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