1 Kingdom of Saudi Arabia
Ministry of Education Umm AlQura University
Adam University College, female branch Computer Science Department
ةيدوعسلا ةيبرعلا ةكلمملا ميلعتلا ةرازو ةعماج ىرقلا مأ تابلاطلا رطش ،مضأب ةيعماجلا ةيلكلا
يللآا بساحلا مولع مسق
First Semester of 2017-2018 Academic Year
Computation Theory Course, 6803415-3 Homework One
Solutions
Question One: 1 Mark
The following are the state diagrams of two DFAs, 𝑴𝟏 and 𝑴𝟐:
Answer the following questions about each of these machines.
a. What is the start state?
b. What is the set of accept states?
c. What sequence of states does the machine go through on input 𝑎𝑎𝑏𝑏?
d. Does the machine accept the string 𝑎𝑎𝑏𝑏?
e. Does the machine accept the string 𝜀?
The Answer of Qeustion One:
a.
M1 M2
q1 q1
b.
M1 M2
{q2} {q1, q4}
c.
M1 M2
q1, q2, q3, q1, q1 q1, q1, q1, q2, q4
d.
M1 M2
No, because the input has beed consumed and we ended up in a none final state.
Yes, because the input has been consumed and we ended up in a final state.
e.
M1 M2
No, it does not. Yes, it does because the start state is an accept state.
2 Question Two: 1 Mark
Give the formal description of the machines 𝑴𝟏 and 𝑴𝟐 pictured in Question One.
The Answer of Qeustion Two:
M1 M2
({q1, q2, q3}, {a, b}, 𝛿, q1, {q2}) 𝛿:
a B
q1 q2 q1
q2 q3 q3
q3 q2 q1
({q1, q2, q3, q4}, {a, b}, 𝛿, q1, {q1, q4}) 𝛿:
a B
q1 q1 q2
q2 q3 q4
q3 q2 q1
q4 q3 q4
Question Three: 1 Mark
The formal description of a DFA 𝑴 is ({𝒒𝒍, 𝒒𝟐, 𝒒𝟑, 𝒒𝟒, 𝒒𝟓}, {𝒖, 𝒅}, 𝜹, 𝒒𝟑, {𝒒𝟑}), where 𝜹 is given by the following table:
Give the state diagram of this machine.
The Answer of Qeustion Three:
Good Luck my Great Students 😉 T.Mariah Sami Ahmed Khayat
Teacher Assistant @ Adam University College [email protected]
u d d
u u u u
d d d
q1 q2 q3 q4 q5
