1. Turing Machines from “On Computable Numbers” Jerry Grochowski – CS 4800

2. Specification Implement the Turing Machines (TM) from Alan Turing's “On Computable Numbers with an Application to the Entscheidungsproblem” Run Turing's first two simple programs Create Turing's Universal Turing Machine (UTM) Implement as a Java Console Application

3. Goals See what a bare bones computing machine does Modern computers are complex but Turing Machines (TM) are simple yet powerful Learn from the Source Turing was a genius – What's actually in his paper “On Computable Numbers”? See how Turing Machines relate to class Understand the potential and limitations of TMs

4. What will it do? Program 1: 010101010101010.... Program 2: 0010110111011110.... Universal Turing Machine (UTM): Repeat Program 1 and 2, but from tape Input: Program 1 and 2 input as text files of quintuples UTM input as text files of function tables (see later slides) Output: steps of the tape to console and file

5. Design Flow Normal Turing Machine A quintuple: ;,q1,S0,S1,R,q2, = In state q1, if blank (Symbol 0), print 0 (Symbol 1), move Right, and go to state q2

6. Univeral Turing Machine (Design Flow) Parser or Table?

7. Classes

8. Problems The UTM would require a lot of quintuples Could parse tables to produce quintuples Could use tables as input, like functions (which they are) Bugs in Turing's tables Discussed in Copeland's “The Essential Turing”

9. Conclusion The initial Turing Machines are doable The Universal Turing Machine is harder but more interesting “On Computable Numbers” is worth reading