# Practice problems on finite automata

**Que-1:** Draw a deterministic and non-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.

**Explanation –** Design a DFA and NFA of a same string if input value reaches the final state then it is acceptable otherwise it is not acceptable.

NFA of the given string is as follows:

DFA of the given string is as follows:

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

**Note –** NFA and DFA both have same power that means if NFA can recognized an language L then DFA can also be defined to do so and if DFA can recognized an language L then NFA can also be defined to do so.

**Que-2:** Draw a deterministic and non-deterministic finite automata which accept a string containing “the” anywhere in a string of {a-z}, e.g., “there” but not “those”.

**Explanation –** Design a DFA and NFA of a same string if input value reaches the final state then it is acceptable otherwise it is not acceptable. It is applicable for all the DFA and NFA. Since, NFA is quit easier then DFA, so first make its NFA and then go through the DFA.

NFA of the given string is as follows:

DFA of the given string is as follows:

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

**Que-3:** Draw a deterministic and non-deterministic finite automata which accept a string containing “ing” at the end of a string in a string of {a-z}, e.g., “anything” but not “anywhere”.

**Explanation –** Design a DFA and NFA of a same string if input value reaches the final state then it is acceptable otherwise it is not acceptable. It is applicable for all the DFA and NFA.

NFA of the given string is as follows:

DFA of the given string is as follows:

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

## Recommended Posts:

- Practice problems on finite automata | Set 2
- TOC | Finite Automata with Output (Set 11)
- Compound Finite Automata (FA)
- TOC | Finite Automata with Output (Set 3)
- TOC | Finite Automata with Output (Set 6)
- TOC | Finite Automata with Output (Set 5)
- TOC | Designing Non-Deterministic Finite Automata (Set 1)
- TOC | Designing Non-Deterministic Finite Automata (Set 3)
- TOC | Designing Deterministic Finite Automata (Set 11)
- TOC | Designing Deterministic Finite Automata (Set 6)
- TOC | Designing Deterministic Finite Automata (Set 10)
- TOC | Designing Deterministic Finite Automata (Set 7)
- TOC | Designing Deterministic Finite Automata (Set 2)
- TOC | Designing Deterministic Finite Automata (Set 5)
- TOC | Designing Deterministic Finite Automata (Set 4)

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