COS3701 Theoretical Computer Science III Exam
Preparation Pack 2026–2027 | Comprehensive
Theoretical Computer Science III Practice Questions
with Verified Answers & Explanations | Latest
COS3701 Syllabus & Exam Prep
Description:
This comprehensive exam preparation pack is designed to simulate the
COS3701 Theoretical Computer Science III examination for 2027, based
on the University of South Africa (UNISA) module . The module
focuses on enabling students to understand the concept of computability,
including context-free languages, recursively enumerable languages, and
the machines that accept them . The 120 multiple-choice questions cover
all key content areas including regular expressions and finite automata,
context-free grammars and Chomsky Normal Form, pushdown
automata, the pumping lemma, Turing machines, and computability
theory . Questions range from foundational recall to complex proof and
model construction scenarios, mirroring the official COS3701 exam
format . Actual COS3701 exams typically consist of 6 to 7 questions
worth 80 to 100 marks, with a 2-hour duration and IRIS invigilation .
COS3701 Theoretical Computer Science III Exam Preparation Pack
,Instructions: This is a closed-book examination with multiple-choice
questions. Select the single best answer for each question. Show all
working for proof and algorithm questions. The actual COS3701 exam
consists of questions covering regular expressions, DFA design, CFG
conversion to CNF, deterministic pushdown automata (DPDA), the
pumping lemma for CFLs, and Turing machine design . The exam is 2
hours and invigilated using the IRIS tool .
SECTION 1: REGULAR EXPRESSIONS AND FINITE AUTOMATA
(Questions 1-30)
1. Determine a regular expression for the language L over the alphabet
{a, b} that consists of all words that start with the substring ab, have one
or more bs, have at least two as, and have no bs after the two or more as.
Examples: abbaaa, abbbbbbaa .
A. ab{2,}(ba){2,}
B. ab+b*aa+
C. ab+aa+
D. ab+b*aa+ a*
Correct Answer: C
Rationale: The language requires words that start with "ab", followed by
one or more "b"s (b+), followed by two or more "a"s (aa+). There should
be no "b"s after the "a"s, so the string ends with the "a"s. The correct
regular expression is ab+aa+ which ensures at least one b between "ab"
and "aa", and at least two a's at the end.
,2. Design a deterministic finite automaton (DFA) that will recognise all
of the words in the language L from Question 1. What is the minimum
number of states required?
A. 3
B. 4
C. 5
D. 6
Correct Answer: C
Rationale: The language L = ab+aa+ requires states to track: reading "a"
(state A), reading "b" after "a" (state B), reading at least one additional
"b" (state C), reading the first "a" after the "b"s (state D), and reading at
least one more "a" (accepting state E). This requires 5 states plus a trap
state for invalid words.
3. Which of the following words is NOT in the language L = {w | w
contains at least one a and exactly one occurrence of the substring bb}?
A. abb
B. abba
C. bba
D. bab
Correct Answer: D
Rationale: The language requires words that have at least one 'a' and
exactly one 'bb' substring. "abb" has one 'bb' and one 'a' - valid. "abba"
, has one 'bb' and two 'a's - valid. "bba" has one 'bb' and one 'a' - valid.
"bab" has no 'bb' substring, so it is not in the language.
4. What is the primary limitation of finite automata that makes them
unable to recognize languages like {a^n b^n | n ≥ 1}?
A. They cannot read input symbols
B. They cannot count unbounded values
C. They cannot handle the alphabet {a,b}
D. They cannot accept the empty string
Correct Answer: B
Rationale: Finite automata have finite memory, meaning they cannot
track unbounded quantities. The language {a^n b^n | n ≥ 1} requires
matching the number of 'a's with the number of 'b's, which requires
unbounded counting. A finite automaton cannot perform this task.
5. A regular expression for all strings over {a,b} that have an even
number of a's is:
A. (b*ab*a)*
B. (b*ab*ab*)*
C. (a*b*a*)*
D. (b*a*b*a)*
Correct Answer: B
Preparation Pack 2026–2027 | Comprehensive
Theoretical Computer Science III Practice Questions
with Verified Answers & Explanations | Latest
COS3701 Syllabus & Exam Prep
Description:
This comprehensive exam preparation pack is designed to simulate the
COS3701 Theoretical Computer Science III examination for 2027, based
on the University of South Africa (UNISA) module . The module
focuses on enabling students to understand the concept of computability,
including context-free languages, recursively enumerable languages, and
the machines that accept them . The 120 multiple-choice questions cover
all key content areas including regular expressions and finite automata,
context-free grammars and Chomsky Normal Form, pushdown
automata, the pumping lemma, Turing machines, and computability
theory . Questions range from foundational recall to complex proof and
model construction scenarios, mirroring the official COS3701 exam
format . Actual COS3701 exams typically consist of 6 to 7 questions
worth 80 to 100 marks, with a 2-hour duration and IRIS invigilation .
COS3701 Theoretical Computer Science III Exam Preparation Pack
,Instructions: This is a closed-book examination with multiple-choice
questions. Select the single best answer for each question. Show all
working for proof and algorithm questions. The actual COS3701 exam
consists of questions covering regular expressions, DFA design, CFG
conversion to CNF, deterministic pushdown automata (DPDA), the
pumping lemma for CFLs, and Turing machine design . The exam is 2
hours and invigilated using the IRIS tool .
SECTION 1: REGULAR EXPRESSIONS AND FINITE AUTOMATA
(Questions 1-30)
1. Determine a regular expression for the language L over the alphabet
{a, b} that consists of all words that start with the substring ab, have one
or more bs, have at least two as, and have no bs after the two or more as.
Examples: abbaaa, abbbbbbaa .
A. ab{2,}(ba){2,}
B. ab+b*aa+
C. ab+aa+
D. ab+b*aa+ a*
Correct Answer: C
Rationale: The language requires words that start with "ab", followed by
one or more "b"s (b+), followed by two or more "a"s (aa+). There should
be no "b"s after the "a"s, so the string ends with the "a"s. The correct
regular expression is ab+aa+ which ensures at least one b between "ab"
and "aa", and at least two a's at the end.
,2. Design a deterministic finite automaton (DFA) that will recognise all
of the words in the language L from Question 1. What is the minimum
number of states required?
A. 3
B. 4
C. 5
D. 6
Correct Answer: C
Rationale: The language L = ab+aa+ requires states to track: reading "a"
(state A), reading "b" after "a" (state B), reading at least one additional
"b" (state C), reading the first "a" after the "b"s (state D), and reading at
least one more "a" (accepting state E). This requires 5 states plus a trap
state for invalid words.
3. Which of the following words is NOT in the language L = {w | w
contains at least one a and exactly one occurrence of the substring bb}?
A. abb
B. abba
C. bba
D. bab
Correct Answer: D
Rationale: The language requires words that have at least one 'a' and
exactly one 'bb' substring. "abb" has one 'bb' and one 'a' - valid. "abba"
, has one 'bb' and two 'a's - valid. "bba" has one 'bb' and one 'a' - valid.
"bab" has no 'bb' substring, so it is not in the language.
4. What is the primary limitation of finite automata that makes them
unable to recognize languages like {a^n b^n | n ≥ 1}?
A. They cannot read input symbols
B. They cannot count unbounded values
C. They cannot handle the alphabet {a,b}
D. They cannot accept the empty string
Correct Answer: B
Rationale: Finite automata have finite memory, meaning they cannot
track unbounded quantities. The language {a^n b^n | n ≥ 1} requires
matching the number of 'a's with the number of 'b's, which requires
unbounded counting. A finite automaton cannot perform this task.
5. A regular expression for all strings over {a,b} that have an even
number of a's is:
A. (b*ab*a)*
B. (b*ab*ab*)*
C. (a*b*a*)*
D. (b*a*b*a)*
Correct Answer: B
