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Hein J.L. — Discrete Structures, Logic, and Computability
Hein J.L. — Discrete Structures, Logic, and Computability



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Название: Discrete Structures, Logic, and Computability

Автор: Hein J.L.

Аннотация:

Discrete Structure, Logic, and Computability introduces the beginning computer science student to some of the fundamental ideas and techniques used by computer scientists today, focusing on discrete structures, logic and computability. The emphasis is on the computational aspects, so that the reader can see how the concepts are actually used. Because of logic's fundamental importance to computer science, the topic is examined extensively in three phases which cover: informal logic; the technique of inductive proof; and formal logic and its applications to computer science.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 866

Добавлена в каталог: 29.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Countably infinite      99
Counterexample      6
Countermodel      362
Counting, bag combinations      265
Counting, bag permutations      259
Counting, combinations      261—265
Counting, difference rule      24
Counting, finite sets      21—24
Counting, inclusion exclusion principle      22
Counting, infinite sets      98—105
Counting, permutations      257—261
Counting, product rule      53
Counting, tuples      52—55
Counting, union of countable sets      100
Counting, union rule      22
cp      see “Conditional proof rule”
Cross product      32
CYCLE      45
Dag      see “Directed acyclic graph”
DD      see “Destructive dilemma”
De Morgans laws, Boolean algebra      521
De Morgans laws, logic      314
De Morgans laws, sets      21
Decidable      365 739
Decision problem      365 739
Decision tree      253—256
Decoding      559—561
Degree      45
Delete function      497
Delong, H.      846
Depth      48
Depth-first search strategy      488
Depth-first traversal      47
Deque      544
Derangement      273 295
Derivation      132 135
Derivation tree      131
Descartes, Rene      32
Descending chain      212
Description problem      503
Destructive dilemma      347
Destructors      114
Deterministic context-free language      659
Deterministic finite automaton      585
Deterministic finite automaton as an algebra      602
Deterministic PDA      643
Deterministic Turing machine      706
DFA      see “Deterministic finite automaton”
Diagonalization      103
dictionary order      221
Difference      19
Difference, counting rule      24
Digital circuit      522—527
Digital circuit, AND gate      522
Digital circuit, full adder      524
Digital circuit, gate      522
Digital circuit, half-adder      523
Digital circuit, logic gate      522
Digital circuit, NOT gate      522
Digital circuit, OR gate      522
Digraph      43
Dilemmas      347
Direct proof      7
Directed acyclic graph      45
Directed graph      43
Directed multigraph      43
Disagreement set      466
Disjoint sets      18
Disjunction      2 309
Disjunctive normal form      320
Disjunctive syllogism      331
Dist      see “Distribute function”
Distribute function      74 153
divides      5 211
Divisible      5
Division algorithm      67
Divisor      5
DNF      see “Disjunctive normal form”
Domain      61 359
Doyle, Arthur Conan      1
DS      see “Disjunctive syllogism”
Duality principle      519
EA      see “Equality axiom”
EDGE      41
EE      see “Equals for equals”
Effective enumeration      736—739
Effective enumeration, single variable computable functions      739
EG      see “Existential generalization”
EI      see “Existential instantiation”
Element      10 30
Ellipsis      11
Embedding      90
Empty clause      455
Empty list      34
Empty relation      41
Empty set      11
Empty string      36
Empty substitution      463
Empty tuple      31
Encoding      559—561
Epimorphism      567
Equal, bags      25
Equal, functions      63
Equal, regular expressions      580
Equal, sets      11
Equal, tuples      31
Equality      406—413
Equality, axiom      407
Equality, axioms for terms      407
Equality, basic      174
Equality, problem      192
Equality, relation      41
Equals for equals      407
Equipotent      92
Equivalence class      194
Equivalence of states      618
Equivalence problem      193 205 743
Equivalence relation      192—207
Equivalence relation, quotient      195
Equivalence relation, smallest      200
Equivalence, algebraic expressions      504
Equivalence, computational models      713
Equivalence, first-order predicate calculus      368
Equivalence, propositional calculus      313
Equivalence, Turing machines      704
Eratosthenes      167
Euclid      8 444
Euclid’s algorithm      67
Euler circuit      46
Euler path      46
Euler, L.      46
Event      267
Excluded middle, law of      349
Existential closure      364
Existential generalization      394
Existential instantiation      386
Existential quantifier      353
Expectation      271
Expected value      271
Expression      463
Expression, algebraic      504
Expression, lambda      754
Expression, reduction rule      751
Expression, rewrite rule      751
Expression, transformation rule      751
Extended context-sensitive grammar      751
Extensionality, principle of      408
Factorial function      151 555
Factoring      475
Family tree problem      450 473
Fibonacci numbers      149 169 171 243 247 282 295 557
Fibonacci, Leonardo      149
Field      514
FIFO property      539
Final state      585 621
Finite automata      584—624
Finite automata as output devices      597
Finite automata, accept      585 588
Finite automata, deterministic      585
Finite automata, equivalent states      618
Finite automata, final state      585
Finite automata, initial state      585
Finite automata, language of      585 588
Finite automata, linear bounded      748
Finite automata, Mealy machine      597
Finite automata, minimum-state DFAs      618
Finite automata, Moore machine      597
Finite automata, NFA for regular expression      609
Finite automata, NFA to DFA algorithm      614
Finite automata, NFA to regular grammar      628
Finite automata, nondeterministic      588
Finite automata, pushdown      642—657
Finite automata, regular grammar to NFA      630
Finite automata, reject      585 588
Finite automata, start state      585
Finite automata, state      585
Finite automata, state transition function      587 589
Finite automata, transition table      601 604
Finite set      12
Finite sums      278
First set      667
First-order logic      439
First-order predicate calculus      351—366
First-order predicate calculus, atomic formula, atom      356
First-order predicate calculus, equivalence      368—381
First-order predicate calculus, existential quantifier      353
First-order predicate calculus, formal proofs      382—400
First-order predicate calculus, literal      376
First-order predicate calculus, meaning, semantics      358—362
First-order predicate calculus, renaming rule      372 394
First-order predicate calculus, restricted equivalences      372—374
First-order predicate calculus, term      356
First-order predicate calculus, universal quantifier      353
First-order predicate calculus, validity      362—366
First-order predicate calculus, well-formed formula      356
First-order theory      405
First-order theory, partial order      411
First-order theory, with equality      406
Fischer, M.J.      205 846
Fixed point      76
Flagged variable      387
Flatten function      544
Floor function      65
Floyd, R.W.      186 433 846
Floyd’s algorithm      186
Follow set      668
Formal power series      283
Formal reasoning system      332
Formal theory      332
Formalizing English sentences      378—379
Four-color theorem      43
FP (functional programming language)      551
fp algebra      554
FP algebra, axioms      554
FP algebra, carriers      554
FP algebra, operations      554
Franklin, Benjamin      249
Free to replace      384
Free variable      358 755
Full adder      524
Full conjunctive normal form      322
Full disjunctive normal form      321
Function      60—95
Function constants      356
Function, argument of      61
Function, arity of      61
Function, codomain of      61
Function, composition      77
Function, definition by cases      63
Function, definition of      60
Function, domain of      61
Function, equality      63
Function, generating      282—293
Function, higher-order      83—88 157
Function, if-then-else      63
Function, image of      61
Function, partial      74
Function, partial recursive      723
Function, pre-image, inverse image of      62
Function, primitive recursive      722
Function, range of      61
Function, recursively defined      146—169
Function, total      74
Function, tupling      78
Function, type      61
Function, value of      61
Functional algebra      550—556
Fundamental conjunction      320
Fundamental disjunction      322
Fundamental Theorem of Arithmetic      237
Fuzzy logic      350
Galler, B.A.      205 846
Gallier, J.      476 849
Gate      522
Gauss, Karl Friedrich      233
GCD      see “Greatest common divisor”
Generalized list      35
Generating equivalence relations      200—204
Generating function      282—293 515
Generator of a binary relation      179
Gentzen, G.      366 846
Geometric progression      235
Geometric series      283
Geometry      444
Gib      see “Greatest lower bound”
Goal      451 479
Godel numbering      714
Godel, K.      404 443 714 846
Goethe, Johann Wolfgang von      449
Graham, R.L.      304 846
Grammar      130—144
Grammar, abstract syntax tree      144
Grammar, ambiguous      143
Grammar, combining rules      139
Grammar, context-free      640
Grammar, derivation      132 135
Grammar, extended context-sensitive      751
Grammar, four parts      134
Grammar, language of      136
Grammar, left factoring      661
Grammar, left-recursive      662
Grammar, leftmost derivation      136
Grammar, LL(k)      659
Grammar, LR(1)      674
Grammar, LR(K)      672 674
Grammar, nonterminals      134
Grammar, parse or derivation tree      131
Grammar, phrase-structure      749
Grammar, production      132
Grammar, recursive      137
Grammar, recursive production      137
grammar, regular      626
Grammar, rightmost derivation      136
Grammar, rule or production      132
Grammar, sentential form      135
Grammar, start symbol      132 134
Grammar, terminals      134
Grammar, type 0      751
Grammar, type 1      751
Grammar, type 2      751
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