i) Analyze about the "Bad Case for the Subset Construction" during DFA to NFA conversion. ii) Describe the "pigeonhole principle" regarding the subset construction.

Convert DFA's to regular expressions by eliminating states (using an arbitrary example).

Convert the NFA from Question 5(a), to DFA. Question 5(a): Build an NFA for the following language: L = {w | w ends in 101}

Build in ε-NFA for the following language: L = {w | w is empty, or if non-empty will end in 01}

What is Automata Theory? Describe the applications of Finite Automata.

Describe the necessities of explicit ε-transitions in finite automata.

Explain the work of lexical analyzer with an on/off switch.

i) Prove the theorem "a mod b = b mod a, if and only if a = b. ii) By method of induction, proof the theorem "if x ≥ 4 then 2* ≥ x².

i) Analyze about the "Bad Case for the Subset Construction" during DFA to NFA conversion. ii) Describe the "pigeonhole principle" regarding the subset construction.

Build in ε-NFA for the following language: L = {w | w is empty, or if non-empty will end in 01}

Convert the NFA from Question 5(a), to DFA. Question 5(a): Build an NFA for the following language: L = {w | w ends in 101}

Convert ε-NFA to DFA based on Question 6(b) Question 6(b): Build an e-NFA for the following language: L= ={w|w is empty, or if non-empty will end in 11}

Make an NFA: Strings where the first symbol is present somewhere later on at least once.

i) Analyze about the "Bad Case for the Subset Construction" during DFA to NFA conversion. ii) Describe the "pigeonhole principle" regarding the subset construction.

Build an NFA for the following language: L = {w | w ends in 101}

Construct a NFA for the following: Strings where the first symbol is present somewhere later on at least once.

i) Analyze about the "Bad Case for the Subset Construction" during DFA to NFA conversion. ii) Describe the "pigeonhole principle" regarding the subset construction.

Describe the basic functionalities of pumping lemma.

Use the pumping lemma to prove that the language is not context free.

What is regular expression? Describe the operations of regular expressions.

Convert DFA's to regular expressions by eliminating states (using an arbitrary example).

Convert the following DFA to an equivalent regular Expression.

i) Prove that if we add a finite set of strings to a regular language, the result is a regular language. ii) A language L is accepted by some e-NFA if and only if L is accepted by some DFA.

What is Automata Theory? Describe the applications of Finite Automata.

Construct a DFA for the following language L={w | w is a binary string that has been even number of 1s and even numbers of 0s}

Explain the work of lexical analyzer with an on/off switch.

Give pushdown automata that recognize the following languages: (a) A = { w∈ {0, 1} * | w contains at least three 1s } (b) B = { w∈ {0, 1} * | w = w^R and the length of w is odd }

Construct a NFA for the following: Strings where the first symbol is present somewhere later on at least once.

Analyze the terms: Theorems, Lemmas and Corollaries.

Use the pumping lemma to prove that the language A is not context free.

Write Bad case where states(DFA)>>states(NFA) describe with pigeonhole principle

Construct a NFA for the following: Strings where the first symbol is present somewhere later on at least once.

Prove that if we add a finite set of strings to a regular language, the result is a regular language.

Build an NFA for the following language: L = { w | w ends in 101}

Convert the NFA from Question 5, to DFA. Question-5: Build an NFA for the following language: L = { w | w ends in 101}

Build an ε-NFA for the following language: L = {w | w is empty, or if non-empty will end in 11}

Convert ε-NFA to DFA based on Question 7. Question-7: Build an ε-NFA for the following language: L = {w | w is empty, or if non-empty will end in 11}

Describe about Chomsky hierarchy (occasionally referred to as the Chomsky-Schützenberger hierarchy). This hierarchy of grammars was described by Noam Chomsky in 1956 It is also named after Marcel-Paul Schützenberger, who played a crucial role in the development of the theory of formal languages. Chomsky Hierarchy represents the class of languages that are accepted by the different machine. The category of language in Chomsky's Hierarchy is as given below: 1. Type 0 known as Unrestricted Grammar or Recursively enumerable grammar. 2. Type 1 known as Context Sensitive Grammar. 3. Type 2 known as Context Free Grammar. 4. Type 3 Regular Grammar Describe all type.

Analyze the terms: Theorems, Lemmas and Corollaries.

Let, Σ = {0, 1} Construct a DFA for the following language: L = {w | w is a binary string that has even number of 1s and even number of 0s}

Build an NFA for the following language: L = { w | w ends in 01}

Why explicit ε-transitions in finite automata is important?

Describe the relation between Regular Expressions (RE) and Finite Automata. Show with figure that they are interchangeable.

Construct a context-free grammar for the following DFA:

Construct a context-free grammar for the following DFA:

Why explicit ε-transitions in finite automata is important?

Differentiate between Finite State and Turing Machines.

Let, ∑ = {0, 1}. Construct a DFA for the following language: L = {w | w is a binary string that has even number of 1s and even number of 0s}

Prove that the following language is either regular or not. A= { w w w | w ∈ {a, b} * }

Describe the relation between Regular Expressions (RE) and Finite Automata. Show with figure that they are interchangeable.

Find DFA's which accepts the following languages: (i) Strings over {a, b} ending in aa. (ii) String over {a, b} containing three consecutive a's (that is, contains the substring aaa) (iii) All strings over {a, b} where each string of length 5 contains at least two a's.

Describe Deductive proof. Prove that, if x is the sum of the squares of four positive integers, then

Regarding conversion of DFA from NFA, a bad case for the Subset Construction is occurred. Analyze this using the Pigeonhole Principle.

Use the pumping lemma to prove that the language A is not context-free.

Summarize the principal closure properties for regular languages.

Construct a context-free grammar for the following DFA:

Elaborate the three operations on languages that the operations of regular expression represent.

Prove that the following are not regular languages: (i) The set of strings of 0's and 1's beginning with 1, such that when interpreted as an integer, that integer is a prime. (ii) The set of strings of the form 0 i1 j such that the greatest common divisor of i and j is 1.

State formal definition of a finite automata. Give an example.

Let, ∑ = {0, 1} Develop a DFA and make a transition table for the following language: L = {w | w is a bit string which contains the substring 11}

What is Automata Theory? Describe the applications of Finite Automata.

Give pushdown automata that recognize the following languages: (a) A = { w ∈ {0, 1} * | w contains at least three 1s } (b) B = { w ∈ {0, 1} * | w = w^R and the length of w is odd }

Construct a Turing Machine that accepts the language of palindromes over {a,b}. Also specify the moves to trace the strings abaa, abba,aabaa.

Construct a NFA for the following: Strings where the first symbol is present somewhere later on at least once.

Build an ε-NFA for the following language: L = {w | w is empty, or if non-empty will end in 01}

Show that the grammar ({S}, {a, b}, R, S) with rules R = S -> aS | aSbS | € is ambiguous.

In compiler, ambiguous testing is a very important matter. Show that the grammar ({S}, {a, b}, R, S) with rules R = S -> aS | aSbS | € is ambiguous.

Build an ε-NFA for the following language: L= {w | w is empty, or if non-empty will end in 01}

Give pushdown automata that recognize the following languages: (a) A = {w ∈ {0, 1} * | w contains at least three 1s } (b) B = {we {0, 1} * | w = w^R and the length of w is odd }

Construct a NFA for the following: Strings where the first symbol is present somewhere later on at least once.

Prove that if we add a finite set of strings to a regular language, the result is a regular language.

Consider the regular expression (a(cd)*b)*. (i) Find a string over {a, b, c, d}^4 which matches the expression. (ii) Find a string over {a, b, c, d}^4 which does not match the expression.

Construct a DFA for the following language: Let, Σ = {0, 1}, L = {w|w is a binary string that has even number of 1s and even number of 0s}.

Build an e-NFA for the following language: L= ={w|w is empty, or if non-empty will end in 11}

Prove that if L=L(A) for some DFA A, then there is a regular expression R such that L=L(R).

Briefly describe, how we can eliminate ε- transitions?

Prove that every language accepted by a multitap TM is recursively enumerable.

Give a regular expression for the following language B over the alphabet {a, b}. B={w | w does not contain the substring aaa}.

Show that the grammar ({S}, {a, b), R, S) with rules R = S-->aS | aSbS | € is ambiguous.

Prove that if we add a finite set of strings to a regular language, the result is a regular language.

State the properties of a parse tree. Construct a parse tree for the following string: S --> S S + | S S * l a

Consider the regular expression (a(cd)*b)* (i) Find a string over {a, b, c, d}^4 which matches the expression. (ii) Find a string over {a, b, c, d}4 which does not match the expression.

Let, ∑ = {0, 1} A DFA for the following language: L = {w | w is a binary string that has even number of 1s and even number of 0s} Let the string 110101. Calculate the extension of transition to paths.

A containment hierarchy of classes of formal languages has been classified as The Chomsky Hierarchy. Describe with suitable figure(s).

Use the pumping lemma to prove that the language A is not context free.

What is meant by a halting problem in a Turing Machine? Explain with an example.

Convert ε-NFA to DFA based on Question 6(b) Question - 6(b): Build an ε-NFA for the following language: L = {w | w is empty, or if non-empty will end in 01}

Use the pumping lemma to prove that the language is not context free.

The Chomsky Hierarchy is a containment hierarchy of classes of formal languages. Describe with suitable figure(s).

Let x be a real number. Then prove that, [x] = [x] if and only if x is an integer.

Prove that if L is a regular language over the following alphabet, then it is also a regular language.

Prove that every language defined by a regular expression is also defined by a finite automata.

Build an e-NFA for the following language: [The question is incomplete]

For the keyword recognizer occurrences of the words "include", Make a transition diagram.

Analyze the terms: Theorems, Lemmas and Corollaries.

Define- i) Associativity ii) Identity and iii) Distributive Law

Make a NFA: Strings where the first symbol is present somewhere later on at least once.