turing machine Flashcards
(20 cards)
What is a Turing machine?
A theoretical model of computation consisting of a finite state machine, a read/write head, and an infinite tape with marked-off squares. It can be viewed as a computer with a single fixed program.
What are the four components that express a Turing machine?
1) A finite set of states in a state transition diagram, 2) A finite alphabet of symbols, 3) An infinite tape with marked-off squares, 4) A sensing read-write head that can travel along the tape one square at a time.
What is the start state in a Turing machine?
One of the states in the finite state machine that is designated as the initial state where computation begins.
What are halting states in a Turing machine?
States that have no outgoing transitions. When a Turing machine enters a halting state, computation stops.
What is a transition function in a Turing machine?
A formal way to represent transitions between states, written in the form: δ(current state, read) = (new state, write, move). It defines what the machine should do based on its current state and the symbol it reads.
How is a state transition diagram related to a transition function?
They are equivalent ways to represent the same information. A transition in a state transition diagram can be written as a transition function and vice versa.
What does the following transition function mean: δ(S0, 1) = (S1, 0, R)?
If the machine is in state S0 and reads a 1, then write a 0, move to state S1, and move the read/write head to the right.
How do you trace a Turing machine?
By following the state transition rules step by step, recording the current state, the symbols on the tape, and the position of the read/write head at each step.
What does the read/write head do in a Turing machine?
It reads symbols from the tape, writes new symbols to the tape, and can move left or right along the tape, one square at a time.
What is the alphabet of a Turing machine?
The finite set of symbols that the Turing machine can read and write on its tape.
What makes Turing machines more powerful than finite state machines?
Turing machines have an infinite tape that serves as unlimited memory, allowing them to recognize a greater range of languages than finite state machines.
What is a Universal Turing Machine (UTM)?
A Turing machine capable of simulating any other Turing machine. It reads both the description of a Turing machine and the input data from the same tape, then simulates that machine on the input data.
Why is the Universal Turing Machine considered an interpreter?
Because it reads instructions (the description of another Turing machine) in sequence before executing operations on the input data, similar to how interpreters process programming languages.
Why are Turing machines important to the subject of computation?
They provide a formal model of computation and a definition of what is computable. They help prove that there are problems which cannot be solved by computers (undecidable problems).
What is the significance of the Universal Turing Machine to computing?
It led to the stored program concept, where both programs and data are stored in memory, which is fundamental to modern computer architecture.
How is a Turing machine represented graphically?
As a series of cells (the tape) each containing a symbol, with a triangular pointer representing the position of the read/write head, and the current state labeled.
What happens when a Turing machine reaches its halting state?
The computation stops. The halting state can be entered at any point in the machine’s execution once all input data has been processed.
Can a Turing machine have multiple halting states?
Yes, a Turing machine may have multiple states from which there are no outgoing transitions (halting states).
What does it mean that a problem is ‘computable’ in terms of Turing machines?
A problem is computable if there exists a Turing machine that will always halt with the correct answer for any valid input to the problem.
How are transitions represented on a state transition diagram for a Turing machine?
As labeled arrows between states, with labels indicating: the symbol read, the symbol written, and the direction to move (e.g., ‘1|0,R’ means read 1, write 0, move right).
