Automata Theory and Formal Language



The course introduces some fundamental concepts in automata theory and formal languages including grammar, finite automaton, regular expression, formal language, pushdown automaton, and Turing machine. Not only do they form basic models of computation, they are also the foundation of many branches of computer science, e.g. compilers, software engineering, concurrent systems, etc. The properties of these models will be studied and various rigorous techniques for analyzing and comparing them will be discussed, by using both formalism and examples.


QUESTIONSANSWERS
TRUEAn alphabet is any finite set of symbols.
LeavesLabeled by a terminal symbol or ε.
S & ANon-terminal symbols
Type-0 grammarsIT 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.
wUnconsumed input.
AcceptFinite Automata all regular languages and only regular languages.
TRUEZ2 uses electricity to convey letters and transmit information quickly in 1844.
PS → aAb, aA →aaAb, A→ε
alphabetA formal language is a set of strings, each string composed of symbols from a finite set called
((a.b)+c)*Having the initial state as a final state, give the deterministic finite state automaton that accepts the regular expression.
1956Noam Chomsky gave a mathematical model in ___ which is effective for writing computer languages.
FA set of accepting states (F ∈ Q)
FSet of final or accepting states
Assembly LanguageAn English like abbreviations representing elementary computer operations.
Parse TreeA of a derivation is a tree in which each internal node is labeled with a nonterminal.
unionThe _____ of two sets A and B is the set containing those elements which are elements of A or elements of B.
No state p has two outgoing transitionsA DPDA is a PDA in which.
RegularIf L1 and L2 are regular sets then intersection of these two will be
Parse TreeAn order rooted tree that graphically represents the semantic information a string derived from a context-free grammar.
FALSETuring hypothesis believed that a function is said to be computable if and only if it can be computed by a Turing machine.
δA transition function: Q × (Σ∪{ε}) × S × Q × S*
FA set of accepting states (F ∈ Q).
SThe start symbol.
AnswerQUESTIONS
NDFAA string is accepted by a, iff the DFA/NDFA starting at the initial state ends in an after reading the string.
wThe unconsumed input
accepted, generatedContext-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.
Derivation treeAn order rooted tree that graphically represents the semantic information a string derived from a context-free grammar.
Type-0 grammarsIT generate recursively enumerable languages. The productions have no restrictions and phase structure grammar including all formal grammars.
Type-2 grammarsIt generate context-free languages. The productions must be in the form A → γ
TRUEAre ambiguous grammar context free?
a,bThe language L contains all strings over the alphabet {a,b} that begin with and end with
Minimizing False PositiveIncreasing accuracy, or precision.
ϵRegular expression Φ* is equivalent to
computerA general purpose, programmable, information processor with input and output.
ΣIs a finite set of symbols called the alphabet.
current state, unprocessed input, stack contentA PDA machine configuration (p, w, y) can be correctly represented as ____________ .
SStart symbol, S ∈ N
3Number of states require to accept string ends with 10.
TRUEThe 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.
bottom-up approach* Starts from tree leaves. It proceeds upward to the root which is the starting symbol S
Noam Chomsky, 1956The 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.
{0a1b|a=2,b=3}Which among the following is the correct option for the given grammar? G->X111|G1,X->X0|00.
ProcessThe following are phases of C++ Programs except
Regular ExpressionsA compact textual representation of a set of strings representing a language.
top-down parserA parsing that starts from the top with the start-symbol and derives a string using a parsetree.
RegularIf L1 and L2 are regular sets then intersection of these two will be.
ENIACOne of the first programmable electronic computers in 1945.
ParsingIs used to derive a string using the production rules of a grammar.
PDAA _____ may or may not read an input symbol, but it has to read the top of the stack in every transition
1936In _____ Allan M. Turing proposed the Turing machine as a model of "any possible computation".
δ__ is the transition function where δ: Q × Σ → Q.
QA finite number of states
Single MoveThe of a Turing machine depends on the current state of finite control and the tape symbol present in the input tape.
Output AlphabetWhich of the following is a not a part of 5-tuple finite automata?
Accepted by DFAA language is regular if and only if.
IThe initial stack top symbol (I ∈ S)
Minimizing False NegativeIncreasing coverage, or recall.
ComputerWhich one is the answer?
TRUEFor every pair of regular expressions R and S, the languages denoted by R(SR)* and (RS)*R are the same.
L1=L2Let the class of language accepted by finite state machine be L1 and the class of languages represented by regular expressions be L2 then.
q0An initial state q0 ∈ Q.
Reduction of CFGElimination of productions and symbols is called simplification of CFGs. Simplification essentially comprises of the following steps:
Null MoveA 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.
rinse, lather, repeatAn algorithms to shampoo your hair.
sThe stack contents.
FSet of final or accepting states.
QFinite set of states.
(a+b)*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
q0An initial state q0 ∈ Q
Living OrganismsIt process information in their efforts to eat, survive, and reproduce.
TransducerAn automaton that produces outputs based on current input and/or previous state is called.
State DiagramA DFA is represented by digraphs called.
LIFO, finiteThe PDA has infinite memory and access in _____ order and the finite automata has ____ memory.
ΣA finite set of input symbols.
AWhat is the final result after converting the following NFA-ε to NFA without Null move.
qThe state.
Partial Derivation Tree, Sub-TreeA 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
q0Starting state
ϵRegular expression Φ* is equivalent to.
No state p has two outgoing transitionsA DPDA is a PDA in which
QA finite set of states.
TRUEFor a regular expression 'a', we can construct the following FA:
TRUEA grammar G is ambiguous if there is a word w Î L(G) having are least two different parse trees.
F__ is a set of final state/states of Q (F ⊆ Q).
Bottom-Up Approach* Starts from tree leaves. It proceeds upward to the root which is the starting symbol S.
1936In ____ Allan M. Turing proposed the Turing machine as a model of "any possible computation".
FA set of final state/states of Q (F⊆Q).
TA set of terminals where N ∩ T = NULL.
1936In Allan M. Turing proposed the Turing machine as a model of "any possible computation".
 
What is the final result after converting the following NFA-ε to NFA without Null move.
IThe initial stack top symbol (I ∈ S).
QIs a finite set of states.
PDAA may or may not read an input symbol, but it has to read the top of the stack in every transition
ΣFinite set of input alphabets
Charles BabbageWho is the father of modern computer?
AlphabetA formal language is a set of strings, each string composed of symbols from a finite set called.
Time ComplexityIt 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.
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 .For bottom-up parsing, a PDA has the following four types of transitions:
sThe stack contents
TRUEThere are 5 tuples in finite state machine.
δA transition function δ : Q × (Σ ∪ {ε}) → 2Q.
ababaabaaWhich of the following will not be accepted by the following DFA?
wThe unconsumed input.
Transitive and Reflexive|-* is the closure of |-
3The minimum number of states required to recognize an octal number divisible by 3 are/is.
NA set on non-terminal symbols.
StackThe transition a Push down automaton makes it additionally dependent upon the
qThe state
wUnconsumed input
Top-Down Approach* Starts with the starting symbol S. It goes down to tree leaves using productions.
Current state, Unprocessed input, Stack contentA PDA machine configuration (p, w, y) can be correctly represented as.
GrammarThe entity which generate Language is termed as:
TRUEA PDA accepts a string when, after reading the entire string, the PDA is in a final state.
Analytic EngineA conceptual design for a machine consisting of a Mill, Store, Printer, and Readers.
MathematicsComputer science has roots in two fields :
VertexLabeled by a non-terminal symbol.
finite control, input tapeThe 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.
ΣEmpty string
Σ *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.
End SymbolWhich among the following is not a part of the Context free grammar tuple?
transitive and reflexive|-* is the _____ closure of |-
FALSEA regular expression consisting of a finite set of grammar rules is a quadruple.
Q__ is a finite set of states.
TRUEFor every CFL, G, there exists a PDA M such that L(G) = L(M) and vice versa
ΣA stack symbols
ΓSet of all tape symbols
AcceptedContext-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.
δTransition function
q0Is the initial state from where any input is processed (q0 ∈ Q).
(a+b)*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.
None of the mentionedNumber of final state require to accept in minimal finite automata.
q0__ is the initial state from where any input is processed (q0 ∈ Q).
Start StateIdentify the modeling recognition of the word "then"
ΔBlank symbol
L is a set of 0n1nWhich among the following cannot be accepted by a regular grammar?
single moveThe __________ of a Turing machine depends on the current state of finite control and the tape symbol present in the input tape.
TRUEFor every CFL, G, there exists a PDA M such that L(G) = L(M) and vice versa.
Alan TuringWho is the father of modern computer science?
FALSEAny set that represents the value of the Regular Expression is called a Property set.
{3,6}If A = {3, 4, 6, 8} and
Type-0 grammarsT generate recursively enumerable languages. The productions have no restrictions and phase structure grammar including all formal grammars.
QA finite number of states.
Accepted, IgnoredContext-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.
TRUEThe recursive inference procedure determines that string w is in the language of the variable A, A being the starting variable.
AbacusThe first counting machine developed 5000 years ago in the Middle East.
Context Sensitive LanguageProduction Rule: aAb->agb belongs to which of the following category?
Bottom-Up ParserIt starts from the bottom with the string and comes to the start symbol using a parse tree.
predicatesare parameterized statement, they are true or false depending on the values of their parameters.
Parsing______ is used to derive a string using the production rules of a grammar.
q0The initial state (q0 ∈ Q)
TRUEEvery context free grammar can be transformed into an equvalent non deterministic push down automata.
complementA language accepted by Deterministic Push down automata is closed under which of the following?
Root VertexLabeled by the start symbol.
Pumping LemmaIs to be applied to show that certain languages are not regular. It should never be used to show a language is regular.
6A Moore machine can be described by a tuple.
Push the current input symbol into the stack.For bottom-up parsing, a PDA has the following four types of transitions:
FALSELeibniz introduced binary notation of calculation.
a & bTerminal symbols
David Hilbertchallenged the mathematical community to find an infallible, mechanical method for constructing and checking truth of mathematical statements.
3,6,2,5,4For the given Regular expression, the minimum number of terminals required to derive its grammar (011+1)*(01)* is
Null MoveA 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
δIs the transition function where δ: Q × Σ → Q.
Minimizing False NegativesIncreasing coverage, or recall.
QFinite set of states
ΣFinite set of input alphabets.
Root with no children is called a leafWhich of the following statement is false in context of tree terminology?
PushA new symbol is added at the top.
PDAA DFA can remember a finite amount of information, but a ____ can remember an infinite amount of information.
1956Noam Chomsky gave a mathematical model in which is effective for writing computer languages.
Every CFG for L is ambiguousWhich of the following statements are correct for a concept called inherent ambiguity in CFL?
TRUEAny production rule in the form A → B where A, B ∈ Non-terminal is called unit production.
TRUERegular sets are closed under union,concatenation and kleene closure.
Minimizing False PositivesIncreasing accuracy, or precision.
Unit ProductionAny production rule in the form A → B where A, B ∈ Non-terminal is called.
PDAA DFA can remember a finite amount of information, but a can remember an infinite amount of information.
ProductionIs used to derive a string using the production rules of a grammar.
QA finite set of states
FALSEThe entity which generate Language is termed as regular languages.
TRUEA pushdown automaton is a way to implement a context-free grammar in a similar way to design DFA for a regular grammar.
PopThe top symbol is read and removed.
Minimizing False PositivesIncreasing accuracy, or precision
Top-Down ParserIt starts from the top with the start-symbol and derives a string using a parse tree.
Go to bathroomAn algorithms to shampoo your hair.
TRUEComputers are general purpose because they can perform many different tasks.
Σ__ is a finite set of symbols called the alphabet.
FALSEThe complement of an infinite language is necessarily finite.
FIs a set of final state/states of Q (F ⊆ Q).
ContextA right-most derivation of a sentential form is one in which rules transforming the are always applied.
PA set of rules, P: N → (N U T)*, it does have any right context or left context.
δA transition function: Q × (Σ∪{ε}) × S × Q × S*.
PDAA may or may not read an input symbol, but it has to read the top of the stack in every transition.
PascalineThe first mechanical calculator using gears for calculation developed in 1642.
Statement 1 is false, Statement 2 is trueAccording to the 5-tuple representation i.e. FA= {Q, ∑, δ, q, F} Statement 1: q ϵ Q'; Statement 2: FϵQ
stackThe transition a Push down automaton makes it additionally dependent upon the _____.
parse treeA __________ of a derivation is a tree in which each internal node is labeled with a nonterminal.
sThe stack content
7The number of elements in the set for the Language L={xϵ(∑r) *|length if x is at most 2} and ∑={0,1} is
1956Noam Chomsky gave a mathematical model in _______ which is effective for writing computer languages.
FALSELanguage may be derived from other strings using the productions in a grammar.
{ 4,6}If A = {3, 4, 6, 8} and
Context sensitive language is a subset of context free languageWhich of the following statement is false?
TrueGlobal Positioning System (GPS) calculates latitude and longitude from satellite signals.