Finite-State Machines, Part 2
Derived from the on-line notes by Dr. Matt Stallmann.
Stripping out comments
Problem: Output each of the words contained in a Java source file while
excluding any that occur in comments.
For this example—
• A word will be defined as any string of alphabetic characters.
• Comments are defined as strings that begin with the characters // and
end with the newline character '\n'. The FSM along with the program
used to accomplish this task is as follows.
Table form of FSM:
State
A–Z a–z
/
\n
other
IGNORE
IN_WORD
ONE_SLASH
IGNORE
IGNORE
IN_WORD
IN_WORD
ONE_SLASH
IGNORE
IGNORE
ONE_SLASH
IN_WORD
IN_COMMENT
IGNORE
IGNORE
IN_COMMENT
IN_COMMENT
IN_COMMENT
IGNORE
IN_COMMENT
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import java.io.*;
public class WordsNotInComments{
// words are output on transitions out of the IN_WORD state
public static void main(String[] args) {
if (args.length == 1) {
try {
BufferedReader br = new BufferedReader(
new FileReader(args[0]));
char ch;
int next;
final int IGNORE = 0;
final int IN_WORD = 1;
final int ONE_SLASH = 2;
final int IN_COMMENT = 3;
int state = IGNORE;
String s = "";
while ((next = br.read()) != −1) {
ch = (char) next;
switch (state) {
case IGNORE: if (Character.isLetter(ch)) {
s = "" + ch;
state = IN_WORD;
}
else if (ch == ’/’)
state = ONE_SLASH;
break;
case IN_WORD: if (Character.isLetter(ch)) {
s += ch;
// state = IN_WORD;
}
else {
System.out.println(s);
if (ch == ‘/’);
state = ONE_SLASH;
else
state = IGNORE;
}
break;
case ONE_SLASH: if (’/’ == ch)
state = IN_COMMENT;
else if (Character.isLetter(ch)) {
s = "" + ch;
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state = IN_WORD;
}
else
state = IGNORE;
break;
case IN_COMMENT: if (ch == ’\n’)
state = IGNORE;
break;
default: System.out.println("Invalid state: " +
state);
}
}
}
catch(IOException e) {
System.out.println("File error: " + e);
System.out.println("usage: java WordsNotInComments
filename");
}
}
else
System.out.println("usage: java WordsNotInComments filename");
}
}
Consider the input “if (ch == ’/’)”. Let's trace through the states the
program moves into. IGNORE, IN_WORD, IN_WORD, IGNORE,
IGNORE, IN_WORD, IN_WORD, IGNORE, IGNORE, IGNORE, IGNORE,
IGNORE, ONE_SLASH, IGNORE, IGNORE.
What is output? if
ch
Exercise: How would you modify the table form of the FSM to strip out
comments but pass anything else through to the output?
Answer:
State
/
\n
Other
PRINT
ONE_SLASH
PRINT
PRINT
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ONE_SLASH
COMMENT
PRINT
PRINT
COMMENT
COMMENT
PRINT
COMMENT
When will output be performed? When we’re in the PRINT state.
When is extra output required? When we’re in state ONE_SLASH and
encounter something other than a slash.
Horner's Rule
A finite-state machine can also be used to convert an ASCII string of
characters representing a real number to its actual numerical value.
It performs the same operation as the
java.lang.Float.parseFloat(String s) function and uses an
algorithm known as Horner's Rule.
The letters shown in the FSM stand for the following:
c
s
v
p
-
current character
sign of the number
value of the number
power
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Note that this FSM assumes that the string contains a valid floating point
number that
• starts with an optional + or –,
• has at least one digit, an optional decimal point,
• and any number (including 0) of digits before and after the decimal point.
A value of 0 is returned if an invalid string is encountered.
Here is a function that implements this FSM.
Table form of FSM:
State
+ or –
.
digit
other
START
INTEGER
DECIMAL
INTEGER
ERROR
INTEGER
ERROR
DECIMAL
INTEGER
ERROR
DECIMAL
ERROR
ERROR
DECIMAL
ERROR
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public class Parser {
static double toDouble(String s) {
double sign = 1; // sign of number (either 1 or −1)
double value = 0; // current value of the number
double power = 0.1; // current power of 10 for
// digits after decimal point
int i = 0;
final int START = 0;
final int INTEGER = 1;
final int DECIMAL = 2;
final int ERROR = 3;
int state = START;
char ch; //current character in string
while (state != ERROR && i < s.length()) {
ch = s.charAt(i++);
switch (state) {
case START: if (ch == ’.’)
state = DECIMAL;
else if (ch == ’−’) {
sign = −1.0;
state = INTEGER;
}
else if (ch == ’+’)
state = INTEGER;
else if (Character.isDigit(ch)) {
value = ch − ’0’;
state = INTEGER;
}
else
state = ERROR;
break;
case INTEGER: if (ch == ’.’)
state = DECIMAL;
else if (Character.isDigit(ch))
value = 10.0 * value + (ch − ’0’);
else {
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value = 0.0;
state = ERROR;
}
break;
case DECIMAL: if (Character.isDigit(ch)) {
value += power * (ch − ’0’);
power /= 10.0;
}
else {
value = 0.0;
state = ERROR;
}
break;
default: System.out.println("Invalid state: " +
state);
}
}
return sign * value;
}
public static void main(String[] args) {
if (args.length == 1)
System.out.println(toDouble(args[0]));
}
}
Question: What would be the right way to add error-checking to the
program?
The State pattern
The code that we have given is not very object oriented. It checks which
state the FSM is in in several places.
In an object-oriented program, we can use polymorphism (Lecture 7,
Horstmann §11.3) to achieve the same effect. This will allow us to check
the state in only one place.
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The first step is to define a State interface. Consider the table form of the
FSM.
 The rows of the table represent the different states.
 The columns of the table represent the different behaviors of each
state.
Therefore, what methods should be defined in the State interface?
public interface State {
public void onPlus();
public void onMinus();
public void onPoint();
public void onDigit();
public void onOther();
}
How should the States be defined?
class Start implements State { ... }
class Integr implements State { ... }
class Decimal implements State { ... }
Where should the States be defined? As inner classes of Parser
How should these methods be implemented for each state? Let’s take the
onPoint() method, for example.
In class Start, it is defined as …
public void onPoint() { state = decimal; };
(We need a variable of type State to hold the current state.)
In class Integr, it is defined as …
public void onPoint() { state = decimal; };
In class Decimal, it is defined as …
public void onPoint() { throw new
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NumberFormatException(); };
Exercise: Divide up into groups, with each group responsible for
implementing one of the following methods in all three classes.
void
void
void
void
onMinus();
onPlus();
onDigit();
onOther();
Write each method on a separate index card.
Then divide into three groups, with each group taking a different class.
Pass the cards for each method to the group that is taking that class, and
have the group assemble the various methods into a class definition.
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