General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

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Chapter 1 Preface This Document This document contains the course notes for the course General Computer Science I & II held at Jacobs University Bremen 1 in the academic years 2003-2012. Contents: The document mixes the slides presented in class with comments of the instructor to give students a more complete background reference. Caveat: This document is made available for the students of this course only. It is still a draft and will develop over the course of the current course and in coming academic years. Licensing: This document is licensed under a Creative Commons license that requires attribution, allows commercial use, and allows derivative works as long as these are licensed under the same license. Knowledge Representation Experiment: This document is also an experiment in knowledge representation. Under the hood, it uses the STEX package [Koh08, Koh12], a TEX/L ATEX extension for semantic markup, which allows to export the contents into the eLearning platform PantaRhei. Comments and extensions are always welcome, please send them to the author. Other Resources: The course notes are complemented by a selection of problems (with and without solutions) that can be used for self-study. [Gen11a, Gen11b] Course Concept Aims: The course 320101/2 “General Computer Science I/II” (GenCS) is a two-semester course that is taught as a mandatory component of the “Computer Science” and “Electrical Engineering & Computer Science” majors (EECS) at Jacobs University. The course aims to give these students a solid (and somewhat theoretically oriented) foundation of the basic concepts and practices of computer science without becoming inaccessible to ambitious students of other majors. Context: As part of the EECS curriculum GenCS is complemented with a programming lab that teaches the basics of C and C ++ from a practical perspective and a “Computer Architecture” course in the first semester. As the programming lab is taught in three five-week blocks over the first semester, we cannot make use of it in GenCS. In the second year, GenCS, will be followed by a standard “Algorithms & Data structures” course and a “Formal Languages & Logics” course, which it must prepare. Prerequisites: The student body of Jacobs University is extremely diverse — in 2011, we have students from 110 nations on campus. In particular, GenCS students come from both sides of the “digital divide”: Previous CS exposure ranges “almost computer-illiterate” to “professional 1 International University Bremen until Fall 2006 i
Java programmer” on the practical level, and from “only calculus” to solid foundations in discrete Mathematics for the theoretical foundations. An important commonality of Jacobs students however is that they are bright, resourceful, and very motivated. As a consequence, the GenCS course does not make any assumptions about prior knowledge, and introduces all the necessary material, developing it from first principles. To compensate for this, the course progresses very rapidly and leaves much of the actual learning experience to homework problems and student-run tutorials. Course Contents To reach the aim of giving students a solid foundation of the basic concepts and practices of Computer Science we try to raise awareness for the three basic concepts of CS: “data/information”, “algorithms/programs” and “machines/computational devices” by studying various instances, exposing more and more characteristics as we go along. Computer Science: In accordance to the goal of teaching students to “think first” and to bring out the Science of CS, the general style of the exposition is rather theoretical; practical aspects are largely relegated to the homework exercises and tutorials. In particular, almost all relevant statements are proven mathematically to expose the underlying structures. GenCS is not a programming course: even though it covers all three major programming paradigms (imperative, functional, and declarative programming) 1 . The course uses SML as its primary pro- EdNote:1 gramming language as it offers a clean conceptualization of the fundamental concepts of recursion, and types. An added benefit is that SML is new to virtually all incoming Jacobs students and helps equalize opportunities. GenCS I (the first semester): is somewhat oriented towards computation and representation. In the first half of the semester the course introduces the dual concepts of induction and recursion, first on unary natural numbers, and then on arbitrary abstract data types, and legitimizes them by the Peano Axioms. The introduction and of the functional core of SML contrasts and explains this rather abstract development. To highlight the role of representation, we turn to Boolean expressions, propositional logic, and logical calculi in the second half of the semester. This gives the students a first glimpse at the syntax/semantics distinction at the heart of CS. GenCS II (the second semester): is more oriented towards exposing students to the realization of computational devices. The main part of the semester is taken up by a “building an abstract computer”, starting from combinational circuits, via a register machine which can be programmed in a simple assembler language, to a stack-based machine with a compiler for a bare-bones functional programming language. In contrast to the “computer architecture” course in the first semester, the GenCS exposition abstracts away from all physical and timing issues and considers circuits as labeled graphs. This reinforces the students’ grasp of the fundamental concepts and highlights complexity issues. The course then progresses to a brief introduction of Turing machines and discusses the fundamental limits of computation at a rather superficial level, which completes an introductory “tour de force” through the landscape of Computer Science. As a contrast to these foundational issues, we then turn practical introduce the architecture of the Internet and the World-Wide Web. The remaining time, is spent on studying one class algorithms (search algorithms) in more detail and introducing the notition of declarative programming that uses search and logical representation as a model of computation. Acknowledgments Materials: Some of the material in this course is based on course notes prepared by Andreas Birk, who held the course 320101/2 “General Computer Science” at IUB in the years 2001-03. Parts 1 EdNote: termrefs! ii
Page 1: General Computer Science 320201 Gen
Page 5 and 6: Contents 1 Preface i 2 Representati
Page 7 and 8: 4 Search and Declarative Computatio
Page 9 and 10: Fundamental Algorithms and Data str
Page 11 and 12: To earn an audit you have to take t
Page 13 and 14: i.e. to function as a member of the
Page 15 and 16: a factor two in speed. This ability
Page 17 and 18: “Applets, Not Craplets tm ” (-
Page 19 and 20: c○: Michael Kohlhase 17 Can be re
Page 21 and 22: Example 10 (Kruskal’s algorithm,
Page 23 and 24: n 100n µs 7n 2 µs 2 n µs 1 100
Page 25 and 26: 2.2 Elementary Discrete Math 2.2.1
Page 27 and 28: Axiom 19 (P 1) “ ” (aka. “zer
Page 29 and 30: Theorem 36 is a very useful fact to
Page 31 and 32: Definition 43 The unary product ope
Page 33 and 34: y stating element-hood (a ∈ S) or
Page 35 and 36: Idea: We need a notion of “counti
Page 37 and 38: Example 64 On sets of persons, the
Page 39 and 40: Definition 82 We say that a set A i
Page 41 and 42: clean enough to learn important con
Page 43 and 44: Definition 90 anonymous variables (
Page 45 and 46: c○: Michael Kohlhase 66 Defining
Page 47 and 48: - fun both_plus (x:int,y:int) = fn
Page 49 and 50: +(〈n, o〉) = n (base) and +(〈m
Page 51 and 52: the axiom says that any object that
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epresent them as a data type, where
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Example 127 〈{N}, {[o: N], [s: N
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The central idea here is what we ha
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Substitutions Definition 149 Let A
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Idea: Well-formed parts of construc
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Other programming languages chose a
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generally: fn+1 := fn + fn−1 plus
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input/output: the interesting bit a
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exception NaN; (* Not a Number *) f
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Example 191 If A = {a, b, c}, then
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Example 210 The Morse Code in the t
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The first 32 characters are control
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Idea: Unicode supports multiple enc
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2.5 Boolean Algebra We will now loo
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What a mess! Iϕ((x1 + x2) + (x1
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c○: Michael Kohlhase 140 The defi
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(f ≤a g), iff there is an n0 ∈
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P.1.2.3 then there are ei ∈ Ebool
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2.5.4 The Quine-McCluskey Algorithm
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the disjunctive normal form, and th
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Proof: by contradiction: let p /∈
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So, the minimal polynomial of f is
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2.6 Propositional Logic 2.6.1 Boole
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Idea: Import semantics from Boolean
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which we can always do, since we ha
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e quite difficult to establish in g
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H 0 axioms are valid Lemma 316 The
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c○: Michael Kohlhase 188 The enta
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The deduction theorem and the entai
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Inference with local hypotheses [A
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2.7 Machine-Oriented Calculi Now we
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Thus the tableau procedure can be u
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A ∨ BT AT BT A ⇒ BT AF BT
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Proof: P.1 It is easy to see tahat
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(P ⇒ Q ⇒ R) ⇒ (P ⇒ Q) ⇒ P
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⎧ ⎪⎨ We represented the maze
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defined a directed graph to be a se
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Paths in Graphs Definition 373 Giv
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This allows us to view Boolean expr
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Computing with Combinational Circui
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Corollary 399 A fully balanced tree
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X 1 X 2 X 3 X n = if L i =X i if L
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3.2 Arithmetic Circuits 3.2.1 Basic
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S S ψ ψ −1 fS = ψ −1 ◦ fT
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The Full Adder Definition 415 The
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first summand 3 4 7 9 8 3 4 7 9 2 s
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c○: Michael Kohlhase 249 The anal
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Problems of Sign-Bit Systems Gener
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generate the n-bit binary number re
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and an + bn + (icn(a, b, c)) = 〈
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Summary: We have built a combinatio
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To understand the operation of the
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Example 443 (Address decoder logic
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3.4 Computing Devices and Programmi
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Our notion of time is in this const
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instructions LOADIN 1 and LOADIN 2
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Definition 457 An ASM program VM is
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instruction effect VPC peek i push
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c○: Michael Kohlhase 289 With the
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Imperative Stack Operations: peek l
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A SW program (see the next slide fo
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arguments to arithmetic operations
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µML, a very simple Functional Prog
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call pushes the return address (of
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[proc 2 26, con 0, arg 2, leq, cjp
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[proc 2 26, con 0, arg 2, leq, cjp
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eturn takes the current frame from
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label instruction effect comment
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Compiling µML Expressions (Continu
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c○: Michael Kohlhase 325 We want
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State Machine: 1 1,R 1 1,R 1 1,L 1
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The coded description acts as a pro
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the turing function uses will_halt
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Terabyte (T B) 1,000,000,000,000 by
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Layers in TCP/IP: TCP/IP uses encap
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name comment 4 version IPv4 or IPv6
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Domain names must be registered to
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That was almost all, but we close t
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c○: Michael Kohlhase 353 Note tha
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Definition 529 HTTP is used by a cl
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structure html,head, body metadata
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Server-Side Scripting: Programming
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c○: Michael Kohlhase 367 Indeed,
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presentation tools), but can also i
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1. reads web page 2. reports it hom
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Definition 570 Let A be a web page
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can combine both to falsify communi
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Candidates for one-way/trapdoor fun
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on a UNIX system, you can create a
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conceptually: transfer of directed
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Definition 591 The XML path languag
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Resources: Globally Identified by U
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R⌉}〉∫⊔⌉∇⌉⌈√⊣∇
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Problem solving Problem: Find algo
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Single-state Problem: Start in 5
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States integer locations of tiles A
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Implementation: States vs. nodes A
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Breadth-First Search c○: Michael
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Breadth-First Search: Romania c○:
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Note: Equivalent to breadth-first s
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A B C D E F G H I J K L M N O Depth
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A B C D E F G H I J K L M N O Depth
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Iterative deepening search Depth-l
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Breadth-first search Iterative deep
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Sibiu 253 Greedy Search: Romania Ar
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P.2 Let n be an unexpanded node on
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A ∗ search: Properties Complete Y
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Definition 618 (n-queens problem) P
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escape certain odd phenomena occurr
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GAs = evolution: e.g., real genes e
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Definition 632 A query is a list of
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(autoload ’run-prolog "prolog" "S
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Example 638 Computing the the n th
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Deduction: knowledge extension Abd
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[Koh06] Michael Kohlhase. OMDoc - A
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astarSearch search, 255 asymmetric-
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infinite, 32 counter program, 152,
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functional variable, 170 gate, 122
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media access control address, 194 M
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procedure abstract, 54 procedure de
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function, 30 spanning tree, 13 spro
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name, 70 variable functional, 170 v
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General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

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