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AS Computer Studies

Learn about finite state machines and their purpose in computer studies, with a focus on traffic lights as an example. Understand the stages of problem solving and how to create and construct a finite state machine.

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AS Computer Studies

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  1. AS Computer Studies Finite State Machines 1

  2. Starter • Imagine yourself stood at a crossing, at a junction with two directions of traffic. • What are the different STATES of the lights (the order, which lights can be on etc). • What would cause the lights to change?

  3. Objectives • Understand the stages of problem solving. • Become familiar with finite state machines and their purpose. • Be able to create and construct a finite state machine.

  4. Starter Review • The lights you have are: • RED • AMBER • GREEN • RED MAN • GREEN MAN • The process is: RED  RED AMBER  GREEN  AMBER  RED • Causes of the lights to change would be: • Traffic coming from a different direction. • A pedestrian activating the crossing • Causing the RED MAN to go off and the GREEN MAN to come on.

  5. Finite State Machines (FSM) I • Traffic crossings can be in ONE state at any ONE time. • Finite means countable. • Traffic crossings have a set number of possible states they can be in. • Traffic crossings have five different states: RED  RED AMBER  GREEN  AMBER  RED • They have a number of inputs (traffic sensors, crossing button). • They have a number of outputs (the different lights)

  6. Finite State Machines (FSM) II • For traffic lights to move between states, it needs to ALWAYS know it’s current state. • The traffic lights couldn’t move from Red to Green if it was already on green for example. • When the pedestrian crossing button is pressed: • The lights change from green to amber • The logic device records the new state. • The lights change from amber to red. • The logic device records the new state. • The red man turns off • The logic device records the new state. • The green man turns on • The logic device records the new state.

  7. How does this look • A diagram of how Traffic Lights Work (at surface level) Inputs (traffic sensor or Pedestrian button) Outputs Actual traffic lights Or Red/Green man LogicalDevice (Traffic Lights) programmed with state transition diagram Memory Change memory to next state (e.g. Red  Red Amber)

  8. What is a finite state machine (FSM)? • A machine that has a fixed set of possible states. • It has a set of inputs that can change the state. • It has a set of outputs which can reflect the state change. • This can range from 2 states to millions!

  9. Quick Task • Write down all the different states for a car (keep it simple) • Think about what inputs and outputs you would need. • Answer: • Engine on, Moving • Engine on, Slowing Down • Engine on, Stationary • Engine off, Stationary Inputs: Key to start ignition, Accelerator, brakes Outputs: Motion, Indicator signals

  10. State Transition Diagrams • These are a way of explaining a FSM in a graphical way. • Each state is represented by a circle. • A transition (movement) between each state is shown by an arrow. • Labelled with the inputs that causes the transition. • Labelled with any outputs which happened because of the transition.

  11. An Example: Showing an FSM in a State Transition Diagram • Let’s take the example of a pen as an Finite State Machine • It has two finite states. • The pen is extended out (i.e. the pen is ON – STATE 1) • The pen is retracted (i.e. the pen is OFF – STATE 0) • It has allowable inputs: clicking the pen’s button. • It has possible outputs: the pen nib extended or retracted. Button clicked State 0 State 1 Button clicked

  12. Quick Task • A light switch is a simple example of a finite state machine. • Draw a FSM illustrate this. • TIPS: • STEP 1: Identify the states • STEP 2: Identify the inputs • STEP 3: Identify the outputs • STEP 4: Identify the transitions

  13. Quick Task Review • A light switch is a simple example of a finite state machine. • STEP 1: Identify the states: Switch On, Switch Off • STEP 2: Identify the inputs: Switching on the switch • STEP 3: Identify the outputs: The light is on or off • STEP 4: Identify the transitions: S0 (switched off) to S1 (switched on) and vice versa. NOTICE: There is no FINAL or ACCEPTING (finishing) state. Light-switch Down State 0 State 1 Light-switch Up

  14. State Transition: Further Knowledge • The combination on my brief case is 249. It will only open when given this sequence. There are no outputs here. • The initial start is shown by the arrow. Constantly loops around state S0 (locked) unless 2 is selected. Once 2 is selected, state s1 is reached. This continues to the final state. • Double circle = Accepting state – shown in S3

  15. FSM: Mealy Machines • So far we have just seen State Transitions which do something. We haven’t seen them output any actual information. • To do this, we use a particular type of FSM • A Mealy Machine – FSM’s with outputs, have an initial state and no accepting states. Initial states have a labelled arrow called “Start”

  16. Activity: Creating a Mealy Machine • We want to develop a machine which converts a set of values into characters. • 0 = A 1 = B 2 = ! • The system begins at state S0. • If the received digit is 0 and the system is in state S0, output the letter A • If the received digits is 1 and the system is in state S0 change to state S1 and output letter B. • If the received digit is 2 and the system is in state S0 change to S2 and output the letter !. • If the received digit is 0 and the system is in state S1, change state to S0 and output the letter A. • If the received digit is 1 and the system is in state S1, output the letter B. • If the received digit is 2 and the system is in state S1, change state to S2 and output character ! • DRAW A STATE TRANSITION DIAGRAM TO SHOW THIS USING THE SHEET PROVIDED.

  17. Conversion Machine: A Solution What would the following sequences produce (you may need to write it down!) 00101102 would produce: AABABBA! 101012 = BABAB! 10010112 = BAABABB! 1110102 = BBBABA! 1, B State1 1, B Start 0, A State 0 0, A State2 2, ! 2, !

  18. Objectives Review • Understand the stages of problem solving. • Become familiar with finite state machines and their purpose. • Be able to create and construct a finite state machine.

  19. Plenary • Teach back. • Each person will be asked to stand up and suggest one thing they have learnt today. • Reflection: What do we need to know more of to deepen our understanding.

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