For the given FSA which is/are the final state and start state

q0 start state , q1 and q2 final state

q3 start state , q1 and q2 final state

q1 start state , q3 and q2 final state

q1start state , q0 and q3 final state

An automaton with a finite number of states is called a________

finite automation , finite state machine

NDFA is an abbreviation of ________

Non-deterministic Finite Machine , Non-deterministic Finite Automaton,Non deterministic Finite Machine , Non deterministic Finite Automaton.

If P does not contain null string, then R = Q + RP has a unique solution that is R = QP* is a ________ Theorem

Aderns, Arden’s , arden’s , ardens

Introduction To Theory Of Computation! Hardest Trivia Quiz

1.

The DFA shown below accepts the set of all strings over {0, 1} that
- A.
  
  End with 00
- B.
  
  End with 0
- C.
  
  Begin either with 0 or 1
- D.
  
  Contain the substring 00
Correct Answer
A. End with 00

Explanation
The DFA shown in the question accepts the set of all strings over {0,1} that end with "00". This means that any string that is accepted by the DFA will have "00" as its last two characters. The DFA starts at the initial state and transitions through different states based on the input symbols (0 or 1). It reaches an accepting state only if the last two characters of the input string are "00". Therefore, the correct answer is "End with 00".

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2.

Which one of the following is true for this automaton?
- A.
  
  B*ab*ab*ab*
- B.
  
  B*a(a+b)*
- C.
  
  B*ab*ab*
- D.
  
  (a+b)*
Correct Answer
B. B*a(a+b)*

Explanation
The correct answer is b*a(a+b)*. This is because the automaton accepts strings that start with zero or more occurrences of 'b', followed by 'a', followed by zero or more occurrences of 'a' or 'b'. The regular expression b*a(a+b)* represents this pattern accurately.

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3.

For the above FSA the equivalent minimum state automaton has the following number of states
- A.
  
  1
- B.
  
  2
- C.
  
  3
- D.
  
  4
Correct Answer
B. 2

Explanation
The given FSA has two states, one initial state and one final state. This means that the FSA can recognize a language with at least one string. Therefore, the equivalent minimum state automaton for this FSA will also have two states.

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4.

The minimum number of states in any DFA accepting the regular language L = (111+11111)* is
- A.
  
  9
- B.
  
  8
- C.
  
  11
- D.
  
  5
Correct Answer
A. 9

Explanation
To accept the regular language L = (111+11111)*, we need to consider two cases: when the input starts with 111 and when the input starts with 11111. In the first case, after reading the initial 111, we can either have another 111 or end the string. In the second case, after reading the initial 11111, we can either have another 11111 or end the string. Therefore, we need two states for each case, totaling four states. Additionally, we need a start state and an accepting state for both cases, totaling six states. Finally, we need two more states to handle the transitions between the two cases. Therefore, the minimum number of states in the DFA is 9.

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5.

For the given FSA which is/are the final state and start state
- A.
  
  Q0 start state , q1 and q2 final state
- B.
  
  Q3 start state , q1 and q2 final state
- C.
  
  Q1 start state , q3 and q2 final state
- D.
  
  Q1start state , q0 and q3 final state
Correct Answer
A. Q0 start state , q1 and q2 final state

Explanation
The correct answer is q0 is the start state, and q1 and q2 are the final states.

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6.

An automaton with a finite number of states is called a________

Correct Answer
finite automation , finite state machine

Explanation
An automaton with a finite number of states is called a finite automation or a finite state machine. This means that the automaton has a limited number of possible states it can be in, and it transitions between these states based on the inputs it receives. The term "finite" in both "finite automation" and "finite state machine" emphasizes the fact that the number of states is finite and not infinite.

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7.

NDFA is an abbreviation of ________

Correct Answer
Non-deterministic Finite Machine , Non-deterministic Finite Automaton,Non deterministic Finite Machine , Non deterministic Finite Automaton.

Explanation
The correct answer is "Non-deterministic Finite Machine, Non-deterministic Finite Automaton". This is because NDFA stands for Non-deterministic Finite Automaton, which is a theoretical model of computation used in computer science and formal language theory. It is a type of finite state machine that can be in multiple states at the same time and can transition to different states based on input symbols. The terms "Non-deterministic Finite Machine" and "Non-deterministic Finite Automaton" are alternative ways of referring to the same concept.

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8.

Moore machine is an FSM whose outputs depend on only the present state.
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
A Moore machine is a type of Finite State Machine (FSM) where the outputs are determined solely by the current state of the machine. This means that the outputs do not depend on any input signals or transitions between states, but rather only on the present state. Therefore, the given statement that "Moore machine is an FSM whose outputs depend on only the present state" is true.

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9.

Moore machine is an FSM whose outputs depend on the present state and input.
- A.
  
  True
- B.
  
  False
Correct Answer
B. False

Explanation
The statement is incorrect because a Moore machine is a finite state machine (FSM) whose outputs depend only on the present state, not on the input. In a Moore machine, the outputs are associated with the states, while in a Mealy machine, the outputs are associated with the transitions. Therefore, the correct answer is False.

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10.

Type 0 Grammer is
- A.
  
  Unrestricted grammar
- B.
  
  Context-sensitive grammar
- C.
  
  Context-free grammar
- D.
  
  Regular grammar
Correct Answer
A. Unrestricted grammar

Explanation
Type 0 grammar, also known as unrestricted grammar, is the most powerful type of grammar in the Chomsky hierarchy. It has no restrictions on the production rules and can generate any language that can be recognized by a Turing machine. This means that it can generate any possible string of symbols, making it more expressive than context-sensitive, context-free, and regular grammars. Therefore, the correct answer is unrestricted grammar.

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11.

Type 1 Grammer is
- A.
  
  Context-sensitive grammar
- B.
  
  Unrestricted grammar
- C.
  
  Context-free grammar
- D.
  
  Regular grammar
Correct Answer
A. Context-sensitive grammar

Explanation
Type 1 grammar, also known as context-sensitive grammar, is a formal grammar that allows rules to have the form α→β, where α and β are strings of terminals and non-terminals, and the length of α is less than or equal to the length of β. This means that the grammar can rewrite any non-terminal symbol into a string of terminals and non-terminals, as long as the context surrounding the non-terminal allows it. Context-sensitive grammars are more powerful than context-free grammars, which have rules of the form A→β, and regular grammars, which have rules of the form A→a or A→aB.

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12.

Type 3 Grammer is
- A.
  
  Unrestricted grammar
- B.
  
  Context-sensitive grammar
- C.
  
  Context-free grammar
- D.
  
  Regular grammar
Correct Answer
D. Regular grammar

Explanation
A Type 3 Grammar, also known as a Regular Grammar, is the simplest form of grammar in the Chomsky hierarchy. It is characterized by rules of the form A -> aB or A -> a, where A and B are non-terminals and a is a terminal symbol. Regular grammars can generate regular languages, which are a subset of context-free languages. These grammars are less powerful than context-sensitive and context-free grammars, as they have fewer restrictions and can only generate languages that can be recognized by finite automata.

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13.

Type 2 Grammer is
- A.
  
  Context-free grammar
- B.
  
  Unrestricted grammar
- C.
  
  Context-sensitive grammar
- D.
  
  Regular grammar
Correct Answer
A. Context-free grammar

Explanation
Context-free grammar is a type of grammar in formal language theory. It is characterized by production rules that consist of a single nonterminal symbol on the left-hand side and a sequence of terminal and/or nonterminal symbols on the right-hand side. This means that the left-hand side can be replaced by the right-hand side in any context without any restrictions. Context-free grammars are widely used in computer science and linguistics to describe the syntax of programming languages and natural languages, respectively.

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14.

If P does not contain null string, then R = Q + RP has a unique solution that is R = QP* is a ________ Theorem

Correct Answer
Aderns, Arden’s , arden’s , ardens

Explanation
If the string P does not contain a null string, then the equation R = Q + RP has a unique solution, which is R = QP*. This is known as the Arden's Theorem.

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15.

The diagram represents which regular expression
- A.
  
  A
- B.
  
  A+b
- C.
  
  Ab
- D.
  
  A*
Correct Answer
A. A

Explanation
The diagram represents the regular expression "a". This is because the diagram shows a single node labeled "a", indicating that the regular expression matches the string "a" exactly.

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16.

The diagram represents which regular expression
- A.
  
  Ab
- B.
  
  A+b
- C.
  
  A
- D.
  
  (a+b)*
Correct Answer
A. Ab

Explanation
The diagram represents the regular expression "ab" because it shows two characters, "a" and "b", connected by an arrow. This indicates that the regular expression matches the sequence "ab" exactly.

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