1. Turing Machines

2. Introduction
Turing machine was invented by the Mathematician Alan Turing in 1934
A machine capable of solving any problem that can be represented algorithmically
The basis from which modern Computers were developed
Anything a modern computer can do can be represented using a Turing machine

3. What is a Turing machine?
It describes an algorithm
It consists of a deterministic finite state machine together with an infinitely long tape
They compute functions or accept a set of strings i.e. language
Input received from initial tape
Output is final content of tape
If it doesn’t halt on inputs specified for function then no algorithm exists and function is not computable

4. Power of Turing Machines
The basic operations of a Turing machine cannot be divided further and all other types of computing machines can be reduced to an equivalent Turing machine
A Turing machine provides a formal definition of the digital computer
A sequence of Turing machines may be connected together to perform more complex operations matching those of any program running on a Pentium processor

5. Universal Turing Machines
A UTM is a Turing machine that can execute other Turing machines by simulating their behaviour
A UTM using a single 1-dim tape, the instructions of the Turing machine being simulated are placed on the tape followed by the data to be processed.
It behaves as an Interpreter
Desktop machines are based on this principle e.g. Java applets downloaded as data but can be executed as programs

6. DNA Computing Modern computers use silicon chips but recently
computers have been developed based on DNA.
In 2002, Ehud Shapiro showed a programmable
molecular device composed of enzymes and
synthetic strands of DNA. This was an
implementation of a Turing Machine. A ‘DNA
Turing Machine’ could be used to compare ratios
of molecules in the human body – detecting
cancers and releasing anti-cancer drugs.

7. Class work Answer questions on Turing machines worksheet.
Answer questions 1-10 in the A2 Computing book pages 43 and 46.
Download and install Java
Download and install TuringKara.
Follow the ‘Learning to use TuringKara’ worksheet.

8. Homework Watch the ‘A Turing Machine overview’ YouTube video
Answer the past paper questions:
Q6 Specimen COMP3
Q8 COMP3 2010
Hand-in answers on Friday 30th March 2012

9. Questions