1 CMSC 28100 Introduction to Complexity Theory

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1 CMSC 28100 Introduction to Complexity Theory

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1 CMSC 28100 Introduction to Complexity Theory Spring 2025 Instructor: William Hoza Which problems can be solved through computation? 2 3 4 5 Which problems can be solved through computation? 6 7 Example 1: Primality testing 8 9 10 11 12 B:

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1 CMSC 28100Introduction to Complexity TheorySpring 2025Instructor: William Hoza

Which problemscan be solvedthrough computation? 2

3

4

5

Which problemscan be solvedthrough computation? 6

7

Example 1: Primality testing 8

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12 B: False D: It’s not well-defined A: True

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Time complexity: Theory vs. practice 15

Is the Turing machine model a good model? 16

Multi-tape Turing machines, revisited 17

18 1 1 0 0 # 1 $ 0

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Word RAM model (RAM = Random Access Machine) 20 +, -, *, /, %, ==, <, >, &&, ||, &, |, ^, <<, >> (The details are not completely standardized. This is just one reasonable version of the model)

Word RAM model 21

Word RAM model 22

Word RAM model 23 The version of the word RAM model described here is based on the lecture notes for CS 1200 at Harvard: https://harvard-cs-1200.github.io/cs1200/

Word RAM model 24 The version of the word RAM model described here is based on the lecture notes for CS 1200 at Harvard: https://harvard-cs-1200.github.io/cs1200/

Word RAM model Word RAM time complexity closely matches time complexity “in practice” on ordinary computers
Some version of the word RAM model is typically assumed (implicitly or explicitly) in algorithms courses and the computing industry 25

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1 CMSC 28100 Introduction to Complexity Theory

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