Finite State Machines / The Turing Machine Flashcards
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
