Finite State Machines / The Turing Machine Flashcards Preview

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Flashcards in Finite State Machines / The Turing Machine Deck (26)
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What is a finite state machine and why are they useful?

- An abstract model that has a finite number of states and can only be in one state at a time
- They're useful for recognising logical sequences
- They can model a range of problems simply


What is a finite state machine with no output called?

A Finite State Automaton (FSA)


What is a state transition diagram?

A visual representation of a FSM
(uses circles and arrows)


How is a state represented in a FSM?
How is a transition function represented in a FSM?
How is the starting state represented in a FSM?
How is the target state represented in a FSM?

A state is represented by a circle and a name that identifies it : S0, S1, S2 ...
A transition is represented by an arrowed line and the input that makes this transition: 0, 1 or A, B, C, D
The starting state is represented with an arrow pointing towards it
The target state has a double circle around the name that identifies it


What is a state transition table?

It records all the states and transitions possible for a specific FSM


What is a mealy machine?

- A mealy machine is a finite state machine whose output is determined by its current state and the current input.
- no more than one transition is possible at a time


How does a mealy machine show what the inputs and outputs are?

Along the transition line it will show two characters or digits : a/b. a is the input and b is the output. a and b can be anything from a number to a letter to a word.


What can mealy machines represent?

Can represent electronic circuits and bitwise operations.
Can carry out an XOR function
They have a range of uses such as traffic light control and vending machines.


Describe the Halting problem

It determines if a program will halt (1 mark)
For a specific input (1 mark)


Why is it not possible to create a Turing machine that solves the Halting problem?

The Halting problem is non-computable, there is no algorithm that solves the Halting problem


State three components of a Turing machine.

- The finite alphabet of symbols that it can use
- Infinite tape
- Finite set of states
- A set of transition rules;
- A read-write head
- Start state
- an accepting / halting states


Explain what a Universal Turing Machine is.

- Instructions for TM and the TM's input are stored on the UTM's tape
- A Turing machine that can execute the behaviour of any other Turing machine // can compute any computable sequence


Why can a Universal Turing Machine be considered to be more powerful than any computer that you can purchase?

Because it has an infinite amount of memory/tape;


What are transition rules?

Rules that describe what a finite state machine should do given certain input.


What do mealy machine state diagrams not have?

A target state


What can mealy machines be used for?

They can provide a simple model for:
- Cipher machines.
- Traffic lights
- Timers
- Vending machines
- Basic electronic circuits


What does the Turning machine consist of?

- An infinitely long strip of tape divided into squares
- A read/write head
- A halting state/stop state


What does a square represent in a Turing Machine?

A square represents a blank state


What notation is used by Turing machines?

(input, output, movement) is used.
for example (1,1,L) means if the input is 1, output 1 and move left


How do Turing machines work?

They find the first blank cell on the tape, to the right of the current position of the read/write head.


What is a transition function?

The transition rules for a Turing Machine


What is the notation for a transition rule in a Turing machine?

δ (Current State, Input symbol) = (Next State, Output symbol, movement)
For example:
δ (S1, 0) = (S2, 1, L) means IF the current state is S1 and the input is 0, then write a 1 on the tape, move left and change state to S2


What can a Turing machine represent?

A Turing machine can theoretically represent any computation


What idea did the Universal Turing Machine lead to and why was this?

- The stored program computer
- Because a Turing Machine reads (off it's own tape) both the description of the machine to be simulated and the input to the machine.


What must a valid identifier consist of in a FSM?

- Must start with a lowercase letter
- Any number of letters or numbers may follow after this
- There is no limit on the length of a identifier


What is a dead state

A state that once arrived in, can never reach the accept state