit internally generated signal, N{1,0} to use with your original 4 states to create 12 states (4 states each bottle). N increments on every transition of 01 -> 00. I counts 0, 1, 2, 0, etc.

I unfortunately don't understand how you mean. Could you please be so kind as to draw an illustration?