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| Nievergelt J., Farrar J.C., Reingold E.M. — Computer approaches to mathematical problems |
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| Предметный указатель |
Probability density function for exponential distribution 170
Probability density function for normal distribution 152
Probability density function, mean 151
Probability density function, standard deviation 151
Probability, law of large numbers 154 156
Procedures 237 246
Procedures, effective numbering of 240
Procedures, equivalence of 241
Production 3—15 24 39
Production as rewriting rule 5
Production, ecursiveness of 15
Production, set of 10
Programming language 1 38 236
Programming language, syntax of 38
Programming, heuristic 99
Pseudo-random, the technical name given to sequences of numbers generated by deterministic devices to simulate true random sequences 141 see
Pure strategy 119—121
Push-down stack 13 84 95
Quadratic convergence 181
Queens problem 44—48 92
QUEUE 162
Quicksort algorithm 78 84 95
Quiescent position 131
Quiescent position, definition 132
Quiescent position, test for 133
Raiffa, H. 137
Ralston, A. 217
Rand Corporation 167
Random 111 222
random device 115
Random number generator 144—146 156
Random number generator in Monte Carlo calculation 157
Random number generator, center-squaring technique 167
Random number generator, evaluation of 146 149
Random number generator, gap test 169
Random number generator, linear congruential method 167 169
Random number generator, periodicity of 146
Random number generator, poker test 150 170
Random number generator, square-root law 146
Random numbers, distribution of 146 147
Random numbers, interaction with boundary of region 171
Random numbers, interaction with patterns 157
Random permutation 170
Random sequence 143 193
Random variable 153 170
Random walk 158
Randomness, contrasted with unpredictability 142
Randomness, contrasted with unpredictability, criteria for 143
Rate of convergence 181 191
Rational expression 21
Rational numbers 45
Rational numbers, algorithm for enumerating 46
Read, R.C. 91
Rebalancing trees 87
Recurrence relation 86 120 187 189 215 220
Recurrence relation, stability of 189
Recursive definition 4
recursive functions 236 245
Recursiveness 6 15 see
Recursiveness in grammar 6
Recursiveness of production 15
redundant parentheses 19 23—30
Redundant parentheses, removal of 24
Reitwiesner, G. 196 201
Relative roundoff error 178
Reproducibility of random sequence 144
Rewriting rule 5
Riesel, H. 210
Riordan, J. 88
Rivest, R.L. 92
Robinson, J. 138
Robinson, R.M. 210
Rogers, H. 245
Root of tree 7 80
Roundabout (traffic circle) 161
Roundoff error 175 177 178
Rules of Inference 2
Ryser, H.J. 88
Saddle point 113—114 116
Sammet, J.E. 38
Samuel, A. 99 136
Scheduling problems 52
Scientific American 137 245
Scientific notation 176
Search, binary 82
Search, comparison of binary and linear 82
Search, depth—first 46 see
Search, exhaustive 44—45 98
Search, linear 82
Search, tree 98 130—133 138
Search, variable depth heuristic 132—133
Selection operator 131—133
Selection sorting 76 79—81
Self-loop 62 73
Self-reproducing machine 233—235 245
Self-reproducing program 246
Selfridge, J.L. 210
Semantics 2 7 10 18—24 38
Semantics and equivalence 20
Semantics of arithmetic expressions 18—20 41
Semantics, algorithmic 20 41
Semantics, functional 18—20
Semantics, literal 20
Semantics, pragmatic 20
Shanks, D. 196 201 218
Shanks, W. 201
Shannon switching game 102—107 133—137
Shannon switching game on planar graph 138
Shannon switching game, computer implementation of 137
Shannon switching game, fast wins in 133—136
Shannon switching game, short game 133
Shannon switching game, static evaluation functions for 135—136
Shannon switching game, strategies 102—105
Shannon, C.E. 98 136
Sharp, A. 200
Shock wave effect 165 see
Short-player 102 see
Shortest path 63—65 91
Shortest path, algorithm 63—65 91
Shortest path, counting the 65
Sibuya, M. 194
Sieve 49 203 219 222 223
Sieve of Eratosthenes 203
Sieve, modular 205—206
Simon, H.A. 138
simplification 21—38
Simplification of arithmetic expressions 21—38
Simplification of arithmetic expressions, algorithm 24 27
Simplification of arithmetic expressions, rules 24—36
Simulation 153 160 168
Simulation in real time 165
Simulation of gas station 172
Simulation of traffic flow, follow-the-leader theory 164
Simulation of traffic flow, interaction between cars 164
Simulation of traffic flow, saturation 164
Simulation of traffic flow, single-lane traffic 164
Simulation of traffic flow, traffic circle 161—162
Slagle, J.R. 132 133
Smith, D.E. 218
Sorting 44 73—87 92
Sorting algorithm 75 77—84 88
Sorting algorithm, bubble sort 77—78
| Sorting algorithm, Quicksort 78 see
Sorting algorithm, selection 75
Sorting algorithm, tournament-selection sort 81 95
Sorting algorithm, transposition 75
Sorting, balanced trees 83
Sorting, external 76
Sorting, internal 76
Sorting, theory of 86
Spanning tree 63 68 72 91
Spanning tree in Shannon switching game 103
Spanning tree, cost of 69
Spanning tree, definition 69
Spanning tree, edge-disjoint 103 105
Spanning tree, generation of all 73 91 105
Spanning tree, minimal—cost 68
Spanning tree, properties of 69
Square—root law 153 155 156 159
Stability 187 221
STACK 13
Standard deviation 145 151 169 170
State of a machine 233
Static evaluation function 129—131 135
Static evaluation function, inadequacy of 129
Static evaluation function, reliability of 131
Static value (of position in game) 132
Stein, S.K. 90
Stormer, C. 201
Strategy 97—101 114—118 133 139
Strategy, mixed 115
Strategy, optimal minimax 116
Strategy, pure 115
STUDENT 166
Subgraph 66
Subgraph, maximal connected 66 see
Substitutor 230
Substring 6
Subtree 24—33
Successor nodes in tree 122 129 131
Suffix notation see "Polish notation suffix"
Symbolic differentiation 21
Symbolic integration 21 41
Symbolic manipulation algorithm 23
Syntactical structure 7—10 15—16 24 41
Syntax 2 10—12 38
Syntax of programming language 38
Syntax—directed algorithm 10 16 38
Takahashi, K 194
Taub, A.H. 245
Taylor series 186
Taylor's theorem 181
Term 6 26
Terminal nodes of tree 7 122 124
Terminal positions in game, values assigned for fast wins 135
Terminal symbol 5
Testing random number generators 149 169 170
Theoretical value of position in game 129—130 135
Theory of computability 236 245
Tic-Tac-Toe 140
Tiled rectangles 56—62
Tiling problems 56 90 94
Time magazine 194
Timetable construction 52 89
Tippett, L.H.C. 167
Tournament-selection sort 95
Traffic circle 161 171—172
Traffic circle, saturation 172
Traffic flow, simulation of 161—164
Traffic flow, theory of 168
Transformation 21
Transformation of parsing tree 27
Transformation of probability distributions 151
Transposition sorting 76—78
Traveling salesman problem 72
TREE 7—13 26—33 39 46 68 80 83—87 214
Tree insertion sorting algorithm 84—86
Tree search 98 130—133 138
Tree transformations 30—32 87 96
Tree, binary search 83
Tree, definition 68
Tree, game 121—136 140
Tree, height of 85
Tree, height—balanced (or balanced) 85
Tree, nodes in, successor 122 129 131
Tree, ordered 121
Tree, parsing 7—13 26—33 39
Tree-traversal algorithm 95
Truesdell, L.E. 92
Tuckerman, B. 210 211 219
Turing machine 236 245
Turing's test 225
Turing, A.M. 98 225 244 245
Tutte, W. 90
Two-person zero-sum game 98 112—118 139
Two-person zero-sum game, minimax strategy for 139
Two-person zero-sum game, model for parlor games 116
Two-person zero-sum game, payoff matrix 112 139
Two-person zero-sum game, payoff matrix, saddle point 113—116
Two-person zero-sum game, program for playing 139
Two-person zero-sum game, value of 115
Uhler, H. 192
Ulam, S. 153 168
Ullman, J.D. 38
Unambiguous grammar 10 39
Underflow 176
Uniqueness 171
Uniqueness of harmonic function 171
Uniqueness of parsing tree 8 10
United States Chess Federation 98
Universal constructor 234
Universal machine 234 236
Universal procedures 241
Unsolvability 241 243 246
Value of a game 112—121 137
Value of a game, bounds for 121
Value of a game, fictitious play for computing 118—121
Value of a position 129—130 132
Van Ceulen, L. 199
van Roomen, A. 199
Variable 4 230
Variable-depth heuristic search 132—133
Viete, F. 199
von Kempelen, W. 225 243
von Neumann, J. 92 111 115 137 153 167 168 196 232 244
von Neumann, J., minimax theorem 115
von Neumann, J., self—reproducing automata 232 244
von Vega, Baron Georg 200
Walker, R.J. 89
Wallis, J. 200
Warshall's algorithm 63 67—68 94
WarshaU, S. 67 91
Wavefront 64
Wegner, P. 38
Weizenbaum, J. 228 244
Wells, M.B. 89
Wheeler, D.J. 210 218 222
Wheeler, R. 196
Wilkinson, J.H. 218
Wrench, J.W. 196 201 218
Wunderlich, M.C. 219
XOR (A,B,O), exclusive-or function of three boolean variables 100
Zero expression 27
Zero term 27
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