Theory of Computation Practice Questions
A-Levels · A-Level Computer Science · 149 free MCQs with instant results and detailed explanations.
149
Total
46
Easy
74
Medium
29
Hard
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Sample Questions from Theory of Computation
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Q1
Easy
What is the main purpose of a finite state machine (FSM) in computation?
A.
To recognize patterns in data sequences.
B.
To perform complex calculations.
C.
To store large amounts of data.
D.
To encrypt sensitive information.
Show Answer & Explanation
Correct Answer: A
A finite state machine (FSM) is primarily used to recognize patterns in data sequences, making it essential for various applications in computational theory.
Q2
Easy
In the context of Turing machines, what does the 'tape' represent?
A.
A storage area for program instructions.
B.
A medium for input and output operations.
C.
An infinite memory source for data manipulation.
D.
A method for error checking during execution.
Show Answer & Explanation
Correct Answer: C
In Turing machines, the tape is an infinite memory source that allows for data manipulation, making it fundamental to the machine's operation.
Q3
Easy
Which of the following languages is considered regular?
A.
The set of all strings over the alphabet {a, b} with an even number of a's.
B.
The set of all strings over the alphabet {a, b} with matching parentheses.
C.
The set of all palindromes over the alphabet {a, b}.
D.
The set of all strings over the alphabet {a, b} that do not contain the substring 'aa'.
Show Answer & Explanation
Correct Answer: D
The language defined by strings that do not contain the substring 'aa' is regular, as it can be expressed by a finite automaton, whereas the other options require more complex structures.
Q4
Medium
Which of the following statements about finite automata is true?
A.
Finite automata can recognize all types of languages.
B.
Finite automata can only recognize regular languages.
C.
Finite automata require infinite memory to operate.
D.
Finite automata are equivalent to context-free grammars.
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Correct Answer: B
Finite automata are specifically designed to recognize regular languages, making option B correct. They cannot recognize context-free or more complex languages without additional computational power.
Q5
Medium
Which algorithm is used for determining whether a context-free grammar is ambiguous?
A.
CYK Algorithm
B.
Earley Parser
C.
LL(1) Parsing
D.
There is no algorithm for this.
Show Answer & Explanation
Correct Answer: D
Currently, there is no algorithm that can definitively determine whether a context-free grammar is ambiguous in all cases. Hence, option D is the correct answer.
Q6
Medium
Consider the language L generated by the grammar S -> aSb | ฮต. What type of language is L?
A.
Regular language
B.
Context-free language
C.
Context-sensitive language
D.
Recursively enumerable language
Show Answer & Explanation
Correct Answer: B
The grammar S -> aSb | ฮต generates strings where the number of 'a's and 'b's are balanced, which is a characteristic of context-free languages, making option B correct.
Q7
Medium
If a Turing machine has a tape that is infinite in both directions, what is the name given to this type of Turing machine?
A.
Deterministic Turing Machine
B.
Non-deterministic Turing Machine
C.
Two-way Infinite Turing Machine
D.
Multi-tape Turing Machine
Show Answer & Explanation
Correct Answer: C
A Turing machine that has an infinite tape in both directions is referred to as a Two-way Infinite Turing Machine, making option C correct.
Q8
Hard
Which of the following languages is not regular? Consider the language L = { a^n b^n | n โฅ 0 } where a's and b's are in equal numbers.
A.
L is regular.
B.
L can be represented by a context-free grammar.
C.
L can be recognized by a DFA.
D.
L is context-sensitive.
Show Answer & Explanation
Correct Answer: B
The language L = { a^n b^n | n โฅ 0 } is not regular because it cannot be recognized by a DFA. It requires a stack to keep track of the count of a's and b's, which is characteristic of context-free languages. Thus, B is correct as it confirms that L can be represented by a context-free grammar.
Q9
Hard
Which of the following languages is not regular?
A.
{ a^n b^n | n โฅ 0 }
B.
{ a^n b^m | n, m โฅ 0 }
C.
{ a^n | n โฅ 0 }
D.
{ a^i b^j c^k | i = j or j = k }
Show Answer & Explanation
Correct Answer: A
The language { a^n b^n | n โฅ 0 } is not regular because it requires matching numbers of 'a's and 'b's, which cannot be achieved with a finite automaton. Regular languages can be recognized by finite automata, which cannot count and thus cannot enforce such a constraint.
Q10
Hard
Given a context-free grammar G with productions: S -> AB, A -> aA | ฮต, B -> bB | b, which of the following strings can be generated by G?
A.
aaab
B.
aabb
C.
ab
D.
aaaabb
Show Answer & Explanation
Correct Answer: D
The grammar generates strings where 'A' produces 'a's followed by 'B' producing at least one 'b'. The pattern allows any number of 'a's followed by at least one 'b', thus 'aaaabb' fits this requirement with three 'a's followed by two 'b's.
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Theory of Computation โ A-Levels A-Level Computer Science Practice Questions Online
This page contains 149 practice MCQs for the chapter Theory of Computation in A-Levels A-Level Computer Science. The questions are organized by difficulty โ 46 easy, 74 medium, 29 hard โ so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.