Engineering BE Electronics and Computer Science Sem 4 May 2023 2023 ECS4 Discrete Structures And Automato Theory Question Paper - Mumbai University | munotes
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Questions asked in this paper
Duration: 3hrs [Max Marks: 80]
N.B.: (1) Question No 1 is Compulsory
(2) Attempt any three questions out of the remaining five
(3) All questions carry equal marks
(4) Assume suitable data, if required and state it clearly
1 Attempt any FOUR [20]
in the set of integers z defined by
Show that the relation R is an equivalence relation
using Mathematical Induction that
c Design an FSM in which input is valid if it ends in “1011” over Y= {0,1}
d_ Design NFA for the regular expression
e Differentiate between DFA and NFA
2 Define Poset. Draw Hasse diagram which represents the partial order relation. [10]
b Convert the following NFA to DFA: [10]
Simplify the following CFG: [10]
Write a short note on Warshall’s algorithm. [10]
Let A = {a1,a2,a3} and R be a relation on A whose matrix is:
0O . Find transitive closure of R using Warshall’s algorithm
4 Design PDA to check odd palindrome over {0,1} [10]
and explain formal definition of pumping lemma for regular language
prove that the following language is not regular
5 Design Moore machine for the following: If input ends in output [10]
should be ‘A’, if input ends in ‘101’ output should be ‘B’, otherwise output
should be ‘C’ and convert it into Mealy machine
a finite automaton to check divisibility by 3 to binary number. [10]
6 Determine if the following graphs G1 and G2 are isomorphic or not. [10]
are defined by the formulas: f(x) = x + 2 and g(x) = Find
N.B.: (1) Question No 1 is Compulsory
(2) Attempt any three questions out of the remaining five
(3) All questions carry equal marks
(4) Assume suitable data, if required and state it clearly
1 Attempt any FOUR [20]
in the set of integers z defined by
Show that the relation R is an equivalence relation
using Mathematical Induction that
c Design an FSM in which input is valid if it ends in “1011” over Y= {0,1}
d_ Design NFA for the regular expression
e Differentiate between DFA and NFA
2 Define Poset. Draw Hasse diagram which represents the partial order relation. [10]
b Convert the following NFA to DFA: [10]
Simplify the following CFG: [10]
Write a short note on Warshall’s algorithm. [10]
Let A = {a1,a2,a3} and R be a relation on A whose matrix is:
0O . Find transitive closure of R using Warshall’s algorithm
4 Design PDA to check odd palindrome over {0,1} [10]
and explain formal definition of pumping lemma for regular language
prove that the following language is not regular
5 Design Moore machine for the following: If input ends in output [10]
should be ‘A’, if input ends in ‘101’ output should be ‘B’, otherwise output
should be ‘C’ and convert it into Mealy machine
a finite automaton to check divisibility by 3 to binary number. [10]
6 Determine if the following graphs G1 and G2 are isomorphic or not. [10]
are defined by the formulas: f(x) = x + 2 and g(x) = Find
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