Finite State Machines

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Finite State Machines

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state

• the state of a system is a snapshot of all the
  relevant elements of the system at the moment the
  snapshot is taken
• the state of a basketball game can be represented
  by...
• number of points
• time remaining
• possession
• fouls accumulated
• the state of a tic-tac-toe game can be
  represented by...
• the placement of Xs and Os on the board

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state of a sequential lock

• the round lock example has several different
  states
• A - not open...
• ...and no relevant operations have been performed
• B - not open...
• ...and the user has completed the R-13 operation
• C - not open...
• ...and the user has completed R-13, followed by
  L-22
• D - open

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a state diagram for the sequential lock
A - not open... B - not open... C - not open... D
- open
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finite state machine (automaton)

• a model of computation
• states
• start state
• input alphabet
• transition function to a next state
• computation begins in start state with an input
  string
• machine changes states depending on the
  transition function
• many variants
• Mealy outputs associated with transitions
• Moore outputs associated with states
• recognizer some states are accepting states

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finite state machine another definition

• a description of a system with the following
  components
• a finite number of states
• a finite number of inputs
• a finite number of outputs
• all state transitions are specified
• cause of each output is specified
• may be described by a state diagram
• deterministic if exactly one transition for each
  given input and state
• otherwise, non-deterministic
• output is possibly misleading
• I prefer to call them side effects
• things that happen as a result of
• making a particular transition
• OR
• entering a state and being in it (regardless of
  where you came from)

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2-bit counter

• count from 0 to 3
• then wrap around to 0 and continue
• can be shown as a state diagram

• what causes a state change?
• synchronous clock
• asynchronous some less predictable event

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traffic light

• north-south may be green
• then east-west must be red
• north-south may be red
• then east-west may be green
• its not quite that simple
• lets model it...

repeat
10 s
10 s
5 s
1 s
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getting a degree

• seek information
• send application materials (all)
• get accepted
• show up
• take courses
• apply for matriculation (graduation)
• receive degree
• leave

is it deterministic?
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cordless phone

• talk
• redial
• memory
• vol UP
• vol DOWN
• flash
• digits(0..9), ,

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device with buttons (PDA)

• on/off
• calendar
• phone
• up
• down
• memo
• todo
• hotsync

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stairway light switch

• two switches
• one at bottom of stairs
• one at top of stairs
• both switches control the light
• how does the control work?

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washing machine or dryer controls
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television controls
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cell phone controls
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automatic door opener (at stores)
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elevator controls (inside and outside cars)
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user interface of an editor

• think of insert mode

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user interface of a Word processor

• what menus are available when?

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the end