250+ TOP MCQs on Eliminating Epsilon Productions and Answers

Automata Theory Multiple Choice Questions on “Eliminating Epsilon Productions”.

1. The use of variable dependency graph is in:
a) Removal of useless variables
b) Removal of null productions
c) Removal of unit productions
d) None of the mentioned

Answer: a
Clarification: We use the concept of dependency graph inorder to check, whether any of the variable is reachable from the starting variable or not.

2. The variable which produces an epsilon is called:
a) empty variable
b) nullable
c) terminal
d) all of the mentioned

Answer: b
Clarification: Any variable A for which the derivation: A->*e is possible is called Nullable.

3. Statement:
For A-> e ,A can be erased. So whenever it appears on the left side of a production, replace with another production without the A.
State true or false:
a) true
b) false

Answer: b
Clarification: A can be erased. So whenever it appears on the right side of the production, replace with another production without the A.

4. Simplify the given grammar:
S->aXb
X->aXb | e
a) S->aXb | ab, X-> aXb | ab
b) S->X | ab, X-> aXb | ab
c) S->aXb | ab, X-> S | ab
d) None of the mentioned

Answer: a
Clarification: As X is nullable, we replace every right hand side presence of X with e and produce the simplified result.

5. Consider the following grammar:
A->e
B->aAbC
B->bAbA
A->bB
The number of productions added on the removal of the nullable in the given grammar:
a) 3
b) 4
c) 2
d) 0

Answer: b
Clarification: The modified grammar aftyer the removal of nullable can be shown as:
B->aAbC| abC
B->bAbA| bbA| bAb| bb
A->bB

6. Let G=(V, T, P, S) be a CFG such that _____________. Then there exists an equivalent grammar G’ having no e productions.
a) e ∈ L(G)
b) w ∉ L(G)
c) e ∉ L(G)
d) w ∈ L(G)

Answer: c
Clarification: Theorem: Let G = (V, T, S, P) be a CFG such that e ∉ L(G). Then there exists an equivalent grammar G’ having no e-productions.

7. For each production in P of the form:
A-> x1x2x3…xn
put into P’ that production as well as all those generated by replacing null variables with e in all possible combinations. If all x(i) are nullable,
a) A->e is put into P’
b) A->e is not put into P’
c) e is a member of G’
d) None of the mentioned

Answer: b
Clarification: It is an exception that A->e is not put into P’ if all x(i) are nullable variables.

8. For the given grammar G:
S->ABaC
A->BC
B->b| e
C->D| e
D-> d
Remove the e productions and generate the number of productions from S in the modified or simplified grammar.
a) 6
b) 7
c) 5
d) 8

Answer: d
Clarification: The grammar after the removal of epsilon production can be shown as:
S->ABaC| AaC| ABa| Aa| a| aC| Ba| BaC
A->BC| B| C
B->b
C->D
D-> d

9. Consider G=({S,A,B,E}, {a,b,c},P,S), where P consists of S →AB, A →a, B →b and E →c.
Number of productions in P’ after removal of useless symbols:
a) 4
b) 3
c) 2
d) 5

Answer: a
Clarification:
P’= S->AB, A->a, B-> b,
V’={S, A, B},
∑’={a, b}

10. Given grammar G:
S->aS| AB
A-> e
B-> e
D-> b
Reduce the grammar, removing all the e productions:
a) S->aS| AB| A| B, D-> b
b) S->aS| AB| A| B| a, D-> b
c) S->aS| AB| A| B
d) None of the mentioned

Answer: b
Clarification: We will replace all the nullables wherever they appear in the right hand side of any production. D will not be erased as we are just removing nullable variables not completely simplifying the grammar.a

250+ TOP MCQs on Simulation of Turing Machine and Answers

Automata Theory Multiple Choice Questions on “Simulation of Turing Machine”.

1. Fill in the blank with an appropriate option.
In automata theory, ___________ is said to be Computationally Universal if can be used to simulate any single taped Turing Machine.
a) Computer’s instruction set
b) A programming language
c) Cellular Automaton
d) All of the mentioned

Answer: d
Clarification: Computationally Universal or Turing Complete is a set of data manipulation rules if it can be used to simulate a single-taped turing machine.

2. Give a classic example of the concept of turing complete.
a) lambda calculus
b) C++
c) Lisp
d) All of the mentioned

Answer: d
Clarification: Most of the programming languages, conventional or unconventional are turing complete. Functional languages like Lisp and Haskell are also turing complete.

3. Let two machines be P and Q. The state in which P can simulate Q and Q can simulate P is called:
a) Turing Equivalence
b) State Equivalence
c) Universal Turing Machine
d) None of the mentioned

Answer: a
Clarification: It is a closely related concept with Turing complete. It says, two computers P and Q are called equivalent if P can simulate Q and Q can simulate P.

4. Which of the following remarks the given statement?
Statement: Any function whose values can be computed by an algorithm, can be computed by a Turing machine.
a) Smn theorem
b) Structured Program theorem
c) Church-Turing thesis
d) None of the mentioned

Answer: c
Clarification: The following conclusion is laid down from the Church-Turing thesis:
Any function whose values can be computed by an algorithm, can be computed by a Turing machine. If any real world computer can be simulated by a turing machine, it is Turing equivalent to a Turing Machine.

5. Which of the following can be used to simulate any turing machine?
a) Finite State Automaton
b) Universal Turing Machine
c) Counter machines
d) All of the mentioned

Answer: b
Clarification: The computational aspect of any possible real world computer can be simulated using an Universal Turing Machine so can be any turing machine.

6. State true or false:
Statement: Inorder to show something is Turing complete, it is enough to demonstrate that it can be used to simulate some Turing complete system.
a) true
b) false

Answer: a
Clarification: Yes it is. For instance, an imperative language is called Turing complete if it tends to have conditional branching and an ability to maintain an arbitrary number of symbols.

7. Which of the following can lack in a Universal computer?
a) Turing Complete Instruction set
b) Infinite memory
c) Infinite time
d) None of the mentioned

Answer: d
Clarification: Real computers which are manufactured till date, all are similar to single taped turing machine. However, they have limited physical resources so they are linearly bounded complete on the contrary.

8. Which among are not the results of computational theory?
a) In general, it is impossible to predict that what a Turing-complete program will do over an arbitrarily long time.
b) It is impossible to determine for every input, whether the program will eventually stop or continue forever.
c) It is not possible to determine whether a program will return true or false.
d) None of the mentioned

Answer: d
Clarification: All of the following mentioned are the conclusions of automata theory or computability theory.

9. Which of the games fill under the category of Turing-complete?
a) Minecraft
b) Minesweeper
c) Dwarf Fortress
d) All of the mentioned

Answer: d
Clarification: Many games fall under the category og turing complete:
a) Minecraft
b) Minesweeper
c) Dwarf Fortress
d) Conway’s Game of Life
e) Pokemon Yellow, etc.

10. Which of the following a Non-turing Complete language?
a) Regular Language
b) Context free grammars
c) Epigram
d) All of the mentioned

Answer: There exists some computational languages which are not turing complete. Regular language which is accepted by finite automata tops the list. Other examples are pixel shader languages embedded in Direct3D and OpenGL extensions.

250+ TOP MCQs on Finite Automata and Answers

Automata Theory Multiple Choice Questions on “Regular Language & Expression”.

1. There are ________ tuples in finite state machine.
a) 4
b) 5
c) 6
d) unlimited

Answer:b
Clarification: States, input symbols,initial state,accepting state and transition function.

2. Transition function maps.
a) Σ * Q -> Σ
b) Q * Q -> Σ
c) Σ * Σ -> Q
d) Q * Σ -> Q

Answer:d
Clarification: Inputs are state and input string output is states.

3. Number of states require to accept string ends with 10.
a) 3
b) 2
c) 1
d) can’t be represented.

Answer:a
Clarification: This is minimal finite automata.

4. Extended transition function is .
a) Q * Σ* -> Q
b) Q * Σ -> Q
c) Q* * Σ* -> Σ
d) Q * Σ -> Σ

Answer:a
Clarification: This takes single state and string of input to produce a state.

5. δ*(q,ya) is equivalent to .
a) δ((q,y),a)
b) δ(δ*(q,y),a)
c) δ(q,ya)
d) independent from δ notation

Answer:b
Clarification: First it parse y string after that it parse a.

6. String X is accepted by finite automata if .
a) δ*(q,x) E A
b) δ(q,x) E A
c) δ*(Q0,x) E A
d) δ(Q0,x) E A

Answer:c
Clarification: If automata starts with starting state and after finite moves if reaches to final step then it called accepted.

7. Languages of a automata is
a) If it is accepted by automata
b) If it halts
c) If automata touch final state in its life time
d) All language are language of automata

Answer:a
Clarification: If a string accepted by automata it is called language of automata.

8. Language of finite automata is.
a) Type 0
b) Type 1
c) Type 2
d) Type 3

Answer:d
Clarification: According to Chomsky classification.

9. Finite automata requires minimum _______ number of stacks.
a) 1
b) 0
c) 2
d) None of the mentioned

Answer:b
Clarification: Finite automata doesn’t require any stack operation .

10. Number of final state require to accept Φ in minimal finite automata.
a) 1
b) 2
c) 3
d) None of the mentioned

Answer:d
Clarification: No final state requires.

11. Regular expression for all strings starts with ab and ends with bba is.
a) aba*b*bba
b) ab(ab)*bba
c) ab(a+b)*bba
d) All of the mentioned

Answer:c
Clarification: Starts with ab then any number of a or b and ends with bba.

12. How many DFA’s exits with two states over input alphabet {0,1} ?
a) 16
b) 26
c) 32
d) 64

Answer:d
Clarification: Number of DFA’s = 2n * n(2*n).

13. The basic limitation of finite automata is that
a) It can’t remember arbitrary large amount of information.
b) It sometimes recognize grammar that are not regular.
c) It sometimes fails to recognize regular grammar.
d) All of the mentioned

Answer:a
Clarification:Because there is no memory associated with automata.

14. Number of states require to simulate a computer with memory capable of storing ‘3’ words each of length ‘8’.
a) 3 * 28
b) 2(3*8)
c) 2(3+8)
d) None of the mentioned

Answer:b
Clarification: 2(m*n) states requires .

15. FSM with output capability can be used to add two given integer in binary representation. This is
a) True
b) False
c) May be true
d) None of the mentioned

Answer:a
Clarification: Use them as a flip flop output .

250+ TOP MCQs on Regular Language & Expression and Answers

Automata Theory Multiple Choice Questions on “Regular Language & Expression”.

1. A regular language over an alphabet a is one that can be obtained from
a) union
b) concatenation
c) kleene
d) All of the mentioned

Answer: d
Clarification: None.

2. Regular expression {0,1} is equivalent to
a) 0 U 1
b) 0 / 1
c) 0 + 1
d) All of the mentioned

Answer: d
Clarification: All are equivalent to union operation.

3. Precedence of regular expression in decreasing order is
a) * , . , +
b) . , * , +
c) . , + , *
d) + , a , *

Answer: a
Clarification: None.

4. Regular expression Φ* is equivalent to
a) ϵ
b) Φ
c) 0
d) 1

Answer: a
Clarification: None.

5. a? is equivalent to
a) a
b) a+Φ
c) a+ϵ
d) wrong expression

Answer: c
Clarification: Zero or one time repetition of previous character .

6. ϵL is equivalent to
a) ϵ
b) Φ
c) L
d) Lϵ

Answer: c,d
Clarification: None.

7. (a+b)* is equivalent to
a) b*a*
b) (a*b*)*
c) a*b*
d) none of the mentioned

Answer: b
Clarification: None.

8. ΦL is equivalent to
a) LΦ
b) Φ
c) L
d) ϵ

Answer: a,b
Clarification: None.

9. Which of the following pair of regular expression are not equivalent?
a) 1(01)* and (10)*1
b) x(xx)* and (xx)*x
c) (ab)* and a*b*
d) x+ and x*x+

Answer: c
Clarification: (ab)*=(a*b*)*.

10. Consider following regular expression
i) (a/b)* ii) (a*/b*)* iii) ((ϵ/a)b*)*
Which of the following statements is correct
a) i,ii are equal and ii,iii are not
b) i,ii are equal and i,iii are not
c) ii,iii are equal and i,ii are not
d) all are equal

Answer: d
Clarification: All are equivalent to (a+b)*.

250+ TOP MCQs on Construction and Yield of a Parse Tree

Automata Theory Multiple Choice Questions on “Construction and Yield of a Parse Tree”.

1. The most suitable data structure used to represent the derivations in compiler:
a) Queue
b) Linked List
c) Tree
d) Hash Tables

Answer: c
Clarification: The tree, known as “Parse tree” when used in a compiler, is the data structure of choice to represent the source program.

2. Which of the following statement is false in context of tree terminology?
a) Root with no children is called a leaf
b) A node can have three children
c) Root has no parent
d) Trees are collection of nodes, with a parent child relationship

Answer: a
Clarification: A node has atmost one parent, drawn above the node, and zero or more children drawn below. Lines connect parents to children. There is one node, one root, that has no parent; this node appears to be at the top of the tree. Nodes with no children are called leaves. Nodes that are not leaves are called interior nodes.

3. In which order are the children of any node ordered?
a) From the left
b) From the right
c) Arbitrarily
d) None of the mentioned

Answer: a
Clarification: The children of a node are ordered from the left and drawn so. If N is to the left of node M, then all the descendents of N are considered to be to the left of all the descendents of M.

4. Which among the following is the root of the parse tree?
a) Production P
b) Terminal T
c) Variable V
d) Starting Variable S

Answer: d
Clarification: The root is labelled by the start symbol. All the leaves are either labelled by a a terminal or with e.

5. For the expression E*(E) where * and brackets are the operation, number of nodes in the respective parse tree are:
a) 6
b) 7
c) 5
d) 2
Answer: b

6. The number of leaves in a parse tree with expression E*(E) where * and () are operators
a) 5
b) 2
c) 4
d) 3
Answer: a

7. A grammar with more than one parse tree is called:
a) Unambiguous
b) Ambiguous
c) Regular
d) None of the mentioned

Answer: b
Clarification: A context free grammar G is ambiguous if there is at least one string in L(G) having two or more distinct derivation trees or equivalently, two or more distinct leftmost derivations.

8. __________ is the acyclic graphical representation of a grammar.
a) Binary tree
b) Oct tree
c) Parse tree
d) None of the mentioned

Answer: c
Clarification: In order to graphically represent a derivation of a grammar we need to use parse trees.

9. Grammar is checked by which component of compiler
a) Scanner
b) Parser
c) Semantic Analyzer
d) None of the mentioned

Answer: Parser or syntax analyzer is the one responsible for checking the grammar and reporting errors. In this phase, parse tree is generated and syntax is analyzed.

250+ TOP MCQs on Eliminating Unit Productions and Answers

Automata Theory Multiple Choice Questions on “Eliminating Unit Productions”.

1. Which among the following is the format of unit production?
a) A->B
b) A->b
c) B->Aa
d) None of the mentioned

Answer: a
Clarification: Any production of the format A-> B where A and B belongs to the V set, is called Unit production.

2. Given Grammar G:
S->aA
A->a| A
B->B
The number of productions to be removed immediately as Unit productions:
a) 0
b) 1
c) 2
d) 3

Answer: c
Clarification: The productions in the format A-> A are removed immediately as they produce self and that is not a terminal or will not lead to a string. Hence, it is removed immediately.

3. Given grammar:
S->aA
A->a
A->B
B-> A
B->bb
Which of the following is the production of B after simplification by removal of unit productions?
a) A
b) bb
c) aA
d) A| bb

Answer: b
Clarification: The simplified grammar can be presented as follows:
S->aA| aB
A->a
B-> bb

4. If grammar G is unambiguous, G’ produced after the removal of Unit production will be:
a) ambiguous
b) unambiguous
c) finite
d) cannot be said

Answer: b
Clarification: With the simplification of Context free grammars, undesirable properties are introduced. It says, if grammar G, before simplification is unambiguous, after simplification will also be unambiguous.

5. If C is A-derivable, C->B is a production, and B ¹ A, then B is
a) nullable
b) Non-derivable
c) A-derivable
d) None of the mentioned

Answer: c
Clarification:
If A-> B is a production, B is called A- derivable.
If C is A-derivable, C->B is a production, and B ¹ A, then B is A -derivable.
No other variables are A-derivable.

6. A can be A-> derivable if and only if __________
a) A-> A is actually a production
b) A->B, B-> A exists
c) Both (a) and (b)
d) None of the mentioned

Answer: a
Clarification: The format says: If A->B is a production, B is called A-derivable.Thus A to be A-derivable, a production : A-> A need to exist.

7. Given Grammar:
T-> T+R| R
R-> R*V| V
V->(T)| u
When unit productions are deleted we are left with
T-> T+R| _______|(T)| u
R->R*V|(T)| u
V-> (T)| u
Fill in the blank:
a) T*V
b) T+V
c) R*T
d) R*V

Answer: d
Clarification: The grammar produced after the elimination of unit production is:
T-> T+R| R*V| (T)| u
R->R*V|(T)| u
V-> (T)| u

8. Given grammar G:
S-> ABA, A->aA|e, B-> bB|e
Eliminate e and unit productions. State the number of productions the starting variable holds?
a) 6
b) 7
c) 9
d) 5

Answer: b
Clarification: After reduction the grammar looks like:
S->ABA| AB| BA| AA| Aa| a| bB| b
A->aA| a
B->bB| b

9. Given grammar G:
S-> A| B| C
A-> aAa| B
B-> bB|bb
C->aCaa|D
D->baD|abD|aa
Eliminate e and unit productions and state the number of variables left?
a) 5
b) 4
c) 3
d) 2

Answer: 5
Clarification: The reduced production:
S->aAa| bB|bb aCaa| baD| abD| aa, A->aAa| bB| bb, B->bB| bb, C->aCaa| baD| abD| aa, D-> baD| abD| aa

10. Which of the following variables in the given grammar is called live variable?
S->AB
A->a
a) S
b) A
c) B
d) None of the mentioned

Answer: b
Clarification: Any variable A for which there is a production A-> x with x Ε Σ* is called live.