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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
$\alpha$-conversion      758
$\beta$-reduction      759
$\eta$-reduction      759
$\lambda$-conversion      758
$\lambda$-conversion, $\beta$-reduction      759
$\lambda$-conversion, $\eta$-reduction      759
$\lambda$-conversion, application      754
$\lambda$-conversion, applicative order reduction      757
$\lambda$-conversion, bound variable      755
$\lambda$-conversion, closed expression      755
$\lambda$-conversion, combinator      755
$\lambda$-conversion, free variable      755
$\lambda$-conversion, innermost redex      757
$\lambda$-conversion, lambda expression      754
$\lambda$-conversion, normal form      756
$\lambda$-conversion, normal order reduction      757
$\lambda$-conversion, outermost redex      757
$\lambda$-conversion, redex      756
$\lambda$-conversion, scope      755
$\lambda$-conversion, weak-head normal form      765
$\lambda$-conversion, Y combinator      764
AA      see “Assignment axiom”
AAA      see “Array assignment axiom”
Absorption laws, Boolean algebra      520
Absorption laws, logic      314
Absorption laws, sets      21 28
Abstract algebra      508
Abstract data type      529—543
Abstract data type, binary trees      541
Abstract data type, lists      534
Abstract data type, natural numbers      530
Abstract data type, priority queues      542
Abstract data type, queues      539
Abstract data type, stacks      537
Abstract data type, strings      536
Abstract syntax tree      144
Abstraction      754
ACCEPT      585 588 644 699
Accumulating parameter      247
Ackermann, W.      343 846
Ackermann’s function      246 723
action      548
Acyclic graph      45
Add      see “Addition rule”
Addition rule      331
Adjacency matrix      184
Adjacent vertices      41
Ait-Kaci, H.      772 845
Al-Khowarizmi      501
Algebra      501—573
Algebra of matrices      514
Algebra of polynomials      514
Algebra of power series      515
Algebra of vectors      514
Algebra, abstract      508
Algebra, abstract data type      529
Algebra, boolean      516—528
Algebra, carrier of      504
Algebra, concrete      508
Algebra, definition of      504
Algebra, expression      504
Algebra, field      514
Algebra, functional      550
Algebra, group      511
Algebra, groupiod      511
Algebra, high school      503
Algebra, moniod      511
Algebra, morphism      564
Algebra, process      548
Algebra, quotient of      562
Algebra, regular expressions      577
Algebra, relational      546
Algebra, ring      513
Algebra, semigroup      511
Algebra, signature of      505
Algebra, subalgebra of      563
Algebraic expression      504
Algorithm      501
Alphabet      36
Ambiguous grammar      143
AND      see “Conjunction”
AND gate      522
Andrews, P.B.      845
Antecedent      309 329
antisymmetric      175
AOR      see “Applicative order reduction”
Appel, K.      43 845
Append operation      118
Applicative order reduction      757
apply function      85
Applying a substitution      463
ApplyToAll function      84
Apt, K.R.      433 845
Arithmetic progression      233
Arity      61
Array assignment axiom      428
Artin, Emil      221
Ascending chain      212
Assignment axiom      416
Asymptotic behavior      296
atom      356 450
Atomic formula      356
Attributes      39
Automata      see “Finite automata” “Pushdown
Average case optimal algorithm      271
Axiom      332
Backtracking      489
Backus — Naur form      144
Backus, J.      551 845
Backwards check      393
Bag      24
Bag, combinations      265
Bag, intersection      25
Bag, permutations      259
Bag, subbag      25
Bag, sum      25
Bag, union      25
Balanced parentheses      729
Basic equality      174
Basis of mathematical induction      230
Bendix, P.      772 847
Bernstein, F.      101
Best operation      542
Better operation      543 545
BIFO property      542
Big oh      301
Big Omega      301
Big theta      296
Bijection      92
Bijective function      92
binary function      61
Binary relation      41 174—227
Binary relation, antisymmetric      175
Binary relation, basic equality      174
Binary relation, closure      179—183
Binary relation, composition      175
Binary relation, converse      180
Binary relation, equivalence      192—207
Binary relation, generator of      179
Binary relation, irreflexive      175
Binary relation, kernel      202
Binary relation, linear order      211
Binary relation, partial order      210—227
Binary relation, reflexive      174
Binary relation, reflexive closure      179
Binary relation, symmetric      174
Binary relation, symmetric closure      179
Binary relation, total order      211
Binary relation, transitive      174
Binary relation, transitive closure      179
Binary resolution      475
Binary search      254
Binary search tree      51 159
Binary tree      51—52 120—122 159—162 541—542
Binary tree, inorder traversal      162
Binary tree, left subtree      50
Binary tree, postorder traversal      162
Binary tree, preorder traversal      161
Binary tree, right subtree      50
Binding      359 463
Binomial coefficient      262
Birthday problem      268
BNF      see “Backus — Naur form”
Boole, George      516
Boolean algebra      516—528
Boolean algebra, absorption laws      520
Boolean algebra, axioms      517
Boolean algebra, complement      517
Boolean algebra, De Morgan’s laws      521
Boolean algebra, digital circuits      522—527
Boolean algebra, duality principle      519
Boolean algebra, idempotent properties      519
Boolean algebra, involution      521
Boolean algebra, minimal CNF      527
Boolean algebra, minimal DNF      527
Boolean algebra, negation      517
Boolean algebra, properties      527
Boolean algebra, simplifying expressions      518—522
Boolean type      760
Bottom-up parsing      659
Bound variable      358 755
Boyle, J.      475 849
Branch      48
Brassard, G.      845
Bratley, P.      845
Breadth-first search strategy      492
Breadth-first traversal      46
Burke, Edmund      173
Burton, David F.      501
Calculus      308
Call by name      757
Call by value      757
Cancellation technique      80 276
Cantor, Georg      26 98 101
Cardinality      21 92
Carrier      504
Carroll, Lewis      305 391
Case definition of function      63
Casting out by nines      570
cat      see “Concatenation”
CD      see “Constructive dilemma”
Ceiling function      65
Chain      212
Chang, C.      474 845
Characteristic function      71
Children      48
Chinese remainder theorem      561
Chomsky normal form      687
Chomsky, N.      687 751 M5
Chromatic number      42
Church — Rosser property      753
Church — Turing thesis      713 712—732
Church, A.      713 754 M5
Churchill, Winston      735 776
Cichelli, R.J.      95 846
Circuit      45
Clausal form      455
Clause      455
Closed      10 563
Closed expression      755
Closed form      278
Closure of binary relation      179—183
Closure, existential      364
Closure, inductive definition      110 241
Closure, lambda      612
Closure, language      130
Closure, positive      130
Closure, properties      130
Closure, reflexive      179
Closure, symmetric      179
Closure, transitive      179 493
Closure, universal      364
CNF      see “Conjunctive normal form”
Codomain      61
Collection      10
Collision      94
Coloring a graph      42
Combinations      261—265
Combinator      755
Comparable      211
Comparison sorting      260
Complement, Boolean algebra      517
Complement, properties      21
Complement, set      20
Complete graph      42
Completeness      342
Completion procedure      769
Component      30
Composition of binary relations      175
Composition of functions      77
Composition of statements      418
Composition of substitutions      464
Composition rule      418 718
Computability      712 735
Computable      712
Computable number problem      102
Computation      712
Computation tree      488
Concatenation of lists      155
Concatenation of strings      127 536
Conclusion      3 309 329
Concrete algebra      508
Conditional      309
Conditional proof      333—338
Conditional proof rule      333
Conditional statement      3
Congruence      557—561
Congruence relation      559
CONJ      see “Conjunction rule”
Conjunction      2 309
conjunction rule      331
Conjunctive normal form      322
Connected      45
Connective      309 310 356
Connective, complete set      326
Cons function      114
Consequence rule      417
Consequent      309 329
Consistent      332
ConsRight function      154
Constructive dilemma      347
constructor      110
Context-free grammar      640
Context-free language      640—642 685—694
Context-free language, Chomsky normal form      687
Context-free language, Greibach normal form      688
Context-free language, properties      693
Context-free language, removing A productions      686
Context-sensitive language      748
Contingency      313
Continuum Hypothesis      105
Contradiction      8 313
Contrapositive      4
CONVERSE      4
Converse of binary relation      180
Converting decimal to binary      70
Conway’s challenge sequence      169
Coppersmith, D.      252 M6
Correct program      415
Countable      99
1 2 3 4 5 6
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