Computation Theory Course, 6803415-3 Homework Two

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 Two

Ch2

Solutions

Question One: 1 Mark

The following is a CFG (Context-Free-Grammar):

𝑬 → 𝑬 + 𝑻 | 𝑻 𝑻 → 𝑻 × 𝑭 | 𝑭 𝑭 → (𝑬) | 𝒂 Give parase trees and derivations for each string.

a.a b.a+a+a

The Answer of Question One:

a.

Parse Tree:

E

T

F

a Derivations:

𝐸 ⟹ 𝑇 ⟹ 𝐹 ⟹ 𝑎

2 b.

Parse Tree:

E

E T

E T F

T F

F

+ a

a + a Derivations:

𝐸 ⟹ 𝐸 + 𝑇 ⟹ 𝑇 + 𝑇 ⟹ 𝑇 + 𝐹 ⟹ 𝐹 + 𝑎 ⟹ 𝑎 + 𝑎

Question Two: 1 Mark

Give context-free grammars that generate the following languages. In all parts the alphabet E is {0,1}.

a. 𝐿 = {𝑤|𝑤 𝑠𝑡𝑎𝑟𝑡𝑠 𝑎𝑛𝑑 𝑒𝑛𝑑𝑠 𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑠𝑦𝑚𝑏𝑜𝑙}

b. 𝐿 = {𝑤||𝑤| 𝑖𝑠 𝑜𝑑𝑑}

The Answer of Question Two:

a.

S0 → 0S10|1S11|ε S1 → 0S1|1S1|ε b.

S0 → 0S1|1S1

S1 → 00S1|01S1|10S1|11S1|ε

3 Question Three: 1 Mark

Answer each part for the following context-free grammar G.

𝑹 → 𝑿𝑹𝑿 | 𝑺 𝑺 → 𝒂𝑻𝒃 | 𝒃𝑻𝒂 𝑻 → 𝑿𝑻𝑿 | 𝑿 | 𝜺

𝑿 → 𝒂 | 𝒃

a.What are the terminals of 𝑮?

b.True or False: 𝑻 ⟹ 𝒂𝒃𝒂.

c. True or False: 𝑻 ⟹ 𝑻.

d. Give three strings in 𝑳(𝑮).

The Answer of Question Three a. The terminals of G are: a, b.

b. False.

c. False.

d. ab, ba, aab.

Good Luck my Lovely Students 😉 T.Mariah Sami Ahmed Khayat

Teacher Assistant @ Adam University College mskhayat@uqu.edu.sa