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COMP11212 Fundamentals of Computation.pdf
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COMP11212Two hours
UNIVERSITY OF MANCHESTER
SCHOOL OF COMPUTER SCIENCE
Fundamentals of Computation
Date: Thursday 26th May 2016
Time: 09:45 - 11:45
Please answer any THREE Questions from the FOUR Questions provided.
Use a SEPARATE answerbook for each SECTION.
This is a CLOSED book examination
The use of electronic calculators is NOT permitted
[PTO]
, COMP11212
Section A
1. a) Consider the language L of all words over the alphabet {a, b, c} in which every
occurrence of the letter b is both preceded and followed by the letter a.
Give a description of L via the following means:
i) using a DFA (3 marks)
ii) using a grammar (2 marks)
iii) using a regular expression (2 marks)
iv) using the language of set theory (2 marks)
b) Give a DFA for the language of all words over the alphabet {a, b, c} that match the
regular expression
a∗ bc∗ | ab∗ c
(8 marks)
c) For a language L over an alphabet Σ, we can construct the language L R :
L R = {xn xn−1 · · · x2 x1 | x1 x2 · · · xn−1 xn ∈ L }.
Proposition: For every regular language L1 , the language L1R is also regular.
Sketch out a proof for the above proposition. (3 marks)
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