1. UNIVERSAL TURING MACHINES

2. OUTLINE Review Algorithm Why

3. TURING MACHINES (TM) An infinitely long tape A finite number of states A set of transitions from one state to one state, depending on the character read

4. REPRESENTING A TM Starting StateSymbol ReadEnding StateSymbol WrittenDirection 1011R 1110R 1∆2∆L 1010101101100101101010110010111011011101 000

5. UNIVERSAL TURING MACHINES (UTM) A TM (U) that takes the representation of another TM (M) and the tape that M would process as inputs, and processes the tape as M would.

6. ALGORITHM - PREPARATION Tape  Working Buffer  Machine Representation  {Initial, Scanned, Final, Written, Direction}  Tape Description

7. ALGORITHM - SUBROUTINES Copier Matcher Substituter

8. ALGORITHM - EXAMPLE X000000Y1010101101100101101010110010111011011101000Z1101011000… X1X000001010101101100101101010110010111011011101000Z1101011000… X1X110001010101101100101101010110010111011011101000Z1101011000… X101100Y1010101101100101101010110010111011011101000Z1101011000… X101100010101011011001Y1101010110010111011011101000Z1101011000… X00000001010101101100101101Y10110010111011011101000Z1101011000… X00000001010101101100101101Y10110010111011011101000Z101011000… X00000001010101101100101101Y1011001011101101110100001Z1011000… X000000010101011011001011Y101011001011101101110100001Z1011000…

9. ANOTHER MACHINE

10. WHY? Computability

11. http://www.sciencedirect.com/science/article/pii/S0304397596000771 http://people.cs.uchicago.edu/~odonnell/Teacher/Courses/UChicago/CMSC31100/ UTM.pdf http://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf