Difference Between Finite Automata and Turing Machine

Finite Automata and Turing Machines are both models of computation used to understand how computers process information. Finite Automata is a simpler machine that recognize patterns within input data. They have a limited amount of memory and can be in one of a finite number of states at any time. Finite Automata are often used in applications like text processing and pattern matching. Turing Machines, on the other hand, are more powerful and complex. They can read and write symbols on an infinite tape and have an unlimited amount of memory. This allows Turing Machines to solve a broader range of problems including those that require more complex processing and calculations.

Finite Automata

Finite Automata or finite state machine is a machine that has five elements or tuples, which are :

• Q: A finite set of states
• Σ (Sigma): A finite set called the input alphabet
• δ (delta): The transition function, which defines state changes based on input
• q₀: The initial state (where the machine starts)
• F: The set of accept (or final) states

It has a set of states and rules for moving from one state to another but it depends upon the applied input symbol. Basically, it is an abstract model of a digital computer. The following figure shows some essential features of general automation.

The above figure shows the following features of automata :

1. Input
2. Output
3. States of automata
4. State relation
5. Output relation

The transition function in finite automata can be represented by:

δ : Q × Σ* → Q

where, Q is the set of states, Σ is the input alphabet and Σ* represents all possible strings formed from Σ. The function maps a state and an input string (from Σ*) to a new state in Q.

Example of Finite Automata

Draw a deterministic finite automate which accept 00 and 11 at the end of a string containing 0, 1 in it, e.g., 01010100 but not 000111010.

Here, q0 shows the initial state, q1 and q2 are the transition states, and q3 and q4 are the final states.

Advantages of Finite Automata

• Simplicity: Finite Automata are easy to understand and design, making them great for basic pattern recognition.
• Speed: They process input quickly since they have a limited number of states and simple transitions.
• Efficiency: They use minimal memory which makes them efficient for tasks like text searching.

Disadvantages of Finite Automata

• Limited Memory: Finite Automata can only remember a small amount of information which restricts their ability to handle complex problems.
• Limited Language Recognition: They can only recognize regular languages.
• No Backtracking: They can only move forward through the input so they can't easily handle situations that require revisiting earlier states.

Turing Machine

Turing Machine is a powerful model which was proposed by Alan Turing in 1936. The earlier models like finite automata and push-down automata are not considered accurate models because they cannot recognize the simple language. But the Turing machine is the most accurate model for personal computers. It is capable of solving every problem that a real computer can do. There are also some problems which can not be solved by it because these problems are beyond the theoretical limits of computation.

The transition function in turing machine can be represented by:

δ : Q × T → Q × T × {L, R}

where,

• Q is the set of states,
• T is the tape alphabet,
• {L, R} indicates the movement of the tape head (Left or Right).

Working of Turing Machine

• The tape holds symbols and acts as the machine’s memory.
• The read/write head reads the symbol on the current cell.
• The finite control decides what symbol to write, which direction to move the head (left or right), and the next state based on the current state and symbol.
• The head writes the new symbol, moves one cell left or right, and updates the state.
• This cycle repeats until the machine halts.

Example of Turing Machine

Draw a Turing machine to find 1's complement of a binary number. 

1’s complement of a binary number is another binary number obtained by toggling all bits in it, i.e., transforming the 0 bit to 1 and the 1 bit to 0. 

• State q0 replaces '1' with '0' and '0' with '1' and moves to the right.
• When BLANK is reached, move towards the right and reach the final state qH. 

Advantages of Turing Machine

• Powerful Computation: Turing Machines can solve a wide variety of problems like complex calculations and algorithmic tasks.
• Unlimited Memory: They have access to infinite tape and allow to store large amounts of information.
• Versatile: Turing Machines can simulate any other computational model and make them very flexible in problem-solving.

Disadvantages of Turing Machine

• Complexity: Turing Machines are more complex to understand and design as compared to Finite Automata.
• Slower Processing: They may be slower in processing since they can move back and forth on the tape and involve more operations.
• Theoretical Nature: They are mostly used for theoretical purposes and practical computers are designed differently.

Difference Between Finite Automata and Turing Machine