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CSCI 100
Think Like Computers
Lecture 4
Fall 2008
Turing Machines
•Alan Turing developed the concept of a
computing machine in the 1930s
•A Turing machine, as his model became
known, consists of a control unit with a
read/write head that can read and write
symbols on an infinite tape
Turing Machines
•Why is such a simple
machine (model) of any
importance?
It is widely accepted that
anything that is intuitively
computable can be computed
by a Turing machine
If we can find a problem for
which a Turing-machine
solution can be proven not to
exist, then the problem must
be unsolvable
Turing machine processing
Halting Problem
•It is not always obvious that a computation
(program) halts
•The Halting problem: Given a program
and an input to the program, determine if
the program will eventually stop with this
input
•This problem is unsolvable
Halting Problem
•Assume that there exists a Turing-machine
program, called SolvesHaltingProblem that
determines for any program Example and input
SampleData whether program Example halts
given input SampleData
Proposed program for solving the Halting problem
Halting Problem
•The intuition: such a program might have a
hard time checking itself.
•We can construct a program that leads to
a contradiction in much the same way as
does the phrase: “This sentence is a lie”.
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