ASSIGNMENT No. 1
(Units: 1–4)
Note: All questions are compulsory. All questions carry equal marks.
Q. 1 (a) Explain the following terms:
i) Automata
ii) Set theory
(b) For the following relations between sets A and B mention if they are one to one and/or onto:
A = {a, b, c} B = {1, 2, 3}
i) {(a, 1), (b, 1), (c, 1)}
ii) {(a, 2), (b, 2), (c, 2)}
iii) {(a, 1), (a, 2), (b, 2), (c, 3)}
iv) {(a, 2), (b, 1), (c, 2)}
Q. 2 (a) Consider the language S*, where S= {aa b}. How many words does this language have of
length 4? Of length 5? What can be said in general?
(b) Construct a regular expression defining each of the following languages over the alphabet ∑
= {a b}:
i) All words in which a appears tripled, if at all. This means that every clump of a’s
contains 3 or 6 or 9 or 12… a’s.
ii) All strings that have exactly one double letter in them.
iii) All words that contain exactly two b’s or exactly three b’s, not more.
Q. 3 (a) What is the relationship between regular languages and context free grammars? Discuss
them? Construct a language that can be generated by CFG.
(b) Consider the Context Free Grammar
S a X X a x | b X | Λ Y b b b
(a +b) * b b b (a + b) *
Q. 4 (a) Construct an example DFA? Write down the steps to convert FA into DFA.
(b) Construct DFA for the following regular expression: (a / b) * a b *.
Q. 5 Define and explain the following terms.
(a) Context Free Grammar
(b) Regular Expression
(c) Context Free Language
(d) Deterministic Finite Automata
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