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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
Program correctness, array assignment axiom      428
Program correctness, assignment axiom      416
Program correctness, composition rule      418
Program correctness, consequence rule      417
Program correctness, correct program      415
Program correctness, if-then rule      420
Program correctness, if-then-else rule      421
Program correctness, loop invariant      422
Program correctness, partial      430
Program correctness, postcondition      415
Program correctness, precondition      415
Program correctness, termination      432
Program correctness, total      430
Program correctness, while rule      422
Program testing      195
Project operation      546
proof      2—9 229—243 329—344 382—400 414—433 473—475
Proof by contradiction      8 338
Proof by example      6
Proof by exhaustive checking      6
Proof, conditional proof rule      333
Proof, contrapositive      7
Proof, direct      7
Proof, if and only if      8
Proof, indirect      7 338—340
Proof, inductive      229—243
Proof, informal      2 308
Proof, mathematical induction      231 237
Proof, multiple variable induction      239
Proof, not subset      14
Proof, reductio ad absurdum      338
Proof, refutation      8
Proof, resolution      461 473
Proof, structural induction      238
Proof, subset      14
Proof, using variables      6
Proof, well-founded induction      236
Proper subset      13
Proposition      309
Propositional calculus      309—327
Propositional calculus, equivalence      313
Propositional calculus, normal forms      318—326
Propositional calculus, proposition      309
Propositional calculus, semantics      313
Propositional calculus, syntax      310
Propositional calculus, well-formed formula (wff      310
Propositional variables      310
Pumping lemma, context-free languages      691
Pumping lemma, regular languages      632 633
Push operation      537
Pushdown automata      642—657
Pushdown automata as an algebra      655
Pushdown automata, accept      644
Pushdown automata, deterministic      643
Pushdown automata, instantaneous description      644
Pushdown automata, interpreter      656
Pushdown automata, language of      644
Pushdown automata, nondeterministic      643
Pushdown automata, pushdown transducer      667
Pushdown automata, reject      644
Pushdown transducer      667
qed      xviii
Quantifier, existential      353
Quantifier, order of      440
Quantifier, scope of      358
Quantifier, symbols      356
Quantifier, universal      353
Quasi-order      212
QUEUE      539
Quine’s method      316
Quotient algebra      562
R (resolution)      469
Rabbit problem      149
Rabin, M.O.      588 848
RANGE      61
rat      see “Reflexive partial order”
Rational numbers      12 197
Real numbers      12
Recognition problem      575
Recurrences      275—293
recursive descent      665
Recursive grammar      137
Recursive production      137
Recursively defined function      146—169
Recursively defined procedure      47 146—169
Recursively enumerable language      749
Redex      756
Reduce      751
Reductio ad absurdum      338
Reduction rule      751
Reduction sequence      752
Redundant element problem      162
refinement      198
Reflexive      174
Reflexive closure      179
Reflexive partial order      212
Refutation      8
Regular expression      577—583
Regular expression, equality      580
Regular expression, properties      581
Regular grammar      626—630
Regular grammar to NFA      630
Regular language      576—580 631—635
Regular language, properties      634
Reject      585 588 644 699
Relation      38
Relation, attributes      39
Relation, congruence      559
Relation, empty      41
Relation, equality      41
Relation, n-ary      40
Relation, universal      41
Relational algebra      546—548
Relational algebra, join      547
Relational algebra, project      546
Relational algebra, select      546
Relative complement      19
Relatively prime      66
Renaming rule      372 394
Replacement rule      315
Resolution      461—462 467—475
Resolution for propositions      461
Resolution for set of clauses      471
Resolution, inference rule      469
Resolution, proof      461
Resolution, the general case      467
Resolution, theorem      472
Resolvant      469
Reverse of string      146 725
Rewrite      751
Rewrite rule      751
Right subtree      50
Rightmost derivation      136
Ring      513
Robinson, J.A.      366 466 472 475 848
Root      48
Rosenkrantz, D.J.      671 848
RRR (remove, reason, restore      382
RST      see “Equivalence relation”
Ruskin, John      109
Russell, B.      26 349 697 849
Russells paradox      26
Sample point      267
Sample space      467
Satisfiable      362
Schoenfield, J.R.      848
Schoning, U.      848
Schroder, E.      101
Scope      358 755
Scott, D.      588 848
Select operation      546
Selector function      82
Semantics, higher-order logic      442
Semantics, propositional wffs      313
Semantics, quantified wffs      360
Semigroup      511
Sentential form      135 660
seq      see “Sequence function”
SEQUENCE      31
Sequence function      74
Sequential search      272
Set      10—26
Set, absorption laws      21 28
Set, cardinality      21
Set, complement      20
Set, countable      99
Set, countably infinite      99
Set, De Morgan’s laws      21
Set, difference      19
Set, disjoint      18
Set, empty      11
Set, equality      11
Set, finite      12
Set, inductive definition      110
Set, infinite      12
Set, intersection      18
Set, null      11
Set, operations      15—21
Set, power set      13
Set, product      32 122—124
Set, proper subset      13
Set, relative complement      19
Set, Russell’s paradox      26
Set, singleton      11
Set, subset      13
Set, symmetric difference      20
Set, uncountable      99
Set, union      15
Set, universe      20
Shepherdson, J.C.      716 849
Shift-reduce parsing      677
Shortest distance algorithm      186
Shortest path algorithm      187
Sieve of Eratosthenes      167
Sign function      720
Signature      505
Signum function      720
simp      see “Simplification rule”
Simple Boolean expression      518
Simple language      716
Simple sort      252
Simplification rule      331
SIMPLIFY      518 751
Singleton      11
Sink      43
skipping      166
Skolem Functions      457
Skolem, T.      456 849
Skolem’s algorithm      457
Skolem’s rule      457
SLD-resolution rule      483
Snyder, W.      476 849
solvable      365 739
Sorting a priority queue      543
Sorting by insertion      156
Sorting problem      216
Soundness      342
Source      43
Spanning tree      51
Specialization ordering      768
Square root      171
STACK      537
Stanat, D.F.      849
Standard order      222
Start state      585 621
Start symbol      132 134
State      585
State of a computation      430
State transition function      587 589
Stearns, R.E.      659 671 847 848
STIRLING, JAMES      299
Stirling’s formula      299
Strassen, V.      251 849
Stream      36 165—169
String      36 38 117—120 157—158 536
String, alphabet      36
String, append      118
String, concatenation      127
String, empty      36
String, head      118
String, Length      36
String, tail      118
Structural induction      238
Sturgis, H.E.      716 849
Subalgebra      563
Subbag      25
Subgraph      44
Subproof      334
Subscripted variable      389
Subset      13
Substitution      463
Subtree      48
Succ      see “Successor function”
Successor      212
Successor function      111
Sufficient condition      3
Sum of bags      25
Summation facts      278
Summation notation      150
summing      166
Suppes, P.      849
Surjection      91
Surjective function      91
symmetric      174
Symmetric closure      179
Symmetric difference      20
T (true statement)      336
Tail of list      34 114
Tail of string      118
Tautology      313
Term      356
Terminals      134
Termination      432
Ternary relation      41
Testing a program      195
Theorem      332
Thompson, K.      609 849
Thoreau, Henry David      446
Three-valued logic      349
Time-oriented task      210 215 228
Top operation      537
Top-down parsing      659
Topological sorting problem      216
Topologically sorted      217
Total correctness      430
Total function      74
Total order      211
Total problem      741
Totally ordered set      211
Tower of Hanoi      293
Transformation      see “Function”
Transformation problem      565
Transformation rule      571
Transition table      601 604
Transitive      174
Transitive closure      179 493
TREE      48—52
Tree, abstract syntax      144
Tree, binary search tree      51
Tree, binary tree      50
1 2 3 4 5 6
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