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

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Index abstract Program, 54 procedure, 54 abstract data type, 47 abstract call-by-value interpreter, 55 abstract computation, 49 interpreter, 49 access random ( memory), 153 accumulator, 152, 153 action table, 185 acyclic, 120 adder carry chain, 135 adder conditional sum, 136 adder full, 134 adder half, 133 adder, 133 addition carry chain, 132 rules, 132 addition operation, 23 address decoder, 149 address IPv4, 195 IPv6, 195 address MAC, 194 admissible, 255 admissible, 95 advanced query operator, 214 agent 275 user, 204 algebra Boolean, 74 algorithm generate-and-test, 85 algorithm, 13 search algorithm, 231 algorithm, 14 alphabet, 63 ALU, 146 ALU, 154 ALU, 152, 153 anchor cell, 178 anonymous variables, 36 answer substitution, 266 antisymmetric, 29 append function, 44 application layer, 197 application web, 209 web ( framework), 209 argument, 50 arithmetic logic unit, 146 arithmetic, 92 arithmetic logic unit, 146 American Standard Code for Information Interchange, 67 assembler, 157 assembler language, 154 assembler language, 152 assignment variable, 73 assumption, 94
astarSearch search, 255 asymmetric-key encryption, 218 asymptotically bounded, 77 asynchronous, 149 atom, 90 atom, 106 atomic, 106 attribute, 225 node, 225 authority certificate, 221 axiom, 94 axiom, 20 Axioms Peano, 48 balanced bracketing structure, 225 base, 130 base sort, 47 base case, 22 condition, 22 base condition, 20 base knowledge, 265 basic operator, 34 type, 34 constructor, 34 basic multilingual plane, 69 bijection, 131 bijective, 31 binary tree, 125 binary, 65 binary natural number, 139 bit carry, 133 sum, 133 bit most significant, 139 sign, 139 Blaise Pascal, 93 Boolean 276 algebra, 74 Boolean function, 75 Boolean polynomial, 76 Boolean sum, 73 Boolean expressions, 123 bootstrapping process, 131 borrow input ( bit), 142 bounded asymptotically, 77 bracketing balanced ( structure), 225 Browser web, 203 browsing, 201 byte code, 167 byte code, 157 calculus, 94 calculus resolution, 112 call-by-value abstract ( interpreter), 55 canonical product, 77 sum, 77 set, 25 card punch, 68 cardinality, 31 carry input, 134 carry bit, 133 carry chain adder, 135 carry chain addition, 132 Cartesian product, 26 case base, 22 step, 22 cell anchor, 178 internal, 178 certificate
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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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Page 233 and 234: 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
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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: [Koh06] Michael Kohlhase. OMDoc - A
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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