Introduction To Theory Of Computation! Hardest Trivia Quiz

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| By Catherine Halcomb
Catherine Halcomb
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| Attempts: 203 | Questions: 18
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1. For the given FSA which is/are the final state and start state

Explanation

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

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Introduction To Theory Of Computation! Hardest Trivia Quiz - Quiz

Dive into the challenging world of automata with the 'Introduction to Theory Of Computation! Hardest Trivia Quiz'. Test your knowledge on DFAs, state minimization, and regular languages, focusing on string patterns and finite automata structures.

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2. Moore machine is an FSM whose outputs depend on only the present state.

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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3. Type 3 Grammer is

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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4. Type 0 Grammer is

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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5. Match the following
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6. Type 1 Grammer is

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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7. Moore machine is an FSM whose outputs depend on the present state and input.

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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8. Type 2 Grammer is

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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9. Which one of the following is true for this automaton?

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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10. The diagram represents which regular expression

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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11. Match the following
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12. The diagram represents which regular expression

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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13. For the above FSA the equivalent minimum state automaton has the following number of states

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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14. The DFA shown below accepts the set of all strings over {0, 1} that

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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15. An automaton with a finite number of states is called a_____

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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16. The minimum number of states in any DFA accepting the regular language L = (111+11111)* is 

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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17. NDFA is an abbreviation of _____

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

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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For the given FSA which is/are the final state and start state
Moore machine is an FSM whose outputs depend on only the present...
Type 3 Grammer is
Type 0 Grammer is
Match the following
Type 1 Grammer is
Moore machine is an FSM whose outputs depend on the present state and...
Type 2 Grammer is
Which one of the following is true for this automaton?
The diagram represents which regular expression
Match the following
The diagram represents which regular expression
For the above FSA the equivalent minimum state automaton has the...
The DFA shown below accepts the set of all strings over {0, 1} that
An automaton with a finite number of states is called a_____
The minimum number of states in any DFA accepting the regular language...
NDFA is an abbreviation of _____
If P does not contain null string, then R = Q + RP has a unique...
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