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

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

document ( model), 225 object document ( model), 211 off worked, 111 offline problem solving, 231 on relation, 29 on strings code, 66 one, 21 one-way function, 219 opening tag, 225 operation addition, 23 operator basic, 34 operator, 233 or exclusive, 128 order lexical, 64 order linear, 29 partial, 29 ordered pair, 116, 117 out-degree, 116 output, 164 overflow, 145 packet IP, 195 packet-switched network, 193 packets network, 193 page web, 200 pair ordered, 116, 117 pair, 26 parent, 121 parse-tree, 122 partial function, 30 partial order, 29 path, 120 path 283 XML ( language), 226 pattern matching, 36 Peano Axioms, 48 Peano Axioms, 19 plaintext, 218 Predicate Logic without Quantifiers, 90 point code, 69 pointer frame, 178 pointer stack, 161 polarity, 139 polynomial Boolean, 76 polynomial minimal, 128 port, 196 positional number system, 130 postulate, 20 power set, 26 pre-image, 32 predecessor, 19 prefix code, 66 prefix, 64 proper, 64 abstract procedure, 49 procedure abstract, 49 argument sort, 49 sort argument, 49 result sort, 49 sort result, 49 rule, 49 prime implicant, 82 PIT, 85 private key, 218 problem halting, 188 problem offline ( solving), 231
procedure abstract, 54 procedure declaration, 53 process bootstrapping, 131 product sort, 47 product term, 76 product, 73 product unary, 24 product canonical, 77 product Cartesian, 26 product of sums, 76 sums product of, 76 Program abstract, 54 program instruction, 154 program, 152 counter, 152, 153 store, 152 program store, 158 programming functional ( language), 154 imperative ( language), 154 Proof, 94 proof, 95 proof, 20 proof, 20 proof tableau, 107 constructive proof, 79 proper prefix, 64 proper subset, 26 proper superset, 26 proposition, 90 T0-theorem, 107 public key certificate, 221 public key, 218 public-key encryption, 218 pull-back, 131 284 pull-back, 133 punch card, 68 query, 266 query advanced ( operator), 214 Quine-McCluskey, 128 radix, 130 raised, 61 RAM, 152, 153 memory random access, 152 random access memory, 152 random access memory, 153 reasoning logical, 20 reasoning hypothetical, 103 recipe, 14 recursion relation, 56 step, 56 recursive, 37 recursive, 56 reflexive, 29 refutation resolution, 112 refutation tableau, 107 register, 152, 153 machine, 152, 153 register state, 185 relation recursion, 56 relation, 118 relation equivalence, 29 relation, 29 on, 29 relative URI, 201 representation, 10 request http, 204 resolve, 87 resolution calculus, 112 refutation, 112
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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⌉}〉∫⊔⌉∇⌉⌈√⊣∇
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 and 286: infinite, 32 counter program, 152,
Page 287 and 288: functional variable, 170 gate, 122
Page 289: media access control address, 194 M
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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