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

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Homework assignments Goal: Reinforce and apply what is taught in class. Homeworks: will be small individual problem/programming/proof assignments (but take time to solve) group submission if and only if explicitly permitted Admin: To keep things running smoothly Homeworks will be posted on PantaRhei Homeworks are handed in electronically in grader (plain text, Postscript, PDF,. . . ) go to the tutorials, discuss with your TA (they are there for you!) materials: sometimes posted ahead of time; then read before class, prepare questions, bring printout to class to take notes Homework Discipline: start early! (many assignments need more than one evening’s work) Don’t start by sitting at a blank screen Humans will be trying to understand the text/code/math when grading it. c○: Michael Kohlhase 4 Homework assignments are a central part of the course, they allow you to review the concepts covered in class, and practice using them. Homework Submissions, Grading, Tutorials Submissions: We use Heinrich Stamerjohanns’ grader system submit all homework assignments electronically to https://jgrader.de you can login with you Jacobs account (should have one!) feedback/grades to your submissions get an overview over how you are doing! (do not leave to midterm) Tutorials: select a tutorial group and actually go to it regularly to discuss the course topics after class (<strong>GenCS</strong> needs pre/postparation) to discuss your homework after submission (to see what was the problem) to find a study group (probably the most determining factor of success) c○: Michael Kohlhase 5 The next topic is very important, you should take this very seriously, even if you think that this is just a self-serving regulation made by the faculty. All societies have their rules, written and unwritten ones, which serve as a social contract among its members, protect their interestes, and optimize the functioning of the society as a whole. This is also true for the community of scientists worldwide. This society is special, since it balances intense cooperation on joint issues with fierce competition. Most of the rules are largely unwritten; you are expected to follow them anyway. The code of academic integrity at Jacobs is an attempt to put some of the aspects into writing. It is an essential part of your academic education that you learn to behave like academics, 5
i.e. to function as a member of the academic community. Even if you do not want to become a scientist in the end, you should be aware that many of the people you are dealing with have gone through an academic education and expect that you (as a graduate of Jacobs) will behave by these rules. The Code of Academic Integrity Jacobs has a “Code of Academic Integrity” this is a document passed by the faculty (our law of the university) you have signed it last week (we take this seriously) It mandates good behavior and penalizes bad from both faculty and students honest academic behavior (we don’t cheat) respect and protect the intellectual property of others (no plagiarism) treat all Jacobs members equally (no favoritism) this is to protect you and build an atmosphere of mutual respect academic societies thrive on reputation and respect as primary currency The Reasonable Person Principle (one lubricant of academia) we treat each other as reasonable persons the other’s requests and needs are reasonable until proven otherwise c○: Michael Kohlhase 6 To understand the rules of academic societies it is central to realize that these communities are driven by economic considerations of their members. However, in academic societies, the primary good that is produced and consumed consists in ideas and knowledge, and the primary currency involved is academic reputation 2 . Even though academic societies may seem as altruistic — scientists share their knowledge freely, even investing time to help their peers understand the concepts more deeply — it is useful to realize that this behavior is just one half of an economic transaction. By publishing their ideas and results, scientists sell their goods for reputation. Of course, this can only work if ideas and facts are attributed to their original creators (who gain reputation by being cited). You will see that scientists can become quite fierce and downright nasty when confronted with behavior that does not respect other’s intellectual property. One special case of academic rules that affects students is the question of cheating, which we will cover next. Cheating [adapted from CMU:15-211 (P. Lee, 2003)] There is no need to cheat in this course!! (hard work will do) cheating prevents you from learning (you are cutting your own flesh) if you are in trouble, come and talk to me (I am here to help you) We expect you to know what is useful collaboration and what is cheating you will be required to hand in your own original code/text/math for all assignments 2 Of course, this is a very simplistic attempt to explain academic societies, and there are many other factors at work there. For instance, it is possible to convert reputation into money: if you are a famous scientist, you may get a well-paying job at a good university,. . . 6
Page 1 and 2: General Computer Science 320201 Gen
Page 3 and 4: Java programmer” on the practical
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: To earn an audit you have to take t
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
Page 53 and 54: epresent them as a data type, where
Page 55 and 56: Example 127 〈{N}, {[o: N], [s: N
Page 57 and 58: The central idea here is what we ha
Page 59 and 60: Substitutions Definition 149 Let A
Page 61 and 62: 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
Page 295:
name, 70 variable functional, 170 v
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General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

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