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ASSIGNMENT 1: AUTOMATA THEORY

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ASSIGNMENT 1: CSC 313: AUTOMATA THEORY

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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Details of the Intelligent System
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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

ASSIGNMENT 1: CSC 313: AUTOMATA THEORY
ASSIGNMENT 1: CSC 313: AUTOMATA THEORY


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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