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# SCSJ3203 - Theory Science Computer - Midterm Paper

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SCSJ3203 - Theory Science Computer - Midterm Paper - Universiti Teknologi Malaysia - UTM

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### SCSJ3203 - Theory Science Computer - Midterm Paper

1. 1. UNIVERSITY TEKNOLOGI MALAYSIA MIDTERM TEST SEMESTER I 2013/2014 CODE OF SUBJECT : SCSJ3203 NAME OF SUBJECT : Theory of Computer Science YEAR/COURSE : 3SCSJ, 3SCSR, 3SCSV, 3SCSI, 3SCSD, 3SCSB TIME : 10.15 am – 12.15 pm (2 hours) DATE : 31 October 2013 VANUE : BK1 – BK6 (N28) _____________________________________________________________________________________ INSTRUCTION TO THE STUDENTS PART A PART B : 10 TRUE/FALSE QUESTIONS (10 MARKS) : 10 SUBJECTIVE QUESTIONS (90 MARKS) THIS PAPER CONSIST OF 2 PARTS. ANSWER ALL QUESTION IN THE SPACE PROVIDED IN THIS QUESTION PAPER. THE MARKS FOR EACH QUESTION IS AS INDICATED. ANSWER ALL QUESTION IN THE SPACES ALLOCATED IN THIS BOOKLET. Name IC (or matric) number Name of lecturer Subject code and section SCJ3203 Section 01 / 02 / 03 / 04 / 05 / 06 (pls. circle tour section) This examination book consists of 6 printed pages excluding this page.
2. 2. Part A – True and false questions [10 marks] _____________________________________________________________________________________ There are 10 questions in this section. For each question, state whether it is TRUE or FALSE and write your answer in the space given. Each question carries 1 marks. Answer 1. λ is always subset of every set. ___________ 2. L1L2 = {xy | x ϵ L1 and y ϵ L2}, if L1 = {a, aa} and L2 = {λ, b, ab}, thus L1L2 = {a, b, aa, ab, aab, aaab}. ___________ 3. A regular expression for set of strings over {a, b} containing two or more b’s is (a + b)*b(a + b)*b(a + b). ___________ 4. Two example expressions that represent the same set of strings are (0 + 1 + λ)* and (0 + 1)*. ___________ 5. R = a* + b* generates any string with the combination of a’s and b’s. ___________ 6. The following grammar; S → aS; S → baSS; S → b over alphabet {a, b} is regular. ___________ 7. abab is generated by S → aX; X → bX; X → a; ___________ 8. A regular grammar does not generate the empty string. ___________ 9. A regular grammar is also a context-free grammar. ___________ 10. The following grammar; S → aX; X → bY; Y → aS; X → b; generates the language of (aba)*ab. ___________ 1
3. 3. PART B – SUBJECTIVE QUESTIONS [90 MARKS] _____________________________________________________________________________________ This part consists of 10 structured questions. Answer all questions in the space provided. The marks for each part of the question is as indicated. 1. Consider the language S* where S = {a, ab, ba}. Write three strings that are IN and NOT IN the language in Table 1. [6 marks] Table 1 IN the language NOT IN the language 2. For the two regular expression: [4 marks] r1 = a* + b* r2 = ab* + ba* + b*a + (a*b)* a. Find two strings corresponding to r2 but not r1. b. Find two strings corresponding to both r1 and r2. _____________________ _____________________ 3. Find a regular expression corresponding to the following languages. a. The language of all strings over the alphabet {a, b} that do not end with ba. [4 marks] ___________________________________________________________________ b. The language of all strings over the alphabet {a, b} that contain no more than one occurrence of the string bb. [4 marks] ___________________________________________________________________ c. The language of strings of even lengths over the alphabet of {a, b}. [4 marks] ___________________________________________________________________ 2
4. 4. 4. Describe as simply as possible in English the language corresponding to the following regular expressions a. (b + aa)(a + b)* [3 marks] _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ b. a*b(a*ba*b)*a* [3 marks] _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ 5. construct a context-free grammar that generate the following language a. {anbm | n<m} [4 marks] ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ b. {a3nb2n | n ≥ 0} [4 marks] ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ c. {a3n+1b2n | n ≥ 0} [4 marks] ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ 3
5. 5. 6. For each of the following context-free grammar, write the equivalent regular grammar and regular expression. [18 marks] Context free grammar Regular grammar Regular expression S → aBa B → bB | λ S → abS | λ S → Aa A → aA | bA | λ 7. Design a CFG rules for the following regular expression. [4 marks] (a + b)*aa(a + b)* ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ 8. Consider the following grammar G1: S → aSa | aBa B → bB | b a. Use the set notations to define the language generated by the grammar, L(G1). [3 marks] ___________________________________________________________________________ b. What is the shortest string that can be produced from the grammar? [1 mark] ___________________________________________________________________________ c. Write another possible string that can be generated from the language. [1 mark] ___________________________________________________________________________ 4
6. 6. 9. Let G2 be the grammar S → AB A → aA | λ B → bB | λ a. Give a leftmost derivation of the string aabbb. [3 marks] ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ b. Give the rightmost derivation of string abbbb. [3 marks] ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ c. Build the derivation tree for the derivations in parts (a) and (b). [4 marks] 5
7. 7. d. Give a regular expression for L(G2). _________________________ [3 marks] 10. The following is a CFG to generate a language. S → A1B A → 0A | λ B → 0B | 1B | λ a. Give leftmost derivations of the following string. [6 marks] i. 00101 ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ii. 10001 ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ b. What is the regular expression for this CFG. [4 marks] ___________________________________________________________________________ -END OF QUESTIONS6