UNIVERSAL TURING MACHINES. OUTLINE Review Algorithm Why.

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Presentation transcript:

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 StateSymbol ReadEnding StateSymbol WrittenDirection 1011R 1110R 1∆2∆L

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 X000000Y Z … X1X Z … X1X Z … X101100Y Z … X Y Z … X Y Z … X Y Z … X Y Z … X Y Z …

ANOTHER MACHINE

WHY? Computability

UTM.pdf