14-Jun-15 State Machines

2 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 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

3 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

4 Example I: Even or odd The following machine determines whether the number of A s 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 A evenodd start A anything but A

5 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

6 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” This is a convention when drawing the machine—it does not mean we look for an asterisk in the input

7 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? start ) ( ) ( ) ( OK Error ) **** ( *

8 Nested parentheses II 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) 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

9 Nested parentheses III This machine is based on a state machine, but it obviously is not just a state machine OK ( do count=1 ) and count==1 do count=0 ( do count++ ) and count>1 do count-- start

10 The states of a Thread 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 ready waiting runningdead start

11 A Memorization program A program to help people memorize paired-associates might be designed like this: Some stimulus is presented The user has to type in a response A paired associate is considered “learned” when the user answers correctly three times in a row Each item (stimulus + response) can be thought of as a state machine Here, however, we are looking at states of data rather than states of a program

12 Item states What’s the value in thinking of this as a state machine? Answer: When I wrote one of these for real use, I was able to adjust the difficulty of the study session by measuring the percentage correct from each state. 0th1st2nd3rd right start wrong out

13 Example: Making numbers bold In HTML, you indicate boldface by surrounding the characters with... Suppose we want to make all the integers bold in an HTML page—we can write a state machine to do this NORMALNUMBER digit output digit nondigit output nondigit *: output * end of input output start digit output digit end

14 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 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 Each case is responsible for resetting the “state” variable as needed to represent transitions

15 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(" ");

16 The two states case NORMAL: if (Character.isDigit(ch)) { result.append(" " + ch); state = NUMBER; break; } else { result.append(ch); } break; case NUMBER: if (!Character.isDigit(ch)) { result.append(" " + ch); state = NORMAL; break; } else { result.append(ch); } break;

17 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

18 The End