Theory of Computation Quiz

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Questions and Answers

For the expression E(E) where and brackets are the operation, discover the total number of nodes in the respective parse tree are:

7 (correct)

If w belongs to L(G), for some CFG, then w has a parse tree, which tells us the ________ structure of w.

syntactic

lexical

all of the mentioned (correct)

semantic

Choose the correct option: Statement: Unambiguity is the ideal structure of a language.

partially true

false (correct)

Can’t be said

Choose which of the following are always unambiguous?

None of the mentioned Signup and view all the answers

Discover among the following is the correct grammar for the given language L={x∈{0,1}*|number of zeroes in x ≠ number of one’s in x}

S-> 0|0S|1SS|SS1|S1S Signup and view all the answers

Define what do we call the process of repeating y 0 or more times before checking that they still belong to the language L or not?

Pumping Signup and view all the answers

Which among the following gives a positive result to the pumping lemma restrictions and requirements?{aibici|i>=0}

{aibici|i>=0} Signup and view all the answers

Using pumping lemma, which of the following cannot be proved as 'not a CFL'?

{ss|s∈{a,b}*} Signup and view all the answers

The class of recursively enumerable language is defined as:

RE Signup and view all the answers

Define the pumping length of a string of length x?

x+1 Signup and view all the answers

Which of the following does not obey the pumping lemma for context-free languages?

Finite languages Signup and view all the answers

Which of the following is true for two stack Turing machines?

One read-only input & two storage tapes Signup and view all the answers

A deterministic Turing machine is defined as:

Unambiguous Turing machine Signup and view all the answers

Choose the number of states required to accept a string that ends with 101.

2 Signup and view all the answers

Given L = {ab, aa, baa}, predict which of the following strings are in L*?

1, 2 and 3 Signup and view all the answers

Can a DFA recognize a palindrome number?

Yes Signup and view all the answers

How many languages are over the alphabet R?

Uncountable infinite Signup and view all the answers

The transition function in a finite automaton is typically represented as:

δ: Q × Σ → Q Signup and view all the answers

Which of the following options is correct?

Statement 1 is true and Statement 2 is false Signup and view all the answers

A regular language over an alphabet Σ is one that cannot be observed from the basic languages using which of the operation?

All of the mentioned Signup and view all the answers

Choose the number of final states required to accept Φ in a minimal finite automaton.

1 Signup and view all the answers

A DFA cannot be represented in which of the following format?

C code Signup and view all the answers

The minimum number of states required to recognize an octal number divisible by 3 can be computed as

1 Signup and view all the answers

Select the statement that is true about the closure of regular languages under intersection:

Regular languages are closed under intersection. Signup and view all the answers

Select the operation that is closed under regular languages:

All of the above Signup and view all the answers

Identify the property that allows regular languages to be recognized by finite automata:

Closure under union Signup and view all the answers

In a Turing machine, what is the significance of the transition function being partial?

It defines transitions only for specific states and symbols. Signup and view all the answers

Recognize the component of a Turing machine that is responsible for determining the next action based on the current state and symbol read:

Transition function Signup and view all the answers

Select the purpose of the input alphabet in a Turing machine:

To define the set of symbols allowed on the tape. Signup and view all the answers

Select the significance of the halting state in a Turing machine:

It marks the end of the computation. Signup and view all the answers

Identify from the following which is NOT a characteristic of a Turing machine:

Finite computation time Signup and view all the answers

Select the following statement that is true regarding the Pumping Lemma for Regular Languages:

It can prove that a language is regular, but not necessarily that a language is not regular. Signup and view all the answers

Select the correct interpretation of the Pumping Lemma for Regular Languages:

It states that every sufficiently long string in the language can be split into parts such that certain properties hold. Signup and view all the answers

Select from the following statements the one that is true regarding the Pumping Lemma for Context-Free Languages:

It can prove that a language is context-free, but not necessarily that a language is not context-free. Signup and view all the answers

Select from the following, the Pumping Lemma for Context-Free Languages can be used to prove:

The existence of a context-free grammar generating the language. Signup and view all the answers

Choose the main purpose of a context-free grammar:

To describe the structure of context-free languages Signup and view all the answers

Choose Which of the following is not a component of a context-free grammar:

Lexemes Signup and view all the answers

Choose in a context-free grammar, a production rule typically consists of:

Both terminal and non-terminal symbols Signup and view all the answers

Choose which of the following is true about context-free grammars:

They can generate some regular languages but not all. Signup and view all the answers

Choose the role of non-terminal symbols in a context-free grammar:

They represent variables that can be replaced by other symbols. Signup and view all the answers

Select the primary purpose of a pushdown automaton (PDA):

To recognize context-free languages Signup and view all the answers

Select the automata equivalent to a pushdown automaton:

Non-deterministic finite automaton Signup and view all the answers

Select the languages that can be recognized by a pushdown automaton:

All context-free languages Signup and view all the answers

Select the significance of the initial stack symbol in a pushdown automaton:

It represents the bottom of the stack. Signup and view all the answers

Choose which component makes a pushdown automaton more powerful than a finite automaton:

Stack Signup and view all the answers

Select the following that is not a limitation of pushdown automata:

They cannot recognize non-context-sensitive languages. Signup and view all the answers

Study Notes

Deterministic Finite Automaton (DFA)

A DFA is a type of finite automaton that can be in one of a finite number of states.
It can change state based on the current state and the input symbol.
The transition function in a DFA is typically represented as δ: Q × Σ → Q.

Nondeterministic Finite Automaton (NFA)

An NFA is a type of finite automaton that can be in multiple states simultaneously.
The transition function in an NFA is typically represented as δ: Q × Σ → P(Q).
An NFA can be converted to a DFA.

Regular Expressions

Regular expressions are a way to describe a set of strings using a pattern.
They are used to define a regular language.
Regular expressions are closed under union, intersection, and complementation.

Context-Free Grammar

A context-free grammar is a set of production rules that define a language.
It is a way to generate a set of strings using a set of rules.
Context-free grammars are used to define a context-free language.

Pushdown Automaton (PDA)

A PDA is a type of automaton that uses a stack to store and retrieve symbols.
It is used to recognize a context-free language.
The transition function in a PDA is dependent on the current state, the input symbol, and the top of the stack.

Deterministic Pushdown Automaton (DPDA)

A DPDA is a type of PDA that is deterministic.
It is used to recognize a deterministic context-free language.
A DPDA is more powerful than a DFA but less powerful than a NFA.

Language Theory

A language is a set of strings over a given alphabet.
A language can be regular, context-free, or recursively enumerable.
Regular languages are closed under union, intersection, and complementation.

Automata and Language

An automaton is a machine that can recognize a language.
A language can be recognized by a DFA, NFA, PDA, or DPDA.
The choice of automaton depends on the type of language being recognized.

Parsing and Derivation

Parsing is the process of analyzing a string to determine its structure.
Derivation is the process of generating a string from a set of production rules.
Parsing and derivation are used to determine the syntax of a string.

Inherent Ambiguity

Inherent ambiguity is a property of a context-free language.
It means that there is no unambiguous grammar for the language.
Inherent ambiguity is a fundamental property of some languages.

Grammar and Language

A grammar is a set of production rules that define a language.
A language is a set of strings over a given alphabet.
A grammar can be ambiguous or unambiguous.

Parse Trees

A parse tree is a tree representation of the syntax of a string.
It is used to show the structure of a string.
Parse trees are used in parsing and derivation.

Acceptance and Recognition

Acceptance is the process of determining whether a string belongs to a language.
Recognition is the process of determining whether a string can be generated by a grammar.
Acceptance and recognition are used to determine the syntax of a string.

Closure Properties

Closure properties are properties of a language that are preserved under certain operations.
Regular languages are closed under union, intersection, and complementation.
Context-free languages are closed under union and concatenation.

Pumping Lemma

The pumping lemma is a technique used to prove that a language is not regular.
It is used to show that a language is not regular by pumping a string in the language.
The pumping lemma is a fundamental tool in language theory.

Arden's Theorem

Arden's theorem is a technique used to prove that a regular language is not context-free.
It is used to show that a regular language is not context-free by constructing a PDA.
Arden's theorem is a fundamental tool in language theory.### Formal Language Theory
Greibach Normal Form: A context-free grammar is in Greibach Normal Form (GNF) if all production rules are of the form A -> aB1 … Bn or A -> ɛ, where A is a non-terminal, a is a terminal, B1, …, Bn are non-terminals, and ɛ is the empty string.

Context-Free Languages

A context-free language is a language that can be described by a context-free grammar.
A context-free grammar is a 4-tuple (V, T, P, S), where V is the set of non-terminal symbols, T is the set of terminal symbols, P is the set of production rules, and S is the start symbol.

Chomsky Hierarchy

The Chomsky hierarchy is a classification of formal languages based on the type of grammar that can be used to generate them.
The hierarchy consists of four levels: Type-3 (Regular Languages), Type-2 (Context-Free Languages), Type-1 (Context-Sensitive Languages), and Type-0 (Recursively Enumerable Languages).

Turing Machines

A Turing machine is a mathematical model for computation that consists of a tape of infinite length divided into cells, each of which can hold a symbol from a finite alphabet.
The Turing machine has a read/write head that can move along the tape and perform operations based on the current state and symbol read.

Regular Expressions

A regular expression is a string that describes a set of strings using a set of rules and patterns.
Regular expressions are used to match patterns in strings and can be used to define regular languages.

Automata Theory

An automaton is a mathematical model for computation that consists of a set of states and a set of transitions between states.
There are several types of automata, including Deterministic Finite Automata (DFAs), Non-Deterministic Finite Automata (NFAs), and Pushdown Automata (PDAs).

Pumping Lemma

The Pumping Lemma is a lemma in formal language theory that provides a way to prove that a language is not regular.
The Pumping Lemma states that if a language is regular, then there exists a pumping length p such that any string w of length at least p can be divided into three parts x, y, z such that |y| > 0 and xy^i z is in the language for all i >= 0.

Context-Free Grammar

A context-free grammar is a 4-tuple (V, T, P, S), where V is the set of non-terminal symbols, T is the set of terminal symbols, P is the set of production rules, and S is the start symbol.
A context-free grammar can be used to generate a context-free language.

Recursively Enumerable Languages

A recursively enumerable language is a language that can be generated by a Turing machine.
Recursively enumerable languages are a class of languages that are more powerful than regular languages and context-free languages.

Other Concepts

Ambiguity: A property of a grammar that means that there is more than one way to parse a string.
Turing Completeness: A property of a system that means that it can simulate a Turing machine.
Pumping Length: A parameter used in the Pumping Lemma to define the length of the pumped string.
Kleene Star: A unary operation that takes a language as input and returns a new language that consists of all possible concatenations of the input language.### Context-Free Grammars and Pushdown Automata
Non-terminal symbols in a context-free grammar represent variables that can be replaced by other symbols.
The primary purpose of a pushdown automaton (PDA) is to recognize context-free languages.

Equivalence of Automata

A pushdown automaton is equivalent to a non-deterministic finite automaton.
A pushdown automaton is not equivalent to a finite automaton, deterministic finite automaton, or Turing machine.

Language Recognition

A pushdown automaton can recognize all context-free languages.
A pushdown automaton cannot recognize all regular languages, context-sensitive languages, or recursively enumerable languages.

Pushdown Automaton Components

The initial stack symbol in a pushdown automaton represents the bottom of the stack.
The stack is the component that makes a pushdown automaton more powerful than a finite automaton.

Limitations of Pushdown Automata

A limitation of pushdown automata is that they cannot recognize non-context-free languages.
A limitation of pushdown automata is that they require more memory compared to finite automata.
Pushdown automata can recognize non-regular languages and non-context-sensitive languages.

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Description

This quiz tests your understanding of various concepts in the Theory of Computation, including finite automata, regular languages, and palindrome recognition. It covers key concepts and their applications in computer science.

Theory of Computation Quiz

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Questions and Answers

For the expression E*(E) where * and brackets are the operation, discover the total number of nodes in the respective parse tree are:

If w belongs to L(G), for some CFG, then w has a parse tree, which tells us the ________ structure of w.

Choose the correct option: Statement: Unambiguity is the ideal structure of a language.

Choose which of the following are always unambiguous?

Discover among the following is the correct grammar for the given language L={x∈{0,1}*|number of zeroes in x ≠ number of one’s in x}

Define what do we call the process of repeating y 0 or more times before checking that they still belong to the language L or not?

Which among the following gives a positive result to the pumping lemma restrictions and requirements?{aibici|i>=0}

Using pumping lemma, which of the following cannot be proved as 'not a CFL'?

The class of recursively enumerable language is defined as:

Define the pumping length of a string of length x?

Which of the following does not obey the pumping lemma for context-free languages?

Which of the following is true for two stack Turing machines?

A deterministic Turing machine is defined as:

Choose the number of states required to accept a string that ends with 101.

Given L = {ab, aa, baa}, predict which of the following strings are in L*?

Can a DFA recognize a palindrome number?

How many languages are over the alphabet R?

The transition function in a finite automaton is typically represented as:

Which of the following options is correct?

A regular language over an alphabet Σ is one that cannot be observed from the basic languages using which of the operation?

Choose the number of final states required to accept Φ in a minimal finite automaton.

A DFA cannot be represented in which of the following format?

The minimum number of states required to recognize an octal number divisible by 3 can be computed as

Select the statement that is true about the closure of regular languages under intersection:

Select the operation that is closed under regular languages:

Identify the property that allows regular languages to be recognized by finite automata:

In a Turing machine, what is the significance of the transition function being partial?

Recognize the component of a Turing machine that is responsible for determining the next action based on the current state and symbol read:

Select the purpose of the input alphabet in a Turing machine:

Select the significance of the halting state in a Turing machine:

Identify from the following which is NOT a characteristic of a Turing machine:

Select the following statement that is true regarding the Pumping Lemma for Regular Languages:

Select the correct interpretation of the Pumping Lemma for Regular Languages:

Select from the following statements the one that is true regarding the Pumping Lemma for Context-Free Languages:

Select from the following, the Pumping Lemma for Context-Free Languages can be used to prove:

Choose the main purpose of a context-free grammar:

Choose Which of the following is not a component of a context-free grammar:

Choose in a context-free grammar, a production rule typically consists of:

Choose which of the following is true about context-free grammars:

Choose the role of non-terminal symbols in a context-free grammar:

Select the primary purpose of a pushdown automaton (PDA):

Select the automata equivalent to a pushdown automaton:

Select the languages that can be recognized by a pushdown automaton:

Select the significance of the initial stack symbol in a pushdown automaton:

Choose which component makes a pushdown automaton more powerful than a finite automaton:

Select the following that is not a limitation of pushdown automata:

Study Notes

Deterministic Finite Automaton (DFA)

Nondeterministic Finite Automaton (NFA)

Regular Expressions

Context-Free Grammar

Pushdown Automaton (PDA)

Deterministic Pushdown Automaton (DPDA)

Language Theory

Automata and Language

Parsing and Derivation

Inherent Ambiguity

Grammar and Language

Parse Trees

Acceptance and Recognition

Closure Properties

Pumping Lemma

Arden's Theorem

Context-Free Languages

Chomsky Hierarchy

Turing Machines

Regular Expressions

Automata Theory

Pumping Lemma

Context-Free Grammar

Recursively Enumerable Languages

Other Concepts

Equivalence of Automata

Language Recognition

Pushdown Automaton Components

Limitations of Pushdown Automata

For the expression E(E) where and brackets are the operation, discover the total number of nodes in the respective parse tree are: