TAILIEUCHUNG - lecture 6 2012

A computer is a general purpose device that can be programmed to carry out a finite set of arithmetic or logical operations. Since a sequence of operations can be readily changed, the computer can solve more than one kind of problem. | Lecture Notes for CS120 An Introduction to Computing1 Subhashis Banerjee S. Arun-Kumar Department of Computer Science and Engineering Indian Institute of Technology New Delhi 110016 email suban sak @ August 2 2003 1Copyright 1997-2003 Subhashis Banerjee and S. Arun-Kumar. All Rights Reserved. These notes may be used in an academic course with the prior consent of the authors. 2 Contents I Models of computation 5 1 Introduction 7 2 Mathematical preliminaries 9 Sets. 9 Relations and Functions. 11 Principle of Mathematical Induction. 11 3 A functional model of computation 17 The primitive expressions. 18 Substitution of functions. 20 Substitution using let. 21 Definition of functions using conditionals. 23 Functions as inductively defined computational processes . 24 Recursive processes. 26 Analysis of correctness and efficiency. 28 Correctness. 28 Efficiency . 28 Efficiency Why and How . 29 In the long run Asymptotic analysis and Orders of growth . 30 More examples of recursive algorithms. 31 Scope rules. 41 Tail-recursion and iterative processes. 43 Correctness of an iterative process. 45 More examples of iterative processes. 46 4 The Imperative model of computation 53 The primitives for the imperative model . 53 Variables and the assignment instruction . 54 Assertions . 56 The if then else instruction. 58 The while do instruction. 61

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