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ASSIGNMENT 1: CSC 313: AUTOMATA THEORY
INSTRUCTIONS: Attempt all the questions. To be done in groups of 5 – 7 students. [30 Marks]
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Question One:
a) Describe what a pushdown automaton (PDA) is, distinguishing it from a deterministic finite automata
b) Let S be the set defined by 0, 3 ∈ S, and if x and y ∈ S, then x+y ∈ S.
Use mathematical induction to show that every natural number that is a multiple of 3 is an element of S
c) Show that the following language is context-free using the Pumping Lemma
L = { ( 0n 1n )n | n≥1 }
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Question Two:
a) Given the sets: U {1, 2, 3, 4, 5, 6, 7, 8} B {2, 3, 5, 6}
Set B is a subset of set U. What is the complement of set B?
b) In a group of 700 people 600 can speak English and 500 can speak Swahili. If all the people can speak at least one of the two languages, find:
i) How many can speak both languages?
ii) How many can speak exactly one language
Question Three:
a) Describe the language accepted by the following grammar
i. S → abS | a
ii. S → aSb | ε
b) Write the grammar for the following language expressions
i. axby, where x = 3y
ii. axby, where x = 2y
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