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

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Bibliography [AES01] Announcing the ADVANCED ENCRYPTION STANDARD (AES), 2001. [BAHS] Mark Birbeck, Ben Adida, Ivan Herman, and Manu Sporny. RDFa 1.1 primer. W3C Working Draft, World Wide Web Consortium (W3C). [BCHL09] Bert Bos, Tantek Celik, Ian Hickson, and Høakon Wium Lie. Cascading style sheets level 2 revision 1 (CSS 2.1) specification. W3C Candidate Recommendation, World Wide Web Consortium (W3C), 2009. [BLFM05] Tim Berners-Lee, Roy T. Fielding, and Larry Masinter. Uniform resource identifier (URI): Generic syntax. RFC 3986, Internet Engineering Task Force (IETF), 2005. [Chu36] Alonzo Church. A note on the Entscheidungsproblem. Journal of Symbolic Logic, pages 40–41, May 1936. [Den00] Peter Denning. Computer science: The discipline. In A. Ralston and D. Hemmendinger, editors, Encyclopedia of Computer Science, pages 405–419. Nature Publishing Group, 2000. [DH98] S. Deering and R. Hinden. Internet protocol, version 6 (IPv6) specification. RFC 2460, Internet Engineering Task Force (IETF), 1998. [Dij68] Edsger W. Dijkstra. Go to statement considered harmful. Communications of the ACM, 11(3):147–148, March 1968. [ECM09] ECMAScript language specification, December 2009. 5 th Edition. [FGM + 99] R. Fielding, J. Gettys, J. Mogul, H. Frystyk, L. Masinter, P. Leach, and T. Berners- Lee. Hypertext transfer protocol – HTTP/1.1. RFC 2616, Internet Engineering Task Force (IETF), 1999. [Gen11a] General Computer Science; Problems for 320101 GenCS I. Online practice problems at http://kwarc.info/teaching/GenCS1/problems.pdf, 2011. [Gen11b] General Computer Science: Problems for 320201 GenCS II. Online practice problems at http://kwarc.info/teaching/GenCS2/problems.pdf, 2011. [Hal74] Paul R. Halmos. Naive Set Theory. Springer Verlag, 1974. [HL11] Martin Hilbert and Priscila López. The world’s technological capacity to store, communicate, and compute information. Science, 331, feb 2011. [Hut07] Graham Hutton. Programming in Haskell. Cambridge University Press, 2007. [KC04] Graham Klyne and Jeremy J. Carroll. Resource Description Framework (RDF): Concepts and abstract syntax. W3C recommendation, World Wide Web Consortium (W3C), 2004. 273
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General Computer Science 320201 Gen
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Java programmer” on the practical
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Contents 1 Preface i 2 Representati
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4 Search and Declarative Computatio
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Fundamental Algorithms and Data str
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To earn an audit you have to take t
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i.e. to function as a member of the
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a factor two in speed. This ability
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“Applets, Not Craplets tm ” (-
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c○: Michael Kohlhase 17 Can be re
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Example 10 (Kruskal’s algorithm,
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n 100n µs 7n 2 µs 2 n µs 1 100
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2.2 Elementary Discrete Math 2.2.1
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Axiom 19 (P 1) “ ” (aka. “zer
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Theorem 36 is a very useful fact to
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Definition 43 The unary product ope
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y stating element-hood (a ∈ S) or
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Idea: We need a notion of “counti
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Example 64 On sets of persons, the
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Definition 82 We say that a set A i
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clean enough to learn important con
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Definition 90 anonymous variables (
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c○: Michael Kohlhase 66 Defining
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- fun both_plus (x:int,y:int) = fn
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+(〈n, o〉) = n (base) and +(〈m
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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
Page 229 and 230: on a UNIX system, you can create a
Page 231 and 232: conceptually: transfer of directed
Page 233 and 234: Definition 591 The XML path languag
Page 235 and 236: Resources: Globally Identified by U
Page 237 and 238: R⌉}〉∫⊔⌉∇⌉⌈√⊣∇
Page 239 and 240: Problem solving Problem: Find algo
Page 241 and 242: Single-state Problem: Start in 5
Page 243 and 244: States integer locations of tiles A
Page 245 and 246: Implementation: States vs. nodes A
Page 247 and 248: Breadth-First Search c○: Michael
Page 249 and 250: Breadth-First Search: Romania c○:
Page 251 and 252: Note: Equivalent to breadth-first s
Page 253 and 254: A B C D E F G H I J K L M N O Depth
Page 255 and 256: A B C D E F G H I J K L M N O Depth
Page 257 and 258: Iterative deepening search Depth-l
Page 259 and 260: Breadth-first search Iterative deep
Page 261 and 262: Sibiu 253 Greedy Search: Romania Ar
Page 263 and 264: P.2 Let n be an unexpanded node on
Page 265 and 266: A ∗ search: Properties Complete Y
Page 267 and 268: Definition 618 (n-queens problem) P
Page 269 and 270: escape certain odd phenomena occurr
Page 271 and 272: GAs = evolution: e.g., real genes e
Page 273 and 274: Definition 632 A query is a list of
Page 275 and 276: (autoload ’run-prolog "prolog" "S
Page 277 and 278: Example 638 Computing the the n th
Page 279: Deduction: knowledge extension Abd
Page 283 and 284: astarSearch search, 255 asymmetric-
Page 285 and 286: infinite, 32 counter program, 152,
Page 287 and 288: functional variable, 170 gate, 122
Page 289 and 290: media access control address, 194 M
Page 291 and 292: procedure abstract, 54 procedure de
Page 293 and 294: 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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