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

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

terminates, 57 test calculi, 108 text node, 225 theorem, 95 theorem, 20 theorem, 20 theory complexity, 16 third party cookies, 210 TLD, 197 top-level domain, 197 total function, 30 total, 29 transition function, 185 transitive, 29 transport layer, 196 trapdoor, 219 function, 219 tree binary, 125 tree spanning, 13 tree, 121 true under ϕ, 91 Turing complete, 187 Turing universal ( machine), 187 Turing Machine, 185 machine specification, 185 twelve, 21 two, 21 two’s complement, 140 type, 35 basic, 34 basic ( constructor), 34 declaration, 35 universal, 36 Universal Character Set, 69 User Datagram Protocol, 196 unary exponentiation, 23 multiplication, 23 product, 24 summation, 23 unary 287 natural numbers, 19 undefined at, 30 underflow, 145 undirected graph, 117 undirected edge, 116 graph, 116 Unicode Standard, 69 uniform resource identifier, 201 uniform resource locator, 202 name, 202 union, 26 union over a collection, 26 Union-Find, 14 Algorithm Union Find, 14 Union Find Algorithm, 14 universal type, 36 universal Turing machine, 187 universe, 73 unsatisfiable, 91 unsatisfiable, 112 URI relative, 201 URI, 201 URL, 202 URN, 202 user agent, 204 UTM, 187 valid, 91 value declaration, 35 value start, 40 variable named, 164 variable list, 75 variable assignment, 73 variable
name, 70 variable functional, 170 variable, 51 variables anonymous, 36 vector, 26 vernacular mathematical, 24 depth, 120 virtual machine, 157 virtual program counter, 158 visualization, 12 VM Arithmetic Commands, 158 control operator, 159 operator control, 159 imperative access to variables, 159 machine virtual, 158 virtual machine, 158 VPC, 158 web server, 204 web search query, 214 web resource, 201 web application, 209 framework, 209 web Browser, 203 web crawler, 213 web search engine, 212 web server, 204 web page, 200 site, 200 spider, 213 Wilhelm Schickard, 93 word, 157 word, 152 worked off, 111 288 WWW, 191 World Wide Web, 191 XML document tree, 225 XML path language, 226 zero, 21
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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
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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
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 and 280: Deduction: knowledge extension Abd
Page 281 and 282: [Koh06] Michael Kohlhase. OMDoc - A
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: function, 30 spanning tree, 13 spro
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General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

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