Cellular Automata are basically collections of simple finite state
machines. We can also consider the controller for an automated self-driving train to be a finite state machine, albeit much more complex than a CA.
a. What is a finite state machine, what are its attributes?
b. What states would there be for a self-driving train? What about
inputs to the finite state machine? Rules?
a. A finite state machine (FSM) is a mathematical model used to describe and analyze systems that exhibit sequential or discrete behavior. It consists of a finite number of states, transitions between those states, and actions or outputs associated with each state transition.
Attributes of a finite state machine include:
1. States: The states represent distinct conditions or modes that the system can be in at any given time. Examples of states could be "idle", "moving forward", or "emergency stop".
2. Transitions: Transitions define the change of state in response to external events or inputs. They specify the conditions or triggers required for the system to move from one state to another. For example, an input such as "start" might trigger a transition from the "idle" state to the "moving forward" state.
3. Inputs: Inputs represent signals or events from the environment that can influence the behavior or state transitions of the system. Examples of inputs in the context of a self-driving train could include sensor readings, such as distance from obstacles or current speed.
4. Outputs: Outputs are actions or signals generated by the system in response to specific states or state transitions. For instance, the self-driving train might output signals to control acceleration, braking, or display information to passengers.
b. The states for a self-driving train could include:
1. Idle: The train is stationary and awaiting further instructions.
2. Moving forward: The train is in motion and traveling in a forward direction.
3. Braking: The train is slowing down or coming to a stop.
4. Emergency stop: The train performs an immediate and abrupt halt due to a critical situation.
Inputs to the finite state machine controlling a self-driving train might include:
1. Sensor readings: Information from proximity sensors, cameras, or LIDAR systems to detect obstacles, track conditions, or other vehicles.
2. GPS data: Location information to determine the train's position and potentially guide its route.
3. Timetable or schedule: Input specifying the train's planned stops, destinations, or departure times.
The rules or transition conditions for the finite state machine would determine how the train transitions between states based on the inputs and its current state. For example:
- If the train is in the "Idle" state and receives a "Start" input, it transitions to the "Moving forward" state.
- If an obstacle is detected by the sensors while in the "Moving forward" state, the system may transition to the "Braking" state.
- In an emergency situation, the system might transition directly from any state to the "Emergency stop" state.