Which of the following pairs have DIFFERENT expressive power?a)Deterministic finite automata (DFA) and Non-deterministic finite automata (NFA)b)Deterministic push down automata (DPDA) and Non-deterministic push down automata (NPDA)c)Deterministic single-tape Turing machine and Non-deterministic single tape Turing machined)Single-tape Turing machine and multi-tape Turing machineCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Introduction

The question asks us to identify the pairs that have different expressive power. Expressive power refers to the ability of a computational model to solve a particular problem or recognize a specific language. In other words, it measures the computational capabilities of different models.

Explanation

Let's analyze each pair to determine their expressive power:

a) Deterministic finite automata (DFA) and Non-deterministic finite automata (NFA)

- DFA and NFA are both types of finite automata that recognize regular languages.
- However, DFA is more restrictive than NFA in terms of expressive power.
- DFA can only recognize regular languages that can be expressed with a finite number of states, while NFA can recognize some non-regular languages as well.
- Therefore, DFA and NFA have different expressive power.

b) Deterministic push down automata (DPDA) and Non-deterministic push down automata (NPDA)

- Both DPDA and NPDA are types of pushdown automata that recognize context-free languages.
- However, in terms of expressive power, DPDA and NPDA have the same level of power.
- Both DPDA and NPDA can recognize the same set of context-free languages.
- Therefore, DPDA and NPDA do not have different expressive power.

c) Deterministic single-tape Turing machine and Non-deterministic single-tape Turing machine

- Both deterministic and non-deterministic single-tape Turing machines have the same expressive power.
- They can recognize the same set of languages, namely the recursively enumerable languages.
- Therefore, deterministic and non-deterministic single-tape Turing machines do not have different expressive power.

d) Single-tape Turing machine and multi-tape Turing machine

- Both single-tape and multi-tape Turing machines have the same expressive power.
- They can recognize the same set of languages, namely the recursively enumerable languages.
- Therefore, single-tape and multi-tape Turing machines do not have different expressive power.

Conclusion

Based on the analysis, the only pair that has different expressive power is (b) Deterministic pushdown automata (DPDA) and Non-deterministic pushdown automata (NPDA). All other pairs have the same expressive power.

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