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

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

set, 26 empty string, 63 empty element, 225 empty clause, 112 enable input, 148 encoding character, 69 encryption asymmetric-key, 218 public-key, 218 end, 120 entails, 91 environment, 167 equality set, 26 equivalence relation, 29 equivalent, 74 equivalent, 75 essential, 85 evaluation function, 255 evaluation function, 73 exception handler, 61 exclusive or, 128 exponentiation unary, 23 expression, 164 expression label, 124 expression, 70 expression, 170 cost, 77 expressions Boolean, 123 extension, 65 fact, 265 false under ϕ, 91 falsifiable, 91 Fibonacci number, 57 sequence, 57 final state, 185 finite, 31 firmware, 155 first 279 depth ( search), 245 folding left ( operator), 40 right ( operator), 41 formal language, 64 formula labeled, 106 Propositional Logic formulation of, 90 formulation of Propositional Logic, 90 frame pointer, 178 fringe, 238 full adder, 134 function declaration, 35 selector, 36 function evaluation, 255 function result, 57 function sort, 47 function Boolean, 75 function evaluation, 73 interpretation, 73 function name, 70 function inverse, 31 function space, 30 function partial, 30 total, 30 function append, 44 function named, 170 function one-way, 219 trapdoor, 219 function transition, 185 composition, 32 cost, 77 functional programming language, 154
functional variable, 170 gate, 122 generate-and-test algorithm, 85 generate-and-test, 15 goal state, 233 goals, 266 Gottfried Wilhelm Leibniz, 93 graph isomorphism, 118 graph directed, 117 undirected, 117 graph directed, 116 undirected, 116 graph labeled, 119 graph, 10 depth, 121 greedy search, 253 ground constructor term, 48 ground, 51 half adder, 133 halting problem, 188 handled, 61 handler exception, 61 head, 48 heuristic, 253 hexadecimal numbers, 154 Horn clause, 271 HyperText Markup Language, 205 HyperText Markup Language, 206 Hypertext Transfer Protocol, 203 http request, 204 hyperlink, 201 hypertext, 201 hypotheses, 95 hypothetical reasoning, 103 280 IANA, 195 Internet Assigned Numbers Authority, 195 ICANN, 198 idempotent, 204 idiom math, 24 IETF, 200 Internet Engineering Task Force, 200 image, 32 immediate subterm, 54 imperative programming language, 154 implicant, 82 prime, 82 implicit definition, 27 implies, 82 in-degree, 116 index search, 215 indexing, 215 induced, 75 inductive, 37 inductively defined, 37 inference rule, 94 inference, 20 inference, 20 inference derived ( rule), 113 inference derived ( rule), 109 inference rule, 112 infinite chain, 57 infinite countably, 32 infinite precision integers, 59 initial, 118 initial state, 233 initial state, 185 injective, 31 input carry, 134 input borrow bit, 142
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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
Page 235 and 236: Resources: Globally Identified by U
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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
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: infinite, 32 counter program, 152,
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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