The Start/Stop automata is a security system commonly used in in industrial applications for controlling starting and stopping of operating machines.
The start (run) and the stop command is distributed on two separate buttons, instead of just one switch. Because both in case of startup, both in case of stop for alarm conditions, operator intervention is more immediate, and is directed on the button marked by appropriate color, generally green for Start end red for Stop. Simultaneous pressure on the two buttons determines, for safety reasons, the priority of the stop key and then stopping the device.

Automata Start/StopSo the inputs are: Running button (R) that starts the device and Stop button (S) that stops the device. The possible states of the system are two: SR = run state, associated with output 1 and SS = stop, associated with output 0. We draw the state transition table. Whatever is the state in which the automata is, pressing only (S) or both buttons (S)+(R), it come to the SS state. Pressing only (R) it come to SR state. If the operator does not press any buttons, automata keeps the state in which it is.
If you want to simulate automata with JFLAP you can download it from 20160125_Automa_Marcia-Arresto.jflap (click with right button of your mouse on the link and select Save destination...).
Now we can design the circuit of the counter and simulate it in NI Multisim. The following figures show the table next state x(t+1) with its map of Karnaugh and table output u(t). They depend from the inputs i (t) and x(t). The output concide with the next state, so it is derived from the same combinational circuit. Finally, one flip flop DFF stores the next state.

this is the logic circuit:

Now I realize a demo about the automata using Multisim 13. You can download it here: 20160125_Automa_Marcia-Arresto.ms13 if you have another version of Multisim you can save the schematic .PNG image that you can see here (click with right button of your mouse on the link and select Save image...). Then open it with Multisim from File>Snippet>Open snippet file...
In this schematic I simulate the lighting of a lamp by means of the Start/Stop circuit.

I achieved the same automata using LabVIEW 2010: documenti/
In a next step I can use it with a DAQ connecting two input buttons (R and S) and a 15V-230V relay in output to drive an automatism.