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# Automata Theory and Formal Language

Delves into the study of abstract machines and their applications in understanding and processing formal languages, such as programming languages and compilers.

## grammar

The first mechanical calculator using gears for calculation developed in 1642.

• Pascaline

Context-free grammars are more expressive than finite automata; if a language L is by a finite automata then L can be by a context-free grammar.

• Accepted, Ignored

|-* is the closure of |-

• Transitive and Reflexive

A - B will contain elements in?

• B not in A
• A not in B
• Neither A nor B
• Both A and B

NFA means:

• Nondeterministic Finite Automaton
• Nondeterministic Final Automaton
• Nondifferentiable Final Automaton
• Nondifferential Finite Automaton

__ is a finite set of symbols called the alphabet.

• Σ

What is an undecidable problem?

• When a TM cannot make a decision on an instance of the problem
• When a CFG cannot make a decision on an instance of the problem
• When a PDA cannot make a decision on an instance of the problem
• When a RE cannot make a decision on an instance of the problem

Which of the following will not be accepted by the following DFA?

• ababaabaa

Connected graphs have components.

• True
• False

The power set of a given set does not contain the set itself.

• True
• False

A set of final state/states of Q (F⊆Q).

• F

The theory of formal languages finds its applicability extensively in the fields of Computer Science. gave a mathematical model of grammar in which is effective for writing computer languages.

• Noam Chomsky, 1956

An order rooted tree that graphically represents the semantic information a string derived from a context-free grammar.

• Derivation tree

The body of a production in CFG is composed of:

• a string of terminals only
• none of the choices given because a CFG production does not have a body
• a string of non-terminals only
• a string of terminals and non-terminals

A finite set of states

• Q

The unconsumed input

• w

Is a set of final state/states of Q (F ⊆ Q).

• F

It generate context-free languages. The productions must be in the form A → γ

• Type-2 grammars

Which among the following cannot be accepted by a regular grammar?

• L is a set of 0n1n

Unconsumed input.

• w

It refers to the measure of the number of times the tape moves when the machine is initialized for some input symbols and the space complexity is the number of cells of the tape written.

• Time Complexity

If A = {0,2) and B = {1,3), then Cartesian product is?

• none of the choices
• A x B not equal B x A
• A x B = B x A
• is not possible

A set of accepting states (F ∈ Q)

• F

A language is regular if and only if.

• Accepted by DFA

The initial stack top symbol (I ∈ S)

• I

JASON can generally be parsed by ______________.

• A C parser
• A CFG
• A Java parser
• A RE

A good regular expression of a person's name is ______________.

• None of the given choices
• [A-Z][a-z]+
• [A-Z][a-z]?
• [A-Z][a-z]*

For bottom-up parsing, a PDA has the following four types of transitions:

• Push the current input symbol into the stack., Replace the right‑hand side of a production at the top of the stack with its left‑hand side. , If the top of the stack element matches with the current input symbol, pop it. , If the input string is fully read and only if the start symbol 'S' remains in the stack, pop it and go to the final state .

What can not be said about CFLs?

• It is closed under ~
• It is closed under —
• All of the given choices
• It is closed under ∩

Checking whether there is a matching parenthesis in a computer code can be done by a ______________.

• regular expression
• automatically by a very patient debugger
• context-free language
• context-free grammar

Which among the following is the correct option for the given grammar? G->X111|G1,X->X0|00.

• {0a1b|a=2,b=3}

A grammar G is ambiguous if there is a word w Î L(G) having are least two different parse trees.

• TRUE

A good regular expression for any valid whole number is ______________.

• [0-9]*
• [0-9]*[0-9]*
• [0-9]+
• [0-9]+[0-9]*

S → aAb, aA →aaAb, A→ε

• P

If L is recursively enumerable then ________________.

• none of the choices given is correct
• L is also recursively enumerable
• L is definitely not recursively enumerable
• L may not be recursively enumerable

Any production rule in the form A → B where A, B ∈ Non-terminal is called.

• Unit Production

Which among the following is the option for the given grammar? G->X111|G1,X->X0|00

• {0a1b|a=2,b=3}

The first counting machine developed 5000 years ago in the Middle East.

• Abacus

A transition function: Q × (Σ∪{ε}) × S × Q × S*.

• δ

A stack symbols

• Σ

A set of strings of a's and b's of any length including the null string. So L= { ε, a, b, aa , ab , bb , ba, aaa.......}, the regular

• (a+b)*

|-* is the _____ closure of |-

• transitive and reflexive

Regular expression Φ* is equivalent to

• ϵ

A transition function: Q × (Σ∪{ε}) × S × Q × S*

• δ

Set of final or accepting states.

• F

The unconsumed input.

• w

The difference between DFA and NFA

• DFA is where you get your passport while NFA is where you get your cheap rice
• NFA can exist in only one state at a given time while DFA can exist in multiple states
• DFA can exist in only one state at a given time while NFA can exist in multiple states
• DFA is also an NFA

A' will contain how many elements from the original set A?

• 1
• all elements in A
• infinite
• 0

The string abe is accepted by this regular expression.

• a*b*c*a*d*
• a+b+c+d+e*
• a*b*c*a*d*e+
• a+b+c+d+

Noam Chomsky gave a mathematical model in which is effective for writing computer languages.

• 1956

A PDA is already in its accept state if:

• and only if it is both in the final state and the stack is empty
• none of the given choices
• it is either in the final state or the stack is empty
• it has no more input to process

A new symbol is added at the top.

• Push

Unconsumed input

• w

Starting state

• q0

A finite number of states.

• Q

A ⊂ B is read as ________________.

• A is less than B
• A is a subset of B
• B is a subset of A
• A is a proper subset of B

The relationship between recursive and recursively enumerable languages is ________________.

A set of strings of a's and b's of any length including the null string. So L= { ε, a, b, aa , ab , bb , ba, aaa.......}, the regular expression is.

• (a+b)*

The start symbol.

• S

The number of elements in the set for the Language L={xϵ(∑r) *|length if x is at most 2} and ∑={0,1} is

• 7

The entity which generate Language is termed as:

• Grammar

Every context free grammar can be transformed into an equvalent non deterministic push down automata.

• TRUE

An ε-NFA with a stack is also regarded as:

• A CFG
• A FSA
• A PDA
• A RE

It starts from the bottom with the string and comes to the start symbol using a parse tree.

• Bottom-Up Parser

A formal language is a set of strings, each string composed of symbols from a finite set called.

• Alphabet

Is a finite set of symbols called the alphabet.

• Σ

A DFA can remember a finite amount of information, but a can remember an infinite amount of information.

• PDA

If A →* ε, then we can say that:

• A is not generating
• A is not reachable
• A is nullable
• A is not generally useful

{Q, Σ, q0, F, δ, Q × Σ → Q} is…

• An NFA
• Either DFA or NFA
• There is no such tuple
• A DFA

The algebraic law of regular expression described by φE = φ = Eφ is _______________.

• Annihilator
• Associative
• Commutative
• Identity

A formal language is a set of strings, each string composed of symbols from a finite set called

• alphabet

Which of the following Set Operations produces the set that contains everything that is in Set A and in Set B?

• Complement
• union
• Intersection
• Set Difference

Global Positioning System (GPS) calculates latitude and longitude from satellite signals.

• True

Given the productions S → αXβ, X → a, ___________________.

• X is not reachable nor generating
• X is reachable but not generating
• X is useful
• X is not reachable but is generating

Which of the following ways can be done to simplify a CFG?

• Eliminate symbols that are not useful
• Eliminate the ε symbol
• Eliminate productions of the form A → B

Empty string

• Σ

In the Chomsky Hierarchy:

• Regular Language ⊂ Context-sensitive Language
• Regular Language ⊃ Context-sensitive Language
• Regular Language| • |Context-sensitive Language
• Regular Language = Context-sensitive Language

All relations are functions

• True
• False

A language accepted by Deterministic Push down automata is closed under which of the following?

• complement

A compact textual representation of a set of strings representing a language.

• Regular Expressions

Every set is a / an ________________ of itself.

• None of the choices
• Complement
• Proper Subset
• Improper Subset

The of a Turing machine depends on the current state of finite control and the tape symbol present in the input tape.

• Single Move

If we can successfully and correctly stimulate a TM with storage by two standard TMs, then ______________________.

• None of the choices
• we have already shown that the TM with storage is at least twice as powerful as one standard TM
• we have already shown that the two are equivalent
• we have already shown that one standard TM is half as powerful as the TM with storage

Computers are general purpose because they can perform many different tasks.

• TRUE

What kind of languages does a TM decide?

• regular expression
• context-sensitive
• recursively enumerable
• context-free

The __________ of a Turing machine depends on the current state of finite control and the tape symbol present in the input tape.

• single move

A pushdown automaton is a way to implement a context-free grammar in a similar way to design DFA for a regular grammar.

• TRUE

Which of the following is a not a part of 5-tuple finite automata?

• Output Alphabet

Context Free Languages is closed under intersection.

• False
• True

For a regular expression 'a', we can construct the following FA:

• TRUE

A pushdown automata can be regarded as:

• a ε-NFA with a stack
• a DFA with a FILO queue
• a NFA with a stack
• a DFA with FIFO queue

Which of the following statement is false in context of tree terminology?

• Root with no children is called a leaf

In ____ Allan M. Turing proposed the Turing machine as a model of "any possible computation".

• 1936

The intersection of sets A and B is expressed as _________________.

• A - B
• A / B
• A x B
• A ∩ B

Circuits in graphs are always simple paths.

• True
• False

The empty set is always a subset of any set.

• True
• False

In words, H → C means…

• Whenever H holds, C follows
• Whenever H does not follow, C does not follow either
• Whenever H is true, then it becomes C
• Whenever H, then it becomes C

Given the language L = {ε}, is L empty?

• none of the given choices
• Definitely, because ε is an empty symbol
• No, because the language has an empty symbol
• You can't say

If L1 and L2 are regular sets then intersection of these two will be.

• Regular

Production Rule: aAb->agb belongs to which of the following category?

• Context Sensitive Language

• Computer

Noam Chomsky gave a mathematical model in _______ which is effective for writing computer languages.

• 1956

The transition a Push down automaton makes it additionally dependent upon the _____.

• stack

The difference between regular expressions and finite automata is _____________.

• that automata are more program syntax-like while regular expression are more machine-like
• |regular expression| - |finite automata| = |Turing Machine| because you can only get the difference by computing for their respective lengths
• that regular expressions are more program syntax-like while automata are more machine-like
• {regular expression} - {finite automata} = { } because they are sets and they are equivalent

An algorithms to shampoo your hair.

• rinse, lather, repeat

The _____ of two sets A and B is the set containing those elements which are elements of A or elements of B.

• union

It process information in their efforts to eat, survive, and reproduce.

• Living Organisms

Empty set is a/an ________________.

• Infinite set
• Finite set
• Invalid set
• None of the choices

The cardinality of the union of two disjoint sets is less than the sum of the cardinality of the given sets.

• True
• False

A set on non-terminal symbols.

• S & A

One of the first programmable electronic computers in 1945.

• ENIAC

Identify the modeling recognition of the word "then"

• Start State

The string aaaabbbccaaad is accepted by this regular expression.

• a+b+c+d+
• a*b*c*a*d*e+
• a*b*c*a*d*
• a+b+c+d+e*

Set of all tape symbols

• Γ

For every CFL, G, there exists a PDA M such that L(G) = L(M) and vice versa

• TRUE

Are ambiguous grammar context free?

• TRUE

T generate recursively enumerable languages. The productions have no restrictions and phase structure grammar including all formal grammars.

• Type-0 grammars

A Finite Automaton with null moves (FA-ε) does transit not only after giving input from the alphabet set but also without any input symbol. This transition without input is called a.

• Null Move

NP-Hard problems are problems that are...

• Easy (they are called hard so that computer programmers can be paid more)
• intractable
• none of the choices
• hard

A sub-tree of a derivation tree/parse tree such that either all of its children are in the sub-tree or none of them are in the

• Partial Derivation Tree, Sub-Tree

A DPDA is a PDA in which

• No state p has two outgoing transitions

A symbol X is reachable _________________________.

• if S → aXβ
• if X →* w, for some w ∈ Σ
• if X → w, for some w ∈ Σ
• if S →* aXβ

The algebraic law of regular expression described by E + E = E is _____________.

• Annihilator
• Identity
• Idempotent

A general purpose, programmable, information processor with input and output.

• computer

All trees contain loops.

• True
• False

Which of the following statements is true about NPDA, DPDA, and RL?

• RL • DPDA • NPDA
• RL* • DPDA* • NPDA*
• RL ⊃ DPDA ⊃ NPDA
• RL ⊂ DPDA ⊂ NPDA

An initial state q0 ∈ Q

• q0

The stack content

• s

A set of accepting states (F ∈ Q).

• F

Which among the following is not a part of the Context free grammar tuple?

• End SymbolCorre

Computer science has roots in two fields :

• Mathematics

A DFA is represented by digraphs called.

• State Diagram

* Starts from tree leaves. It proceeds upward to the root which is the starting symbol S

• bottom-up approach

A conceptual design for a machine consisting of a Mill, Store, Printer, and Readers.

• Analytic Engine

According to the 5-tuple representation i.e. FA= {Q, ∑, δ, q, F} Statement 1: q ϵ Q'; Statement 2: FϵQ

• Statement 1 is false, Statement 2 is true

What can be said about undecidable problems?

• They are definitely recursive
• They are surely iterative
• They are not recursive
• They are not iterative

A good regular expression for any valid real number using engineering notation is ______________.

• [0-9]+[0-9]*[(E|e)[0-9]+]
• [0-9]*
• [0-9]+[0-9]*[(E|e|∈)[0-9]+]
• [0-9]+

A finite number of states

• Q

The complement of an infinite language is necessarily finite.

• FALSE

Is to be applied to show that certain languages are not regular. It should never be used to show a language is regular.

• Pumping Lemma

Labeled by a terminal symbol or ε.

• Leaves

Finite set of input alphabets.

• Σ

__ is a finite set of states.

• Q

Start symbol, S ∈ N

• S

Having the initial state as a final state, give the deterministic finite state automaton that accepts the regular expression.

• ((a.b)+c)*

What is a Universal TM?

• a TM that stimulates another TM
• A TM that can solve all problems
• A TM that can solve all undecidable problems
• a Universal TM does not exist

Terminal symbols

• a & b

A finite set of input symbols.

• Σ

A DFA can remember a finite amount of information, but a ____ can remember an infinite amount of information.

• PDA

Number of states require to accept string ends with 10.

• 3

Z2 uses electricity to convey letters and transmit information quickly in 1844.

• TRUE

Who is the father of modern computer?

• Charles Babbage

Transition function

• δ

Context-free grammars are more expressive than finite automata; if a language L is _____ by a finite automata then L can be _______ by a context-free grammar.

• accepted, generated

A Moore machine can be described by a tuple.

• 6

A Finite Automaton with null moves (FA-ε) does transit not only after giving input from the alphabet set but also without any input symbol. This transition without input is called a

• Null Move

The top symbol is read and removed.

• Pop

Labeled by a non-terminal symbol.

• Vertex

If a problem can be shown that it belongs to the class of recursively enumerable languages then ______________________.

• It may be solved by any TM
• It may be solved by a special RE
• It may be solved by a special TM
• It may be solved by any RE

An alphabet is any finite set of symbols.

• TRUE

The tape head is positioned at one of the tape cells for scanning the input symbol from the input tape and initially the tape head points at the left most cell of the input tape.

• TRUE

The initial stack top symbol (I ∈ S).

• I

A string is accepted by a, iff the DFA/NDFA starting at the initial state ends in an after reading the string.

• NDFA

How many sets belong to the power set of A = {a,b,c,d}?

• 4
• 8
• 7
• 16

A may or may not read an input symbol, but it has to read the top of the stack in every transition

• PDA

A regular expression consisting of a finite set of grammar rules is a quadruple.

• FALSE

“If H then ” is also the same as saying _______.

• “If H then C else do nothing”
• “If C then H”
• “If H then C else {}”
• “C if H”

* Starts with the starting symbol S. It goes down to tree leaves using productions.

• Top-Down Approach

__ is a set of final state/states of Q (F ⊆ Q).

• F

A _____ may or may not read an input symbol, but it has to read the top of the stack in every transition

• PDA

* Starts from tree leaves. It proceeds upward to the root which is the starting symbol S.

• Bottom-Up Approach

The minimum number of states required to recognize an octal number divisible by 3 are/is.

• 3

“Whenever H holds, C follows” can also be said as _______.

• H → ε and ε → C
• H → C
• C → H
• ε → H and C → ε

What is a grammar?

• How a sentence should be constructed to avoid syntax error
• "Them cowboys is dumb!" is an example of a wrong grammar
• "We ain't gonna make mistakes" is an example of correct grammar
• A device that enumerates the sentences of a language

The transition a Push down automaton makes it additionally dependent upon the

• Stack

If Σ2 is {00, 01, 10, 11}, then Σ =

• {0, 1}
• {false, true}
• {true, false}
• {F, T}

What is an ε-NFA?

• It is a DFA where all transitions are ε-transitions
• It is an NFA where all transitions are ε-transitions
• It is a DFA with at least one explicit ε-transition defined
• It is an NFA with at least one explicit ε-transition defined

A set of terminals where N ∩ T = NULL.

• T

The string "0000111" is accepted by _____________.

• the CFG S → 0S1 | A, A → A1 | ε
• the CFG S → 1S0 | A, A → A0 | ε
• the CFG S → 0S1 | A, A → 0A | ε
• none of the choices

An example string w of a language L characterized by equal number of As and Bs is _______________.

• BABAE
• ABABA
• ABBBAA
• ALIBABA

It is a unary operator on a set of symbols or strings, that gives the infinite set of all possible strings of all possible lengths.

• Σ *

The initial state (q0 ∈ Q)

• q0

Is the initial state from where any input is processed (q0 ∈ Q).

• q0

The following are phases of C++ Programs except

• Process

IT generate recursively enumerable languages. The productions have no restrictions and phase structure grammar including all formal grammars.

• Type-0 grammars

The stack contents

• s

If A = {3, 4, 6, 8} and

• { 4,6}

A DFA is defined ____________________.

• as Department of Finite Automaton
• by a 5-tuple which is {Q, Σ, q0, F, δ}
• by a 6-tuple which is {Q, Σ, q0, F, δ, Q × Σ → Q}
• as Department of Foreign Affairs

Recursive : TM that always halt = ________________ : TM that may or may not halt

• iterative
• recursively enumerable
• none of the choices given
• iteratively enumerable

Which of the following statements are for a concept called inherent ambiguity in CFL?

• Every CFG for L is ambiguous

The entity which generate Language is termed as regular languages.

• FALSE

For every pair of regular expressions R and S, the languages denoted by R(SR)* and (RS)*R are the same.

• TRUE

A may or may not read an input symbol, but it has to read the top of the stack in every transition.

• PDA

A of a derivation is a tree in which each internal node is labeled with a nonterminal.

• Parse Tree

A PDA accepts a string when, after reading the entire string, the PDA is in a final state.

• TRUE

Set of final or accepting states

• F

An initial state q0 ∈ Q.

• q0

In mathematical notation, the symbol → means...

• implication
• an element of
• not an element of
• assignment statement

Finite set of states

• Q

An automaton that produces outputs based on current input and/or previous state is called.

• Transducer

A finite set of states.

• Q

The union of sets A and B is expressed as?

• A U B
• A - B
• A / B
• A x B

__ is the transition function where δ: Q × Σ → Q.

• δ

The string acde is accepted by this regular expression.

• a+b+c+d+
• a+b+c+d+e*
• a*b*c*a*d*
• a*b*c*a*d*e+

In Allan M. Turing proposed the Turing machine as a model of "any possible computation".

• 1936

What concept did Alan Turing introduce?

• The concept of programs and programmabilities of problems
• The concept of decidability
• The concept of functions and relations
• The concept of undecidability

Is a finite set of states.

• Q

challenged the mathematical community to find an infallible, mechanical method for constructing and checking truth of mathematical statements.

• David Hilbert

Regular sets are closed under union,concatenation and kleene closure.

• TRUE

Who is the father of modern computer science?

• Noam Chomsky
• Alan Turing
• Steve Jobs
• Bill Gates

Context-free grammars are more expressive than finite automata; if a language L is by a finite automata then L can be blank by a context-free grammar.

• Accepted

A parsing that starts from the top with the start-symbol and derives a string using a parsetree.

• top-down parser

An English like abbreviations representing elementary computer operations.

• Assembly Language

Increasing accuracy, or precision.

• Minimizing False Positives

Let w = 100011, is w a member of a language of string with equal number of 0s and 1s?

• Yes, because the number of 1s is the same as the number of 0s, which is 3
• It is hard to ascertain because 100011 is 35 in decimal, which is an odd number
• No, because even if the symbols 1 and 0 are of the same number, they are not palindromic
• This is an NP-hard problem

Any set that represents the value of the Regular Expression is called a Property set.

• FALSE

Finite Automata all regular languages and only regular languages.

• Accept

Number of final state require to accept in minimal finite automata.

• None of the mentioned

A nested if-then statement is one of these:

• If w then x if y then z
• If w if x then y then z
• If w then if x then y else z
• All of the choices are examples of nestedness

______ is used to derive a string using the production rules of a grammar.

• Parsing

A DPDA is a PDA in which.

• No state p has two outgoing transitions

The commutativity property of set operations states that the union of any set with same set is the set itself.

• True
• False

For every CFL, G, there exists a PDA M such that L(G) = L(M) and vice versa.

• TRUE

What can be said about CFLs?

• It is closed under ~
• It is closed under ∩
• All of the given choices
• It is closed under •

“C if H” is also the same as saying _______.

• “If H then ”
• “If C then H”
• “If H then C else {}”
• “If H then C else do nothing”

The PDA has infinite memory and access in _____ order and the finite automata has ____ memory.

• LIFO, finite

Increasing coverage, or recall.

• Minimizing False Negatives

The CFG "S → (S) | SS | ε" accepts:

• the string "<<>><><<>>"
• the string "(((((((((())))))))))"
• the string "((()))(())(())"
• the string "{} { {} } [[]]"

Non-terminal symbols

• S & A

What are strings?

• A string is an infinite area of symbols chosen from Σ
• A string is a finite sequence of symbols chosen from Σ
• A string is a finite area of symbols chosen from Σ
• A string is an infinite sequence of symbols chosen from Σ

Some graphs contain cycles.

• True
• False

A PDA machine configuration (p, w, y) can be ly represented as ____________

• current state, unprocessed input, stack content

What is the final result after converting the following NFA-ε to NFA without Null move.

• What is the final result after converting the following NFA-ε to NFA without Null move.

are parameterized statement, they are true or false depending on the values of their parameters.

• predicates

The stack contents.

• s

How many rational and irrational numbers are possible between 0 and 1?

• 0
• Infinite
• Finite
• 1

Blank symbol

• Δ

Regular expression Φ* is equivalent to.

• ϵ

If R ={(1,1),(2,3),(4,5)}, then the Range of the function is?

• Range R {1,1,4,5}
• Range R {1,2,5}
• Range R = {2,3,4,5}
• Range R = {1,3,5}

Given that the language L = {ε}, is L empty?

• None of the given choices
• No, because the language has an empty symbol
• Definitely, because ε is an empty symbol
• This is a case of apples and oranges, you really can't compare!

An indirect way of building a CFG is to _____________

• build a regular expression and then construct a PDA from it, and then construct CDF from it
• You can only build a CFG directly
• build a PDA and then construct a CFG from it
• none of the given choices

A set of rules, P: N → (N U T)*, it does have any right context or left context.

• P

The recursive inference procedure determines that string w is in the language of the variable A, A being the starting variable.

• TRUE

What is a language?

• A way to communicate with other humans
• A collection of finite-length sentences that were constructed from a finite set of symbols
• A code that you use when writing a computer program
• English, Filipino and Valyrian are examples of a language

Is the transition function where δ: Q × Σ → Q.

• δ

Finite set of states.

• Q

Elimination of productions and symbols is called simplification of CFGs. Simplification essentially comprises of the following steps:

• Reduction of CFG

According to what concept is CFL a superset of RL?

• Chomsky Hierarchy
• Chomsky Normal Form
• Backus-Naur Form
• None of the given choices

A PDA machine configuration (p, w, y) can be correctly represented as ____________ .

• current state, unprocessed input, stack content

If A has m elements and B has n elements, then A x B has elements?

• m - n
• m + n
• 2n
• m x n

Labeled by the start symbol.

• Root Vertex

Noam Chomsky gave a mathematical model in ___ which is effective for writing computer languages.

• 1956

A PDA machine configuration (p, w, y) can be correctly represented as.

• Current state, Unprocessed input, Stack content

If we can successfully and ly stimulate a TM with storage by two standard TMs, then ______________________

• we have already shown that the two are equivalent

__ is the initial state from where any input is processed (q0 ∈ Q).

• q0

A transition function δ : Q × (Σ ∪ {ε}) → 2Q.

• δ

IT generate recursively enumerable languages. The productions have no restrictions and phase structure grammar including all formal grammars. They generate the languages that are recognized by a Turing machine.

• Type-0 grammars

Let the class of language accepted by finite state machine be L1 and the class of languages represented by regular expressions be L2 then.

• L1=L2

Is used to derive a string using the production rules of a grammar.

• Production

Language may be derived from other strings using the productions in a grammar.

• FALSE

There are 5 tuples in finite state machine.

• TRUE

What is automata theory?

• To answer the fundamental questions in computer science
• All of the choices
• To find out if a problem is computable
• Study of abstract computing devices or machines

The symbol used for the empty string is ____________.

• ε
• φ
• a blank
• ψ

Leibniz introduced binary notation of calculation.

• FALSE

The language L contains all strings over the alphabet {a,b} that begin with and end with

• a,b

Which of the following statements are correct for a concept called inherent ambiguity in CFL?

• Every CFG for L is ambiguous

If L1 and L2 are regular sets then intersection of these two will be

• Regular

A right-most derivation of a sentential form is one in which rules transforming the are always applied.

• Context

In _____ Allan M. Turing proposed the Turing machine as a model of "any possible computation".

• 1936

Any production rule in the form A → B where A, B ∈ Non-terminal is called unit production.

• Unit Production

It starts from the top with the start-symbol and derives a string using a parse tree.

• Top-Down Parser

Finite set of input alphabets

• Σ

If A = {5,6,7} and B = {7,8,9} then A U B is equal to:

• {5,6,7}
• None of the choices
• {7,8,9}
• {5,6,7,8,9}

Increasing accuracy, or precision

• Minimizing False Positives

A __________ of a derivation is a tree in which each internal node is labeled with a nonterminal.

• parse tree

For the given Regular expression, the minimum number of terminals required to derive its grammar (011+1)*(01)* is

• 3,6,2,5,4

The basic model of a Turing machine consists of _______ and _______ , in which the finite control has finite set of states and the transition between the states.

• finite control, input tape

Turing hypothesis believed that a function is said to be computable if and only if it can be computed by a Turing machine.

• FALSE

A 2-Tape Turing Machine ___________________.

• can infer that recursive languages are closed under union
• can show that recursive languages are closed under union
• has two outputs
• has two inputs

A set has n elements, then the number of elements in its power set is?

• 2n
• 2 ^ n
• None of the choices
• 2n-1

All functions are relations

• True
• False

If R = {(1,1),(2,3),(4,5)}, then domain of the function is?

• Dom R = {2,3,4,5}
• Dom R = {1,2,4}
• Dom R {1,3,5}
• Dom R {1,1,4,5}

What cannot be said about automata theory?

• None of the choices
• Automata theory is the study of abstract computing devices or machines
• Automata theory is used to find out if a problem is computable
• Automata theory answers the fundamental questions in computer science