# UNIVERSAL TURING MACHINES OUTLINE Review Algorithm Why TURING

• Slides: 11

UNIVERSAL TURING MACHINES

OUTLINE Review Algorithm Why

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

REPRESENTING A TM Starting State Symbol Read Ending State Symbol Written Direction 1 0 1 1 R 1 1 1 0 R 1 ∆ 2 ∆ L 10101011011001011010101100101101110 1000

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.

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

ALGORITHM - SUBROUTINES Copier Matcher Substituter

ALGORITHM - EXAMPLE X 000000 Y 101010110110010110101011001011101000 Z 1101011000… X 1 X 0000010110110010110101011001011101000 Z 1101011000… X 1 X 1100010110110010110101011001011101000 Z 1101011000… X 101100 Y 101010110110010110101011001011101000 Z 1101011000… X 10110001011011001 Y 1101010110010111011011101000 Z 1101011000… X 00000001010101101100101101 Y 1011001011101000 Z 101011000… X 0000000101101100101101 Y 101100101110100001 Z 1011000… X 00000001011011001011 Y 10101100101110100001 Z 1011000…

ANOTHER MACHINE

WHY? Computability

http: //www. sciencedirect. com/science/article/pii/S 0304397596000771 http: //people. cs. uchicago. edu/~odonnell/Teacher/Courses/UChicago/CMSC 3 1100/UTM. pdf http: //www. cs. virginia. edu/~robins/Turing_Paper_1936. pdf