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Comp sci. Paper 1 Topic 6: (4) Turing Machines
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Textbook chapter:19
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What is a Turing machine?
A Turing machine is a finite state machine (FSM) with the ability to read and write data to an unlimited tape. It is a theoretical and can carry out any algorithm and produce a model of what is computable.
What 3 parts does a Turing machine consist of?
A Turing Machine consists of:
1. The tape, which is unlimited and can be written to or read from. Each cell can have a value of 0, 1, or blank.
2. The controller (the program), which determines what happens at each cell.
3. The read/write head, which can read from and write symbols to the tape.
What 3 functions can be carried out by the controller on the Turing machine?
1. Read the symbol on the tape
2. Erase or write a new symbol on the tape
3. Move the head left or right by a single space
What is an alphabet?
The acceptable symbols (characters and numbers) for a given Turing machine.
What are the halting and starting states?
The halting state stops the Turing machine
The start state is the initial state at the start of the program.
What is a transition function?
A transition function is a way to represent the transition arc between two states on a state transition diagram.
It indicates what should be written at each cell when the read/write head is over a cell and whether to move left or right along the tape based on the input.
This is the notation for a transition function.
δ (Current state, Input symbol) = (Next state, Output symbol, Head move)
What does this transition function mean? δ (S0, 1) = (S1, 0, L)
If the machine is currently in state S0 and the symbol 1 is read from the tape, then transition to state S1, write 0 on the tape, and move head left.
What is a state transition diagram?
A visual representation of the transition function.
What is the Universal Turing Machine?
the Universal Turing Machine simulates the behaviour of any Turing machine by reading a description of the machine along with the input of its own tape. Like a series of Turing machines linked together.
What are the 3 ways of representing a Turing machine?
1. As a state transition diagram
2. As written out transition functions
3. As an instruction table with columns titled: state, read, write, move, next state.
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