Transcript State machines

State Machines
Abbreviated lecture
26-Jul-16
What is a state machine?
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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
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A “pure” state machine only knows which state it is in—it has
no other memory or knowledge
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State machines are useful when you need to respond to a sequence of
inputs
This is the kind of state machine you learn about in your math classes
When you program a state machine, you don’t have that restriction
A state machine may produce output as it goes along
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Alternatively, the “output” may be what state it ends up in
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Example I: Even or odd
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The following machine determines whether the number of As
in a string is even or odd
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Circles represent states; arrows represent transitions
A
start
even
A
anything but A
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odd
anything but A
Inputs are the characters of a string
The “output” is the resultant state
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Simplifying drawings I
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Some state machines may have a error state with the following
characteristics:
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We can simplify the drawing by leaving out the error state
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An illegal input will cause a transition to the error state
All subsequent inputs cause the state machine to remain in 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 inputs”
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This is a convention when drawing the machine—it does not mean we
look for an asterisk in the input
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Example II: Nested parenthesis
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The following example tests whether parentheses are properly
nested (up to 3 deep)
(
(
(
OK
start
)
)
*
*
)
*
)
(
*
Error
*
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How can we extend this machine to handle
arbitrarily deep nesting?
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Nested parentheses II
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Question: How can we use a state machine to
check parenthesis nesting to any depth?
Answer: We can’t (with a finite number of states)
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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 aren’t 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
( do count=1
start
OK
) and count==1
do count=0
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( do count++
) and count>1
do count--
This machine is based on a state machine, but it
obviously is not just a state machine
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Example: Making numbers bold
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In HTML, you indicate boldface by surrounding the
characters with <b> ... </b>
Suppose we want to make all the integers bold in an HTML
page—we can write a state machine to do this
end of input
output </b>
digit
output <b>digit
start
NORMAL
*: output *
NUMBER
end
digit
output digit
nondigit
output </b>nondigit
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State machines in Java
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In a state machine, you can have transitions from any
state to any other state
This is difficult to implement with Java’s loops and if
statements
The trick is to make the “state” a variable, and to
embed a switch (state) statement inside a loop
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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 < 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("</b>");
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The two states
case NORMAL:
case NUMBER:
if (Character.isDigit(ch)) {
if (!Character.isDigit(ch)) {
result.append("<b>" + ch);
result.append("</b>" + ch);
state = NUMBER;
state = NORMAL;
break;
break;
}
}
else {
else {
result.append(ch);
result.append(ch);
}
}
break;
break;
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Conclusions
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A state machine is a good model for a number of
problems
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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
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Java lets you do all kinds of additional tests and actions;
you can ignore these limitations
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