State Machines

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State Machines
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What is a state machine?

• A state machine is a different way of thinking
  about computation
• A state machine has some number of states, and
  transitions between those states
• Transitions occur because of inputs
• A pure state machine only knows which state it
  is in--it has no other memory or knowledge

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State machine I/O

• State machines are designed to respond to a
  sequence of inputs, such as
• The individual characters in a string
• A series of external events
• State machines may produce output (often as a
  result of transitions)
• Alternatively, the result of a state machine
  may be the state it ends up in

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Example I Even or odd

• The following machine determines whether the
  number of As in a string is even or odd
• Circles represent states arrows represent
  transitions

• Inputs are the characters of a string
• The output is the resultant state

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Error states

• Some state machines may have a error state with
  the following characteristics
• An unexpected input will cause a transition to
  the error state
• All subsequent inputs cause the state machine to
  remain in the error state

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Simplifying drawings I

• State machines can get pretty complicated
• We can simplify the drawing by leaving out the
  error state
• The error state is still part of the machine
• Any input without a transition on our drawing is
  assumed to go to the error state
• Another simplification use to indicate all
  other characters

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Example II Nested parenthesis

• The following example tests whether parentheses
  are properly nested (up to 3 deep)

• How can we extend this machine to handle
  arbitrarily deep nesting?

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Nested parentheses II

• Question How can we use a state machine to check
  parenthesis nesting to any depth?
• Answer We cant (with a finite number of states)
• We need to count how deep we are into a
  parenthesis nest 1, 2, 3, ..., 821, ...
• The only memory a state machine has is which
  state it is in
• However, if we arent required to use a pure
  state machine, we can add memory (such as a
  counter) and other features

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Nested parentheses III

• This machine is based on a state machine, but it
  obviously is not just a state machine

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The states of a Thread

• A Thread is an object that represents a single
  flow of execution through a program
• A Threads lifetime can be described by a state
  machine

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German vocabulary tutor I

• I once wrote a program to provide memorization
  drill on English-German vocabulary
• Words were presented in English
• The user had to type in the German translation
• A word was considered learned when the user
  answered correctly three times in a row
• Each word pair could be thought of as a state
  machine

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German vocabulary tutor II

• Whats the value in thinking of this as a state
  machine?
• Answer By measuring the percentage correct from
  each state, I was better able to adjust the
  difficulty of the study session

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Example Making numbers bold

• In HTML, you indicate boldface by surrounding the
  characters with ltbgt ... lt/bgt

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State machines in Java

• In a state machine, you can have transitions from
  any state to any other state
• This is difficult to implement with Javas loops
  and if statements
• The trick is to make the state a variable, and
  to embed a switch (state) statement inside a loop
• Each case is responsible for resetting the
  state variable as needed to represent
  transitions

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Outline of the bold program
void run() int state NORMAL
for (int i 0 i lt testString.length() i)
char ch testString.charAt(i)
switch (state) case
NORMAL not inside a number
case NUMBER inside a number
if (state NUMBER)
result.append("lt/bgt")
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The two states
case NORMAL if (Character.isDigit(ch))
result.append("ltbgt" ch) state
NUMBER break else
result.append(ch) break
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Conclusions

• A state machine is a good model for a number of
  problems
• You can think of the problem in terms of a state
  machine but not actually do it that way (e.g.
  German vocabulary)
• You can implement the problem as a state machine
  (e.g. making integers bold)
• Best done as a switch inside some kind of loop
• Pure state machines have some severe limitations
• Java lets you do all kinds of additional tests
  and actions you can ignore these limitations

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The End