Transcript State Machines 6-Nov-15 What is a state machine?     A state machine is a different way of thinking about computation A state machine has some.

State Machines
6-Nov-15
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
A “pure” state machine only knows which state it is
in—it has no other memory or knowledge
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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
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State machine I/O
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State machines are designed to respond to a sequence
of inputs, such as
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The individual characters in a string
A series of external events
State machines may produce output (often as a result
of transitions)
Alternatively, the only “result” of a state machine may
be the 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
The double circle represents a “final” (accepting) state
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Error states
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Again, a state machine is a way of doing certain kinds of computations
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The input is a sequence of values (typically, a String)
Some inputs may be illegal (for example, syntax errors in a program)
A state machine is used to recognize certain kinds of inputs
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We say the machine succeeds if it recognizes its input, otherwise it fails
Some states may be marked as final states (they are drawn with concentric
circles)
A state machine succeeds if:
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A state machine fails if:
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It is in a final state when it reaches the end of its input
It encounters an input for which it has no defined transition
It reaches the end of its input, but is not in a final state
State machines may have a error state with the following characteristics:
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The error state is not a final state
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
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State machines can get pretty complicated
The formal, mathematical definition of a state machine requires it
to have a transition from every state for every possible input
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When we draw a state machine, we don’t need to draw the error
state--we can just assume it’s there
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To satisfy this requirement, we often need an error state, so we can have
transitions for illegal (unrecognized) inputs
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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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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The states of a Thread
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A Thread is an object that represents a single flow of
execution through a program
A Thread’s lifetime can be described by a state machine
waiting
start
ready
running
dead
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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
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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The End
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