November 15

# November 15 - CSCI 2670 Introduction to Theory of Computing...

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CSCI 2670 Introduction to Theory of Computing November 15, 2005

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November 15, 2005 Agenda Today Comparing complexity of different computing models This week Finish 7.1 and do 7.2
November 15, 2005 Announcement Office hours changed tomorrow 11:30 to 1:00 instead of 11:00 – 12:30

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November 15, 2005 Analyzing algorithms We can examine an algorithm to determine how  long it will take to halt on an input of length n The amount of time to complete is called the  algorithms complexity class Definition:   Let t:N N be a function.  The time  complexity class, TIME(t(n)), is defined as  follows. TIME(t(n))={L|L is a language decided by an  O(t(n)) time TM}
November 15, 2005 Another example Finding minimum element in a set Amount of time depends on the  structure  of the  input If set is a sorted array? O(1) If set is an unsorted array? O(n) If set is a balanced sorted tree? O(log n)

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November 15, 2005 Importance of model The complexity of our algorithms depends on  assumptions The complexity of an algorithm can vary  depending on the machine we use Recall we assume reasonable encoding of all  numbers Any integer of value v should take   O(log v) space
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## This note was uploaded on 02/07/2011 for the course CS 501 taught by Professor Sm during the Spring '11 term at Indiana.

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November 15 - CSCI 2670 Introduction to Theory of Computing...

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