Automata Theory and Formal Language

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

• Analytic Engine

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

• Regular Expressions

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

Is a finite set of states.

• Q

Set of all tape symbols

• Γ

Finite set of states.

• Q

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

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

• Living Organisms

A DPDA is a PDA in which.

• No state p has two outgoing transitions

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

• TRUE

Labeled by the start symbol.

• Root Vertex

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

• A CFG
• A FSA
• A PDA
• A RE

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

• Type-0 grammars

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

• Alphabet

Identify the modeling recognition of the word "then"

• Start State

The stack contents.

• s

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

• predicates

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

• q0

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

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

• F

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

The entity which generate Language is termed as regular languages.

• FALSE

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

• None of the mentioned

What can be said about undecidable problems?

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

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

• 1936

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

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

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

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

• TRUE

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]+

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

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

• True
• False

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

• Top-Down Approach

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

• Annihilator
• Identity
• Additive idempotent
• Idempotent

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

• δ

Leibniz introduced binary notation of calculation.

• FALSE

A Moore machine can be described by a tuple.

• 6

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

• Context

A new symbol is added at the top.

• Push

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

• PDA

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

• stack

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

• Current state, Unprocessed input, Stack content

Who is the father of modern computer?

• Charles Babbage

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

• FALSE

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

Blank symbol

• Δ

__ is a finite set of symbols called the alphabet.

• Σ

Unconsumed input

• w

Transition function

• δ

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

Start symbol, S ∈ N

• S

The initial stack top symbol (I ∈ S).

• I

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

• TRUE

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

• End SymbolCorre

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}

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

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

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 .

A DPDA is a PDA in which

• No state p has two outgoing transitions

Unconsumed input.

• w

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

• ababaabaa

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

• TRUE

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

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

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

• 3

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

• Reduction of CFG

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

• FALSE

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

• F

Circuits in graphs are always simple paths.

• True
• False

Labeled by a non-terminal symbol.

• Vertex

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

• complement

The initial state (q0 ∈ Q)

• q0

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

• union

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

A finite set of input symbols.

• Σ

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

• Stack

Connected graphs have components.

• True
• False

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

• PDA

An alphabet is any finite set of symbols.

• TRUE

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

• current state, unprocessed input, stack content

If A →* ε, then we can say that:

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

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

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

• TRUE

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

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

• Every CFG for L is ambiguous

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

The union of sets A and B is expressed as?

• A U B
• A - B
• A / B
• A x B

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

• a,b

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

• TRUE

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

• TRUE

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

• Annihilator
• Associative
• Commutative
• Identity

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

An algorithms to shampoo your hair.

• rinse, lather, repeat

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

• Unit Production

A finite set of states

• Q

If Σ2 is {00, 01, 10, 11}, then Σ =

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

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

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

• Abacus

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

• bottom-up approach

Set of final or accepting states.

• F

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

• single move

“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”

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

• TRUE

Context Free Languages is closed under intersection.

• False
• True

An English like abbreviations representing elementary computer operations.

• Assembly Language

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 *

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 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

Is a finite set of symbols called the alphabet.

• Σ

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

• Regular

One of the first programmable electronic computers in 1945.

• ENIAC

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

• Type-0 grammars

Empty string

• Σ

In mathematical notation, the symbol → means...

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

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

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

• FALSE

There are 5 tuples in finite state machine.

• TRUE

The top symbol is read and removed.

• Pop

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

• 1956

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

• Bottom-Up Parser

Some graphs contain cycles.

• True
• False

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

• { 4,6}

Increasing accuracy, or precision.

• Minimizing False Positives

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

• Transducer

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

• δ

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

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

• TRUE

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]*

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

Set of final or accepting states

• F

A set of terminals where N ∩ T = NULL.

• T

The stack content

• s

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

Which one is the answer?

• Computer

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+

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

• Single Move

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!

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*

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

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

• NDFA

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

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

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

• δ

The relationship between recursive and recursively enumerable languages is ________________.

• ∈
• ⊂
• ∉
• ⊃

Starting state

• q0

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

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

__ is a finite set of states.

• Q

S → aAb, aA →aaAb, A→ε

• P

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

• FALSE

NFA means:

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

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)*

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

• TRUE

The complement of an infinite language is necessarily finite.

• FALSE

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

• Production

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

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

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

The following are phases of C++ Programs except

• Process

The start symbol.

• S

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

• Output Alphabet

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

• top-down parser

Finite set of input alphabets.

• Σ

The initial stack top symbol (I ∈ S)

• I

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

• Regular

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

• PDA

Labeled by a terminal symbol or ε.

• Leaves

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

A stack symbols

• Σ

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}

A - B will contain elements in?

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

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

• True
• False

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

• Parse Tree

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+

|-* is the _____ closure of |-

• transitive and reflexive

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

• Top-Down Parser

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

• Type-2 grammars

JASON can generally be parsed by ______________.

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

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

• 1936

All relations are functions

• True
• False

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

• TRUE

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

• Root with no children is called a leaf

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

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

• Bottom-Up Approach

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

• TRUE

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

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

• 1956

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

• David Hilbert

|-* is the closure of |-

• Transitive and Reflexive

Regular expression Φ* is equivalent to

• ϵ

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

The symbol used for the empty string is ____________.

• ε
• φ
• a blank
• ψ

Terminal symbols

• a & b

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

• δ

The CFG "S → (S) | SS | ε" accepts:

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

A finite number of states.

• Q

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

A set of accepting states (F ∈ Q).

• F

Are ambiguous grammar context free?

• TRUE

The entity which generate Language is termed as:

• Grammar

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

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

• LIFO, finite

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

According to what concept is CFL a superset of RL?

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

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

• L is a set of 0n1n

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

• True
• False

Who is the father of modern computer science?

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

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

• P

A DFA is represented by digraphs called.

• State Diagram

Number of states require to accept string ends with 10.

• 3

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

• Pascaline

A finite number of states

• Q

“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”

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)*

{Q, Σ, q0, F, δ, Q × Σ → Q} is…

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

All functions are relations

• True
• False

Finite Automata all regular languages and only regular languages.

• Accept

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

• Parsing

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

• Derivation tree

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.

The unconsumed input.

• w

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

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

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

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

• alphabet

A language is regular if and only if.

• Accepted by DFA

What kind of languages does a TM decide?

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

A set on non-terminal symbols.

• S & A

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

• δ

Increasing accuracy, or precision

• Minimizing False Positives

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

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

• current state, unprocessed input, stack content

Computer science has roots in two fields :

• Mathematics

The unconsumed input

• w

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

• A - B
• A / B
• A x B
• A ∩ B

What can be said about CFLs?

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

Regular expression Φ* is equivalent to.

• ϵ

All trees contain loops.

• True
• False

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

• computer

Empty set is a/an ________________.

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

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

• {0a1b|a=2,b=3}

A set of accepting states (F ∈ Q)

• F

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

• Every CFG for L is ambiguous

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

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

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

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

• parse tree

What can not be said about CFLs?

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

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}

The empty set is always a subset of any set.

• True
• False

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

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

• PDA

Increasing coverage, or recall.

• Minimizing False Negatives

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

• True

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

• Unit Production

Non-terminal symbols

• S & A

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

• {0a1b|a=2,b=3}

The stack contents

• s

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

• q0

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

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

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

• ((a.b)+c)*

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

• m - n
• m + n
• 2n
• m x n

An initial state q0 ∈ Q.

• q0

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

Every set is a / an ________________ of itself.

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

Finite set of states

• Q

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

• 0
• Infinite
• Finite
• 1

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

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

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

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

• Context Sensitive Language

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

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

• F

Finite set of input alphabets

• Σ

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

• PDA

An initial state q0 ∈ Q

• q0

In the Chomsky Hierarchy:

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

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

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

• 4
• 8
• 7
• 16

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

• 1956

A finite set of states.

• Q

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

• 1936

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