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| Ïîèñê ïî óêàçàòåëÿì |
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| Mott J., Kandel A., Baker T. — Discrete mathematics for computer scientists and mathematicians |
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| Ïðåäìåòíûé óêàçàòåëü |
"An Investigation of the Laws of Thought" 577
"Analysis-synthesis" reasoning 24—26
"Degree spectrum" of a directed graph 334
"Dictionary" ordering of strings 373—375
"Don't care" conditions 609
"Double hashing" algorithms 357—358
"Extraordinary" sets 9
"Greedy" method for increasing flow 663
"hard" AND for fuzzy set operations 705
"Hub" vertex 457
"Ordinary" sets 9
"Probe" sequence 358
"Ring" pattern 607
"Smallest" Boolean algebra 588—589
"Soft" AND for fuzzy set operations 705
"Soft" expert systems (SES) 722—724
"Soft" expert systems (SES), ARIES 727—731
"Soft" expert systems (SES), EKB 725—727
"Soft" expert systems (SES), FRKB 724—727
"Soft" expert systems (SES), VKB 725—727
"The First Theorem of Graph Theory" 440—441
"The Sum of Degrees Theorem" 440—441
"Vicious circle" fallacy 29
 -balanced binary tree 514
 -reflexive general fuzzy relation 726
 -transitive general fuzzy relation 726
 -transitivity of a similarity relation 726
2's complement form 620—621
2-valued Boolean function 134—136
5-Color Theorem 569—571
@-transitive fuzzy binary relation 713
Abreviated truth table 38—39
Absolute complement of a set 4
Absorption laws 582—583
Abstract set theory 2 see
Absurdity 38
Ackerman's Function 326
Ada programming language 378 428
Addend bit 614
Adder, full-adder 614 615—621
Adder, half-adder 614—615
Addition rule of inference 49
Adjacency matrix 396—402 450
Adjacency matrix, multiplicity matrix 536—537
Adjacency matrix, Warshall's algorithm 407—412 539
Adjacent primes 76
Adjacent to edge 333
Adjacent vertices 439
AI see "Artificial intelligence"
Algebra, boolean see "Boolean algebras"
Algebra, switching see "Switching mechanisms"
Algorithms, "double hashing" 357—358
Algorithms, asymptotic performance of 405
Algorithms, BFS 482—485
Algorithms, binary search 415—418
Algorithms, bubble sort 297 423
Algorithms, complexity of 407
Algorithms, correctness of 404
Algorithms, deterministic 419
Algorithms, DFS 482 485
Algorithms, division 64
Algorithms, efficiency of 404—407
Algorithms, Euclidean 78 117
Algorithms, flow-augmenting path 676
Algorithms, greedy 486—487
Algorithms, greedy, for vertex coloring 567
Algorithms, inefficient 406
Algorithms, inorder traversal (LNR) 515 518
Algorithms, interchange sort 418—423
Algorithms, Kruskal's 486—489
Algorithms, labeling 674—675
Algorithms, Merge Sort 282—284 425—426
Algorithms, minimal spanning tree 494
Algorithms, nondeterministic 419
Algorithms, partial correctness of 404
Algorithms, polynomial-bounded 406
Algorithms, postorder traversal (LRN) 515 518
Algorithms, preorder traversal (NLR) 514 515 518
Algorithms, Prim's 494
Algorithms, run times of 347
Algorithms, Shell sort 419
Algorithms, successive minima 419
Algorithms, termination of 404
Algorithms, topological sort 428—432
Algorithms, tree traversal 514—515 518
Algorithms, vertex labeling 674—675
Algorithms, Warshall's 407—412 539
Algorithms, Welsh — Powell 565—566
Alphabet 373
Alternating geometric series 250—251
ALU see "Arithmetic logic unit"
Ambiguity, fallacy of 28
Amphiboly, fallacy of 28
Ancestor of a vertex 482
AND Boolean operator 398—400
AND function 601 603
AND, "hard" and "soft" 705
AND-VERTEX 729—731
AND/OR graph 728—731
ANSI Standard Y 32.14, 1973 for logic symbols 601
Antecedent of an implication 35
Antisymmetry of a binary relation 339 340
Antisymmetry of a fuzzy binary relation 713
Antisymmetry of a set relation 11
Appel, K. 569
Approximate reasoning inference engine (ARIES) 727—731
Argument, basic elements of 19—20
Argument, diagonal 377—378
Argument, Kempe-chain 569—571
ARIES see "Approximate reasoning inference engine"
Arithmetic logic unit (ALU) see also "Boolean functions minimization "Switching
Arithmetic logic unit (ALU), arithmetic operations, table of 621
Arithmetic logic unit (ALU), carry look-ahead technique 627
Arithmetic logic unit (ALU), full-adder 614 615—621
Arithmetic logic unit (ALU), half-adder 614—615
Arithmetic logic unit (ALU), logic operations, table of 620
Arithmetic logic unit (ALU), micro-operations 619—621
Arithmetic logic unit (ALU), multiplexers 621—626
Arithmetic micro-operations in an ALU 619—621
Arithmetic series 110 115
Arrangement see "Combinations" "Permutations"
Artificial intelligence (AI) 720 731 see ""Soft"
Aspects of discovery 21—22
Associative binary operation on a set 16
Associative property of sets 5
Asymmetry of a binary relation 339 340
Asymptotic performance of algorithms 405
Atom of a Boolean algebra 588
Attribute values in the FRKB 725—726
Augend bit 614
B-tree of order k 503—504
Backtracking 26—27
Backward chaining in expert systems 724
Backward edge 666
Backward labeling 675
Basis of induction 103 111
BCD see "Binary coded decimal"
Begging the question 29—30
Beta probability density function 733
BFS see "Breadth-first search"
Biconditional proposition 37
Big O notation 344—346
Big O notation and algorithm efficiency 404—407
Big O notation, performance of height balanced binary trees 511
Big O notation, performance of sorting algorithms 347
Binary coded decimal (BCD) representation 596
Binary de Bruijn sequences 539—541
Binary operation on a set 16
Binary relations see also "Relations"
Binary relations, adjacency matrix 396—402
| Binary relations, antisymmetry 339 340
Binary relations, asymmetry 339 340
Binary relations, Boolean matrix 396—402
Binary relations, Boolean operations on 398—400
Binary relations, composition 382—383
Binary relations, fuzzy 713
Binary relations, inner product 397—398
Binary relations, inverse 381—382
Binary relations, irreflexivity 339 340
Binary relations, reflexivity 339 340
Binary relations, set 10
Binary relations, symmetry 339 340
Binary relations, transitive (reflexive) closure 383
Binary relations, transitivity 339—340
binary search algorithm 415—418
Binary search tree 512—514
Binary trees, -balanced 514
Binary trees, binary search tree 512—514
Binary trees, complete 509—510
Binary trees, conventions for drawing 508
Binary trees, defined 507
Binary trees, height balanced 510—512
Binary trees, inorder traversal (LNR) 515 518
Binary trees, left child, edge, subtree 507
Binary trees, level-order index of vertex 509
Binary trees, parent 507
Binary trees, postorder traversal (LRN) 515 518
Binary trees, preorder traversal (NLR) 514 515 518
Binary trees, right child, edge, subtree 507
Binary trees, traversal algorithms 514—515 518
binomial 201
Binomial coefficients see also "Multinomial coefficients"
Binomial coefficients, as combinations 189—190
Binomial coefficients, as factorials 191
Binomial coefficients, boundary conditions 194—195
Binomial coefficients, column summation 197—198
Binomial coefficients, diagonal summation 196
Binomial coefficients, identities, additional 204
Binomial coefficients, Newton's identity 191—192
Binomial coefficients, Pascal's identity 192—194
Binomial coefficients, Pascal's triangle 193—194
Binomial coefficients, row square summation 197
Binomial coefficients, row summation 196
Binomial coefficients, secondary conditions 194—195
Binomial coefficients, symmetry property 191
Binomial coefficients, table of 195
Binomial coefficients, Vandermonde's identity 204—205
Bipartite graph 457 547—548 see
Block diagrams of logic circuits 601—602
Boole, George 577
Boolean algebras, "smallest" 588—589
Boolean algebras, absorption laws 582—583
Boolean algebras, atom 588
Boolean algebras, axioms 578
Boolean algebras, canonical form of expressions 589—591
Boolean algebras, conjunctive normal form 591—592
Boolean algebras, dagger function 593
Boolean algebras, defined 578
Boolean algebras, DeMorgan's laws 584
Boolean algebras, direct sum 585—586
Boolean algebras, disjunctive normal form 591—592
Boolean algebras, expressions for 588—593
Boolean algebras, finite 588
Boolean algebras, free 590
Boolean algebras, functionally complete operations 592—593
Boolean algebras, homomorphism 585
Boolean algebras, idempotent laws 580—581
Boolean algebras, involution law 583
Boolean algebras, isomorphism 585
Boolean algebras, lattice as 578
Boolean algebras, literal 590
Boolean algebras, maxterm, minterm expressions 590—592
Boolean algebras, modular law 587
Boolean algebras, notation for 579
Boolean algebras, partial order on 580
Boolean algebras, principle of duality 580
Boolean algebras, product-of-sums form 591 612
Boolean algebras, sheffer stroke function 593
Boolean algebras, subalgebra 584
Boolean algebras, sum-of-products form 591 605
Boolean algebras, switching mechanisms see "Switching mechanisms"
Boolean algebras, theorems for 580—585
Boolean functions, 2-valued 134—136
Boolean functions, minimization of Karnaugh maps 607—609 610—611 see "Switching
Boolean functions, minimization of Karnaugh maps, product-of-sums forms 612
Boolean functions, minimization of Karnaugh maps, sum-of-products forms 605
Boolean functions, minimization of Karnaugh maps, Veitch diagrams 606
Boolean functions, self-dual 2-valued 135
Boolean matrices 396—402
Boolean operators 398—400
Boolean subalgebra 584
Boolean sum of sets 5
Bound, glb, lower, lub, upper 364
Boundary conditions of a recurrence relation 268
Breadth-first search (BFS) 482—485
Bridge edge 472 541
Bubble sort algorithm 297 419 423
Buck, R.C. 110
Canonical form for Boolean expressions 589—591
Canonical representative of equivalence class 356
Cantor's paradox for sets 7
Cantor, Georg 1 377
Capacity constraint 638
Capacity function of a directed graph 633
Capacity of a cut 647—648
Capacity of an edge 633—634 647—648
Cardinality of a fuzzy set 714
carry bit 614
Carry look-ahead technique 627
Cartesian product of fuzzy sets 707
Cartesian product of sets 8 10 128
Catenation of strings 373
Cauchy probability density function 733
Cayley's formula 497
Cells of a set 178
Certainty factor 722 724
Chain 363
Chaining in expert systems 724
character strings 373—375
Characteristic function of a set 2
Characteristic function of a set in IHR solutions 310—319
Characteristic function of a set, defined 301
Characteristic function of a set, distinct roots 301—302
Characteristic function of a set, multiple roots 302—304
Characteristic roots, method of 300—304
Child of a vertex 482
Chromatic numbers for planar graphs 569—571
Chromatic numbers, 5-Color Theorem 569—571
Chromatic numbers, defined 558
Chromatic numbers, greedy algorithm for vertex coloring 567
Chromatic numbers, Kempe-chain argument 569—571
Chromatic numbers, rules for determining 560—563
Chromatic numbers, The Four-Color Problem 569—571
Chromatic numbers, The Scheduling Problem 558—560
Chromatic numbers, Welsh — Powell algorithm 565—566
Circuit rank of a graph 481
Circuits in graphs 388 442
Circuits, combinatorial see "Switching mechanisms"
Circuits, Eulerian 537—539
Circuits, full-adder 614 615—621
Circuits, half-adder 614—615
Circuits, Hamiltonian cycle 543—551
Circuits, logic see "Logic gates"
Circuits, Simple 388 442
Circuits, switching see "Switching mechanisms"
Circular permutations 150—151
Circular Reasoning 29—30
Circumference of a graph 465—466
Class, congruence 12
Class, equivalence 350—351 354—358
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