Question

Consider the following automata in increasing processing power :
A. Linear bounded automata
B. Turing machine
C. Finite automata
D. Pushdown automata
Choose the correct answer from the options given below :

• A. A, B, D, C
• B. C, D, A, B
• C. B, A, C, D
• D. C, D, B, A

Hint:

Remember the acronym FP-LT for the Chomsky Hierarchy machines: Finite, Pushdown, Linear-Bounded, Turing. Power increases as you go from F to T!

Answer 1

The Correct Option is B

The computational power of different automata is defined by the Chomsky Hierarchy, which ranks languages and the machines capable of recognizing them from least powerful to most powerful. 1. Ranking by Language Complexity:
• Finite Automata (C): Recognizes Regular Languages. These have no memory other than their current state (e.g., matching a simple string pattern). This is the least powerful.
• Pushdown Automata (D): Recognizes Context-Free Languages. These use a stack for memory, allowing them to recognize balanced structures like $a^n b^n$.
• Linear Bounded Automata (A): Recognizes Context-Sensitive Languages. These have memory proportional to the size of the input string.
• Turing Machine (B): Recognizes Recursively Enumerable Languages. These have an infinite tape for memory and can simulate any algorithmic process. This is the most powerful. 2. Final Order: Arranging them in increasing order of processing power gives: Finite Automata $\to$ Pushdown Automata $\to$ Linear Bounded Automata $\to$ Turing Machine. 3. Verification: This sequence corresponds to the identifiers C, D, A, B.