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| Hein J.L. — Discrete Mathematics |
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| Предметный указатель |
Permutations with replacement 262
Permutations without replacement 262
Pigeonhole Principle 95 139
Planar graph 44
Plus operation 538
Polish notation 352
Polynomial algebra 520
Pop operation 543
POSET See Partially ordered set
Poset diagram 218
Positive literal 454
Postcondition 421
Postfix evaluation 544
Postorder 166 550
Power series algebra 521
Power set 14
Power set problem 168
Pre-image 64
Precedence hierarchy 360
Precondition 420
Predecessor 217 539
Predicate 356
Predicate constants 360
Predicate, order of 444
Prefix-closed 555
Premise 313 332
Prenex, conjunctive normal form 380
Prenex, disjunctive normal form 380
Prenex, disjunctive/conjunctive normal form algorithm 380
Prenex, normal form 378
Prenex, normal form algorithm 378
Preorder 164 550
Preserve a relation 564
Preserve an operation 572
Prim's algorithm 54
Prim, R.C 53 641
Prime number 5
Prime number theorem 242
Principle of inclusion exclusion 23
Priority queue 548
probability 270 271—277
Probability of an event 271
Probability, average case 275
Probability, distribution 271
Probability, event 271
Probability, expected value 275
Probability, sample point 271
Probability, sample space 271
Procedure 150 156 165
Procedure, recursively defined 49 151—173
Process 554
Process algebra 555
Process algebra, action 554
Process algebra, nil 554
Process algebra, nondeterminism 554
Process algebra, prefixing 554
Process algebra, process 554
Product as arrays 34
Product as record 8 35
Product of sets 33
Product, cartesian 33
Product, counting rule 54
Product, cross 33
Product, language 131
Product, notation 154
Product, set 124—127
Production 135
Production, indirectly recursive 140
Production, recursive 140
Program correctness 420—439
Program correctness, array assignment axiom 434
Program correctness, assignment axiom 422
Program correctness, composition rule 424
Program correctness, consequence rule 423
Program correctness, correct program 421
Program correctness, if-then rule 426
Program correctness, if-then-else rule 427
Program correctness, loop invariant 428
Program correctness, partial 435
Program correctness, postcondition 421
Program correctness, precondition 420
Program correctness, termination 437
Program correctness, total 435
Program correctness, while rule 428
Program testing 200
Project operation 552
proof 2—9 234—248 335—347 386—404 420—439 473—475
Proof by contradiction 8 341
Proof by example 6
Proof by exhaustive checking 6
Proof, conditional proof rule 336
Proof, contrapositive 7
Proof, direct 7
Proof, if and only if 8
Proof, indirect 7 341—343
Proof, inductive 234—248
Proof, informal 2 312
Proof, mathematical induction 236 242
Proof, multiple variable induction 244
Proof, not subset 15
Proof, reductio ad absurdum 341
Proof, refutation 8
Proof, resolution 461
Proof, structural induction 243
Proof, subset 15
Proof, using variables 6
Proof, well-founded induction 241
Proper subset 13
Proposition 313
Propositional calculus 313—330
Propositional calculus, equivalence 317
Propositional calculus, normal forme 323
Propositional calculus, proposition 313 321
Propositional calculus, semantics 316
Propositional calculus, syntax 314
Propositional calculus, well-formed formula (wff) 314
Propositional variables 314
Push operation 543
qed xv
Quantifier, existential 357
Quantifier, order of 445
Quantifier, scope 361
Quantifier, symbols 360
Quantifier, universal 357
Quasi-order 217
QUEUE 545
Quine's method 320
Quotient algebra 568
Rabbit problem 153
RANGE 63
rat See Reflexive partial order
Rational numbers 12 202
Real numbers 12
Recurrences 280—296
Recursive grammar 140
Recursive production 140
Recursively defined function 151—173
Recursively defined procedure 49 151—173
Reductio ad absurdum 341
Redundant element problem 166
refinement 203
Reflexive 178
Reflexive closure 183
Reflexive partial order 216
Refutation 8
Relation 40
Relation, attributes 41
Relation, congruence 564
Relation, empty 42
Relation, equality 42
| Relation, n-ary 42
Relation, universal 42
Relational algebra 551
Relational algebra, join 553
Relational algebra, project 552
Relational algebra, select 552
Relative complement 20
Relatively prime 68
Renaming rule 376 399
Replacement rule 318
Resolution 369 460—461 467—475
Resolution for set of clauses 471
Resolution Theorem 472
Resolution, proof 461
Resolution, the general case 467
Resolvant 469
Reverse of string 150
Right subtree 52
Ring 519
Robinson, J.A. 369 466 472 476 641
Root 50
RRR (remove, reason, restore) 386
RST See Equivalence relation
Ruskin, John 111
Russell's paradox 27
Russell, В. 27 352 641
Sample point 271
Sample space 271
Satisfiable 366
Schoenfield, J.R. 641
Schroder, E. 104
Scope 361
Select operation 552
Selector function 84
Semantics, higher-order logic 447
Semantics, propositional wffs 316
Semantics, quantified wffs 364
Semigroup 517
Sentential form 138
seq See Sequence function
SEQUENCE 32
Sequence function 76
Sequential search 276
Set 10—25
Set, absorption laws 22 29
Set, cardinality 22
Set, complement 21
Set, countable 101
Set, countably infinite 101
Set, De Morgan's laws 22
Set, difference 20
Set, disjoint 18
Set, empty 11
Set, equality 11
Set, finite 12
Set, inductive definition 112
Set, infinite 12
Set, intersection 18
Set, null 11
Set, operations 16—22
Set, power set 14
Set, product 33 124—127
Set, proper subset 13
Set, relative complement 20
Set, Russell's paradox 27
Set, singleton 11
Set, subset 13
Set, symmetric difference 21
Set, uncountable 101
Set, union 16
Set, universe 21
Shortest distance algorithm 192
Shortest path algorithm 192
Sieve of Eratosthenes 172
Signature 511
simp See Simplification rule
Simple Boolean expression 524
Simple sort 257
Simplification rule 334
Singleton 11
Sink 44
skipping 171
Skolem Functions 456
Skolem'e algorithm 457
Skolem's rule 456
Skolem, Т. 455 641
SLD-resolution rule 488
Snyder, W. 476 641
solvable 369
Sorting a priority queue 549
Sorting by insertion 160
Sorting problem 221
Soundness 344
Source 44
Spanning tree 53
Square root 175
STACK 543
Stanat, D.F. 641
Standard order 227
Start symbol 135 137
State of a computation 436
Stirling's formula 303
STIRLING, JAMES 303
Strassen, V. 256 641
Stream 37 169—173
String 37—39 120—122 161—163 541 542
String, alphabet 37
String, append 120
String, concatenation 131
String, empty 37
String, head 121
String, Length 37
String, tail 121
Structural induction 243
Subalgebra 569
Subbag 25
Subgraph 46
Subproof 337
Subscripted variable 393
Subset 13
Substitution 462
Subtree 50
Succ See Successor function
Successor 217
Successor function 113
Sufficient condition 3
Sum of bags 26
Summation facts 282
Summation notation 154
summing 170
Suppes, P. 641
Surjection 93
Surjective function 93
symmetric 178
Symmetric closure 183
Symmetric difference 21
T (true statement) 339
Tail of list 35 116
Tail of string 121
Tautology 317
Term 360
Terminals 137
termination condition 437
Ternary relation 42
Testing a program 200
Theorem 335
Thoreau, Henry David 451
Three-valued logic 353
Time-oriented task 215 220 233
Top operation 543
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