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Hein J.L. — Discrete Structures, Logic, and Computability |
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Предметный указатель |
Countably infinite 99
Counterexample 6
Countermodel 362
Counting, bag combinations 265
Counting, bag permutations 259
Counting, combinations 261—265
Counting, difference rule 24
Counting, finite sets 21—24
Counting, inclusion exclusion principle 22
Counting, infinite sets 98—105
Counting, permutations 257—261
Counting, product rule 53
Counting, tuples 52—55
Counting, union of countable sets 100
Counting, union rule 22
cp see “Conditional proof rule”
Cross product 32
CYCLE 45
Dag see “Directed acyclic graph”
DD see “Destructive dilemma”
De Morgans laws, Boolean algebra 521
De Morgans laws, logic 314
De Morgans laws, sets 21
Decidable 365 739
Decision problem 365 739
Decision tree 253—256
Decoding 559—561
Degree 45
Delete function 497
Delong, H. 846
Depth 48
Depth-first search strategy 488
Depth-first traversal 47
Deque 544
Derangement 273 295
Derivation 132 135
Derivation tree 131
Descartes, Rene 32
Descending chain 212
Description problem 503
Destructive dilemma 347
Destructors 114
Deterministic context-free language 659
Deterministic finite automaton 585
Deterministic finite automaton as an algebra 602
Deterministic PDA 643
Deterministic Turing machine 706
DFA see “Deterministic finite automaton”
Diagonalization 103
dictionary order 221
Difference 19
Difference, counting rule 24
Digital circuit 522—527
Digital circuit, AND gate 522
Digital circuit, full adder 524
Digital circuit, gate 522
Digital circuit, half-adder 523
Digital circuit, logic gate 522
Digital circuit, NOT gate 522
Digital circuit, OR gate 522
Digraph 43
Dilemmas 347
Direct proof 7
Directed acyclic graph 45
Directed graph 43
Directed multigraph 43
Disagreement set 466
Disjoint sets 18
Disjunction 2 309
Disjunctive normal form 320
Disjunctive syllogism 331
Dist see “Distribute function”
Distribute function 74 153
divides 5 211
Divisible 5
Division algorithm 67
Divisor 5
DNF see “Disjunctive normal form”
Domain 61 359
Doyle, Arthur Conan 1
DS see “Disjunctive syllogism”
Duality principle 519
EA see “Equality axiom”
EDGE 41
EE see “Equals for equals”
Effective enumeration 736—739
Effective enumeration, single variable computable functions 739
EG see “Existential generalization”
EI see “Existential instantiation”
Element 10 30
Ellipsis 11
Embedding 90
Empty clause 455
Empty list 34
Empty relation 41
Empty set 11
Empty string 36
Empty substitution 463
Empty tuple 31
Encoding 559—561
Epimorphism 567
Equal, bags 25
Equal, functions 63
Equal, regular expressions 580
Equal, sets 11
Equal, tuples 31
Equality 406—413
Equality, axiom 407
Equality, axioms for terms 407
Equality, basic 174
Equality, problem 192
Equality, relation 41
Equals for equals 407
Equipotent 92
Equivalence class 194
Equivalence of states 618
Equivalence problem 193 205 743
Equivalence relation 192—207
Equivalence relation, quotient 195
Equivalence relation, smallest 200
Equivalence, algebraic expressions 504
Equivalence, computational models 713
Equivalence, first-order predicate calculus 368
Equivalence, propositional calculus 313
Equivalence, Turing machines 704
Eratosthenes 167
Euclid 8 444
Euclid’s algorithm 67
Euler circuit 46
Euler path 46
Euler, L. 46
Event 267
Excluded middle, law of 349
Existential closure 364
Existential generalization 394
Existential instantiation 386
Existential quantifier 353
Expectation 271
Expected value 271
Expression 463
Expression, algebraic 504
Expression, lambda 754
Expression, reduction rule 751
Expression, rewrite rule 751
Expression, transformation rule 751
Extended context-sensitive grammar 751
Extensionality, principle of 408
Factorial function 151 555
Factoring 475
Family tree problem 450 473
| Fibonacci numbers 149 169 171 243 247 282 295 557
Fibonacci, Leonardo 149
Field 514
FIFO property 539
Final state 585 621
Finite automata 584—624
Finite automata as output devices 597
Finite automata, accept 585 588
Finite automata, deterministic 585
Finite automata, equivalent states 618
Finite automata, final state 585
Finite automata, initial state 585
Finite automata, language of 585 588
Finite automata, linear bounded 748
Finite automata, Mealy machine 597
Finite automata, minimum-state DFAs 618
Finite automata, Moore machine 597
Finite automata, NFA for regular expression 609
Finite automata, NFA to DFA algorithm 614
Finite automata, NFA to regular grammar 628
Finite automata, nondeterministic 588
Finite automata, pushdown 642—657
Finite automata, regular grammar to NFA 630
Finite automata, reject 585 588
Finite automata, start state 585
Finite automata, state 585
Finite automata, state transition function 587 589
Finite automata, transition table 601 604
Finite set 12
Finite sums 278
First set 667
First-order logic 439
First-order predicate calculus 351—366
First-order predicate calculus, atomic formula, atom 356
First-order predicate calculus, equivalence 368—381
First-order predicate calculus, existential quantifier 353
First-order predicate calculus, formal proofs 382—400
First-order predicate calculus, literal 376
First-order predicate calculus, meaning, semantics 358—362
First-order predicate calculus, renaming rule 372 394
First-order predicate calculus, restricted equivalences 372—374
First-order predicate calculus, term 356
First-order predicate calculus, universal quantifier 353
First-order predicate calculus, validity 362—366
First-order predicate calculus, well-formed formula 356
First-order theory 405
First-order theory, partial order 411
First-order theory, with equality 406
Fischer, M.J. 205 846
Fixed point 76
Flagged variable 387
Flatten function 544
Floor function 65
Floyd, R.W. 186 433 846
Floyd’s algorithm 186
Follow set 668
Formal power series 283
Formal reasoning system 332
Formal theory 332
Formalizing English sentences 378—379
Four-color theorem 43
FP (functional programming language) 551
fp algebra 554
FP algebra, axioms 554
FP algebra, carriers 554
FP algebra, operations 554
Franklin, Benjamin 249
Free to replace 384
Free variable 358 755
Full adder 524
Full conjunctive normal form 322
Full disjunctive normal form 321
Function 60—95
Function constants 356
Function, argument of 61
Function, arity of 61
Function, codomain of 61
Function, composition 77
Function, definition by cases 63
Function, definition of 60
Function, domain of 61
Function, equality 63
Function, generating 282—293
Function, higher-order 83—88 157
Function, if-then-else 63
Function, image of 61
Function, partial 74
Function, partial recursive 723
Function, pre-image, inverse image of 62
Function, primitive recursive 722
Function, range of 61
Function, recursively defined 146—169
Function, total 74
Function, tupling 78
Function, type 61
Function, value of 61
Functional algebra 550—556
Fundamental conjunction 320
Fundamental disjunction 322
Fundamental Theorem of Arithmetic 237
Fuzzy logic 350
Galler, B.A. 205 846
Gallier, J. 476 849
Gate 522
Gauss, Karl Friedrich 233
GCD see “Greatest common divisor”
Generalized list 35
Generating equivalence relations 200—204
Generating function 282—293 515
Generator of a binary relation 179
Gentzen, G. 366 846
Geometric progression 235
Geometric series 283
Geometry 444
Gib see “Greatest lower bound”
Goal 451 479
Godel numbering 714
Godel, K. 404 443 714 846
Goethe, Johann Wolfgang von 449
Graham, R.L. 304 846
Grammar 130—144
Grammar, abstract syntax tree 144
Grammar, ambiguous 143
Grammar, combining rules 139
Grammar, context-free 640
Grammar, derivation 132 135
Grammar, extended context-sensitive 751
Grammar, four parts 134
Grammar, language of 136
Grammar, left factoring 661
Grammar, left-recursive 662
Grammar, leftmost derivation 136
Grammar, LL(k) 659
Grammar, LR(1) 674
Grammar, LR(K) 672 674
Grammar, nonterminals 134
Grammar, parse or derivation tree 131
Grammar, phrase-structure 749
Grammar, production 132
Grammar, recursive 137
Grammar, recursive production 137
grammar, regular 626
Grammar, rightmost derivation 136
Grammar, rule or production 132
Grammar, sentential form 135
Grammar, start symbol 132 134
Grammar, terminals 134
Grammar, type 0 751
Grammar, type 1 751
Grammar, type 2 751
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