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

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$Mathematical Documents want to Active Digital Math ... - Kwarc$

Server: Apache/2.2.9 (Debian) DAV/2 SVN/1.5.1 mod_fastcgi/2.4.6 PHP/5.2.6-1+lenny8 with Suhosin-Patch mod_python/3.3.1 Python/2.5.2 mod_ssl/2.2.9 OpenSSL/0.9.8g Last-Modified: Sun, 02 May 2010 13:09:19 GMT ETag: "1c78b-db1-4859c2f221dc0" Accept-Ranges: bytes Content-Length: 3505 Content-Type: text/html ... c○: Michael Kohlhase 359 Multimedia Documents on the World Wide Web We have seen the client-server infrastructure of the WWWeb, which essentially specifies how hypertext documents are retrieved. Now we look into the documents themselves. In Subsection 2.4.2 have already discussed how texts can be encoded in files. But for the rich docments we see on the WWWeb, we have to realize that documents are more than just sequences of characters. This is traditionally captured in the notion of document markup. Document Markup Definition 534 (Document Markup) Document markupmarkup is the process of adding codes (special, standardized character sequences) to a document to control the structure, formatting, or the relationship among its parts. Example 535 A text with markup codes (for printing) c○: Michael Kohlhase 360 There are many systems for document markup ranging from informal ones as in Definition 534 that specify the intended document appearance to humans – in this case the printer – to technical ones which can be understood by machines but serving the same purpose. WWWeb documents have a specialized markup language that mixes markup for document structure with layout markup, hyper-references, and interaction. The HTML markup elements always concern text fragments, they can be nested but may not otherwise overlap. This essentially turns a text into a document tree. HTML: Hypertext Markup Language Definition 536 The HyperText Markup Language (HTML), is a representation format for web pages. Current version 4.01 is defined in [RHJ98]. Definition 537 (Main markup elements of HTML) HTML marks up the structure and appearance of text with tags of the form (begin) and (end), where el is one of the following 205
structure html,head, body metadata title, link, meta headings h1, h2, . . . , h6 paragraphs p, br lists ul, ol, dl, . . . , li hyperlinks a images img tables table, th, tr, td, . . . styling style, div, span old style b, u, tt, i, . . . interaction script forms form, input, button Example 538 A (very simple) HTML file with a single paragraph. Hello <strong>GenCS</strong> students! c○: Michael Kohlhase 361 HTML was created in 1990 and standardized in version 4 in 1997. Since then there has HTML has been basically stable, even though the WWWeb has evolved considerably from a web of static web pages to a Web in which highly dynamic web pages become user interfaces for web-based applications and even mobile applets. Acknowledging the growing discrepancy, the W3C has started the standardization of version 5 of HTML. HTML5: The Next Generation HTML Definition 539 The HyperText Markup Language (HTML5), is believed to be the next generation of HTML. It is defined by the W3C and the WhatWG. HTML5 includes support for audio/video without plugins, a canvas element for scriptable, 2D, bitmapped graphics SV G for Scalable Vector Graphics MathML inline and display-style mathematical formulae The W3C is expected to issue a “recommendation” that standardizes HTML5 in 2014. Even though HTML5 is not formally standardized yet, almost all major web browsers already implement almost all of HTML5. c○: Michael Kohlhase 362 As the WWWeb evolved from a hypertext system purely aimed at human readers to an Web of multimedia documents, where machines perform added-value services like searching or aggregating, it became more important that machines could understand critical aspects web pages. One way to facilitate this is to separate markup that specifies the content and functionality from markup that specifies human-oriented layout and presentation (together called “styling”). This is what “cascading style sheets” set out to do. Another motivation for CSS is that we often want the styling of a web page to be customizable (e.g. for vision-impaired readers). CSS: Cascading Style Sheets Idea: Separate structure/function from appearance. Definition 540 The Cascading Style Sheets (CSS), is a style sheet language that allows authors and users to attach style (e.g., fonts and spacing) to structured documents. Current version 2.1 is defined in [BCHL09]. 206
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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
Page 161 and 162: Our notion of time is in this const
Page 163 and 164: instructions LOADIN 1 and LOADIN 2
Page 165 and 166: Definition 457 An ASM program VM is
Page 167 and 168: instruction effect VPC peek i push
Page 169 and 170: c○: Michael Kohlhase 289 With the
Page 171 and 172: Imperative Stack Operations: peek l
Page 173 and 174: A SW program (see the next slide fo
Page 175 and 176: arguments to arithmetic operations
Page 177 and 178: µML, a very simple Functional Prog
Page 179 and 180: call pushes the return address (of
Page 181 and 182: [proc 2 26, con 0, arg 2, leq, cjp
Page 183 and 184: [proc 2 26, con 0, arg 2, leq, cjp
Page 185 and 186: eturn takes the current frame from
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Page 189 and 190: Compiling µML Expressions (Continu
Page 191 and 192: c○: Michael Kohlhase 325 We want
Page 193 and 194: State Machine: 1 1,R 1 1,R 1 1,L 1
Page 195 and 196: The coded description acts as a pro
Page 197 and 198: the turing function uses will_halt
Page 199 and 200: Terabyte (T B) 1,000,000,000,000 by
Page 201 and 202: Layers in TCP/IP: TCP/IP uses encap
Page 203 and 204: name comment 4 version IPv4 or IPv6
Page 205 and 206: Domain names must be registered to
Page 207 and 208: That was almost all, but we close t
Page 209 and 210: c○: Michael Kohlhase 353 Note tha
Page 211: Definition 529 HTTP is used by a cl
Page 215 and 216: Server-Side Scripting: Programming
Page 217 and 218: c○: Michael Kohlhase 367 Indeed,
Page 219 and 220: presentation tools), but can also i
Page 221 and 222: 1. reads web page 2. reports it hom
Page 223 and 224: Definition 570 Let A be a web page
Page 225 and 226: can combine both to falsify communi
Page 227 and 228: 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
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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
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Page 257 and 258: Iterative deepening search Depth-l
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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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