A Class for Turing Machine Tapes

A Turing machine works on a "tape" that is used for both input and output. The tape is made up of little squares called cells lined up in a horizontal row that stretches, conceptually, off to infinity in both directions. Each cell can hold one character. Initially, the content of a cell is a blank space. One cell on the tape is considered to be the current cell. This is the cell where the machine is located. As a Turing machine computes, it moves back and forth along the tape, and the current cell changes.

A Turing machine tape can be represented by a doubly-linked list where each cell has a pointer to the previous cell (to its left) and to the next cell (to its right). The pointers will allow the machine to advance from one cell to the next cell on the left or to the next cell on the right. Each cell can be represented as an object of type Cell as defined by the class:

 public class Cell { public char content; // The character in this cell. public Cell next; // Pointer to the cell to the right of this one. public Cell prev; // Pointer to the cell to the left of this one. } 

This class is already defined in the file Cell.java, so you don't have to write it yourself.

Your task is to write a class named Tape to represent Turing machine tapes. The class should have an instance variable of type Cell that points to the current cell. To be compatible with the classes that will use the Tape class, your class must include the following methods:

public Cell getCurrentCell() -- returns the pointer that points to the current cell.

public char getContent() -- returns the char from the current cell.

public void setContent(char ch) -- changes the char in the current cell to the specified value.

public void moveLeft() -- moves the current cell one position to the left along the tape. Note that if the current cell is the leftmost cell that exists, then a new cell must be created and added to the tape at the left of the current cell, and then the current cell pointer can be moved to point to the new cell. The content of the new cell should be a blank space. (Remember that the Turing machine's tape is conceptually infinite, so your linked list must must be prepared to expand on demand, when the machine wants to move past the current end of the list.)

public void moveRight() -- moves the current cell one position to the right along the tape. Note that if the current cell is the rightmost cell that exists, then a new cell must be created and added to the tape at the right of the current cell, and then the current cell pointer can be moved to point to the new cell. The content of the new cell should be a blank space.

public String getTapeContents() -- returns a String consisting of the chars from all the cells on the tape, read from left to right, except that leading or trailing blank characters should be discarded. The current cell pointer should not be moved by this method; it should point to the same cell after the method is called as it did before. You can create a different pointer to move along the tape and get the full contents. (This method is the hardest one to implement.)

It is also useful to have a constructor that creates a tape that initially consists of a single cell. The cell should contain a blank space, and the current cell pointer should point to it. (The alternative -- letting the current cell pointer be null to represent a completely blank tape -- makes all the methods in the class more difficult to implement.)

To test your Tape class, you can should run the programs that are defined by the files TestTape.java below...

package turing; // A test program for the Tape class that calls most of the methods in that class. // // The output from this program should be: Tape Conents: Hello World // Final position at the W public class TestTape { public static void main(String[] args) { Tape tape = new Tape(); for (int i = 0; i < "World".length(); i++) { tape.setContent("World".charAt(i)); tape.moveRight(); } for (int i = 0; i < "Hello World".length(); i++) tape.moveLeft(); for (int i =0; i < "Hello".length(); i++) { tape.setContent("Hello".charAt(i)); tape.moveRight(); } System.out.println("Tape Conents: " + tape.getTapeContents()); tape.moveRight(); System.out.println("Final position at the " + tape.getContent()); } } 

TestTapeGUI.java below.....

package turing; // A test program for the Tape class that creates a window containing // a graphical representation of the tape with an arrow pointing to // the current cell. There are buttons for moving the current cell to // the left and to the right. A text-input box shows the content of // the current cell. This box can be edited, and there is a "Set" button // that copies the contents of the cell (actually just the first character) // to the current cell. import java.awt.*; import java.awt.event.*; import javax.swing.*; public class TestTapeGUI extends JPanel { public static void main(String[] args) { JFrame window = new JFrame("Test Tape"); window.setContentPane( new TestTapeGUI("Test") ); window.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); window.pack(); window.setLocation(100,100); window.setVisible(true); } private Tape tape; private TapePanel tapePanel; private JButton moveLeftButton, moveRightButton, setContentButton; private JTextField contentInput; private class TapePanel extends JPanel { public void paintComponent(Graphics g) { super.paintComponent(g); int mid = getWidth() / 2; g.drawLine(0,30,getWidth(),30); g.drawLine(0,60,getWidth(),60); g.drawLine(mid,70,mid,110); g.drawLine(mid,70,mid+15,85); g.drawLine(mid,70,mid-15,85); int ct = (mid / 30) + 1; for (int i = 0; i <= ct; i++) { g.drawLine(mid + 30*i - 15, 30, mid + 30*i - 15, 59); g.drawString("" + tape.getContent(), mid + 30*i - 8, 53); tape.moveRight(); } for (int i = 0; i <= ct; i++) tape.moveLeft(); for (int i = 1; i <= ct; i++) { g.drawLine(mid - 30*i - 15, 30, mid - 30*i - 15, 59); tape.moveLeft(); g.drawString("" + tape.getContent(), mid - 30*i - 8, 53); } for (int i = 1; i <= ct; i++) tape.moveRight(); } } private class ButtonListener implements ActionListener { public void actionPerformed(ActionEvent evt) { if (evt.getSource() == moveLeftButton) tape.moveLeft(); else if (evt.getSource() == moveRightButton) tape.moveRight(); else { String content = contentInput.getText(); if (content.length() == 0) tape.setContent(' '); else tape.setContent(content.charAt(0)); } contentInput.setText("" + tape.getContent()); contentInput.selectAll(); contentInput.requestFocus(); tapePanel.repaint(); } } public TestTapeGUI(String initialContent) { tape = new Tape(); if (initialContent != null && initialContent.length() > 0) { for (int i = 0; i < initialContent.length(); i++) { tape.setContent(initialContent.charAt(i)); tape.moveRight(); } tape.moveLeft(); // move back over last character written } ButtonListener listener = new ButtonListener(); tapePanel = new TapePanel(); tapePanel.setPreferredSize(new Dimension(500,130)); tapePanel.setFont(new Font("Serif", Font.PLAIN, 24)); tapePanel.setBackground(new Color(180,180,255)); tapePanel.setBorder(BorderFactory.createLineBorder(Color.BLUE, 2)); moveLeftButton = new JButton("Left"); moveLeftButton.addActionListener(listener); moveRightButton = new JButton("Right"); moveRightButton.addActionListener(listener); setContentButton = new JButton("Set"); setContentButton.addActionListener(listener); contentInput = new JTextField(1); contentInput.setText("" + tape.getContent()); contentInput.setFont(new Font("Serif", Font.PLAIN, 18)); contentInput.addActionListener(listener); JPanel bottom = new JPanel(); bottom.add(moveLeftButton); bottom.add(moveRightButton); bottom.add(Box.createHorizontalStrut(15)); bottom.add(new JLabel("Content:")); bottom.add(contentInput); bottom.add(setContentButton); setLayout(new BorderLayout()); add(tapePanel,BorderLayout.CENTER); add(bottom,BorderLayout.SOUTH); } } 

and TestTuringMachine.java.

package turing; // A test program for the TuringMachine class. It creates three machines // and runs them. The output from the program indictes the expected behavior. public class TestTuringMachine { public static void main(String[] args) { TuringMachine writeMachine = new TuringMachine(); writeMachine.addRules( new Rule[] { // writes Hello on the tape then halts new Rule(0,' ',1,'H',false), new Rule(1,' ',2,'e',false), new Rule(2,' ',3,'l',false), new Rule(3,' ',4,'l',false), new Rule(4,' ',-1,'o',false) }); System.out.println("Running machine #1. Output should be: Hello"); String writeMachineOutput = writeMachine.run(new Tape()); System.out.println( "Actual output is: " + writeMachineOutput ); TuringMachine badMachine = new TuringMachine(); badMachine.addRules( new Rule[] { // writes ERROR on the tape then fails new Rule(0,' ',1,'R',true), new Rule(1,' ',2,'O',true), new Rule(2,' ',3,'R',true), new Rule(3,' ',4,'R',true), new Rule(4,' ',5,'E',true) // no rule for state 5! }); System.out.println(" Running machine #2. Should throw an IllegalStateExcpetion."); try { badMachine.run( new Tape() ); System.out.println("No Error was thrown."); } catch (IllegalStateException e) { System.out.println("Caught Illegal Argument Exception, with error message:"); System.out.println(e.getMessage()); } String input = "aababbbababbabbaba"; // a string of a's and b's for input to the copy machine Tape tape = new Tape(); for (int i = 0; i < input.length(); i++) { tape.setContent(input.charAt(i)); tape.moveRight(); } tape.moveLeft(); // now, input is written on the tape, with the machine on the rightmost character TuringMachine copyMachine = new TuringMachine(); // copies a string of a's and b's; // machine must start on leftmost char in the string copyMachine.addRules(new Rule[] { new Rule(0,'a',1,'x',true), // rules for copying an a new Rule(1,'a',1,'a',true), new Rule(1,'b',1,'b',true), new Rule(1,' ',2,' ',true), new Rule(2,'a',2,'a',true), new Rule(2,'b',2,'b',true), new Rule(2,' ',3,'a',false), new Rule(3,'a',3,'a',false), new Rule(3,'b',3,'b',false), new Rule(3,' ',3,' ',false), new Rule(3,'x',0,'x',true), new Rule(3,'y',0,'y',true), new Rule(0,'b',4,'y',true), // rules for copying a b new Rule(4,'a',4,'a',true), new Rule(4,'b',4,'b',true), new Rule(4,' ',5,' ',true), new Rule(5,'a',5,'a',true), new Rule(5,'b',5,'b',true), new Rule(5,' ',7,'b',false), new Rule(7,'a',7,'a',false), new Rule(7,'b',7,'b',false), new Rule(7,' ',7,' ',false), new Rule(7,'x',0,'x',true), new Rule(7,'y',0,'y',true), new Rule(0,' ',8,' ',false), // rules that change x and y back to a and b, then halt new Rule(8,'x',8,'a',false), new Rule(8,'y',8,'b',false), new Rule(8,' ',-1,' ',true) }); System.out.println(" Running machine #3. Output should be: " + input + " " + input); String copyMachineOutput = copyMachine.run(tape); System.out.println("Actual output is: " + copyMachineOutput); } } 

The first two programs just do things with a tape, to test whether it is functioning properly. TestTuringMachine actually creates and runs several Turing machines, using your Tape class to represent the machines' tapes.