State Machines

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State Machines
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What are they?

• Sometimes called a Finite State Machine
• Depicted as a state diagram
• Its a tool for specifying a systems behavior
• Used in many disciplines
• Language parsing
• Software design
• Systems design
• Hardware design
• Giving directions and other every day life
  things

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Example

• Consider a subway turnstile system
• The gate is either locked or unlocked
• If locked, the patron inserts a coin to unlock it
• If unlocked, the patron passes through
• This wordy definition is somewhat awkward
  although it does get the message across

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A Better Description Through Symbols

• Subway turnstile as a state machine

Actions (outputs)
Insert coin
/Unlock gate
Locked
Unlocked
States
Pass thru
/Lock gate
Transitions
Triggers (events)
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Example

• Subway turnstile as a state machine
• There 2 states that the gate can be in
• Unlocked
• Locked
• These are represented as circles in the diagram
• There are 2 events that can change the state of
  the system
• Insert coin
• Pass thru
• These are represented as state-to-state lines
  with text designators (before the / character)
• There are 2 outputs/actions from the system
• Lock gate
• Unlock gate
• These are represented as state-to-state lines
  with text designators (after the / character)

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Symbology (notation)

• The start state

Insert coin/Unlock gate
Locked
Unlocked
Pass thru/Lock gate
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Symbology (notation)

• System is always in exactly one state
• The solid circle marks the start state
• When the system starts up this is the first state
  visited
• The link out of the start state has no event
  associated with it
• There are no links into the start state
• This is called an unconditional transition and
  always happens

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Symbology (notation)

• The final (end) state

Insert coin/Unlock gate
Locked
Unlocked
Close down
Close down
Pass thru/Lock gate
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Symbology (notation)

• The system may have zero or more final states
• The solid circle with the ring around it
• Anytime the system transitions into one of these
  states, this diagram is completed
• The system may shut down
• The system may transition to another state
  machine (up in the hierarchy more later)

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Better than words?

• In this case the wordy version wasnt too bad
• But what if we need to add more, unforeseen stuff?

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Example

• Lets add some more options
• If the gate is locked and someone passes through,
  set off an alarm
• If the gate us unlocked and someone inserts
  money, thank them for the donation
• The wordiness just doubled

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Example

• But the picture still isnt overly complicated

close
Coin/unlock
locked
unlocked
Coin/thank you
Pass/sound alarm
Pass/lock
close
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Additions

• Changing things midstream isnt even that hard
• Instead of sounding an alarm on a dead-beat
  perhaps we might want to do more

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Example

• Addition of states/transitions/actions

violation
close
reset
Coin/unlock
locked
unlocked
Pass/sound alarm
Coin/thank you
Pass/lock
close
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Additions

• We could go on and on, but we wont

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Implementation

• The software implementation is basically a switch
  statement in Java (or the equivalent if/else
  if/else)
• switch (state)
• case locked
• case unlocked
• case violation

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Implementation

• The implementation in hardware is through
  sequential circuits with flip-flops (memory
  elements) and gates

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And so on

• There are a lot more features related to state
  machines
• They can be Hierarchical
• One super state can contain many sub states

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Hierarchical
Enters state C at sub-state B
A
B
Enters state C at start state
C
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Parallel

• Two state machines may run in parallel,
  interacting with one another

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Parallel
A
C
event_1/action_1
B
action_1/action_2
D
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And so on

• They can contain conditional connectors
• Can put if statements on the transitions

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Conditional connectors
A
B
event
case x
case y
C
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And so on

• Guarded transitions
• Like a conditional transition but with just one
  case

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Guarded Transitions
A
B
event case x
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And so on

• States can have
• Entry actions
• These are things that occur as soon as the state
  is entered
• Transition actions
• These are things that occur on the transition
  to/from the state
• Exit actions
• These are things that occur as a state is being
  exited

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Summary

• They can be as simple or as complicated as
  necessary.
• But, if they get too complicated they are not
  serving their stated purpose and should be broken
  up into multiple state machines

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Assignment The wordy version

• Two buttons (call them B1 and B2)
• Three LEDs,1 yellow, 1 red, 1 green (call them Y,
  R, and G)
• System specification
• Start in home position
• LEDs off
• Press B1 one time
• Press B2 one time flash Y slow
• Press B2 two times in succession flash Y medium
• Press B2 three times in succession flash Y fast
• Press B1 return to home position
• Press B1 two times in succession
• Press B2 one time flash R slow
• Press B2 two times in succession flash R medium
• Press B2 three times in succession flash R fast
• Press B1 return to home position
• Press B1 three times in succession
• Press B2 one time flash G slow
• Press B2 two times in succession flash G medium
• Press B2 three times in succession flash G fast

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Notes

• one time, two times, three times means
  button presses in rapid succession
• So for example
• , B1 , B2-B2
  , , B1,
  all LEDs off
• , B1-B1-B1 , B2
  , , B2
  changes G continues to flash at slow speed,
  B1,

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Deliverables

• A state-machine diagram depicting the operation
  of the system
• Source code
• A working demonstration on the Basic Stamp
  development board