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| Авторизация |
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| Nievergelt J., Farrar J.C., Reingold E.M. — Computer approaches to mathematical problems |
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| Предметный указатель |
 -cutoff 124 126
-value 124
 -cutoff 124 126 see
—value 124 see
 21 171 191—192 198 218 222
, computation of 171 198 218
 , computation of 191 192
::=(symbol used in productions) 3
< > metasymbol (e.g., operator ) 3 12
Adjacency matrix 63 66—68 94
Akers, S.B. 91
Algebra word problems 229
Algol 60 38
Algorithm 1 10 16 19 23
Algorithm, backtrack 47
Algorithm, existence, decidability 241—243
Algorithm, fictitious play 118—119 137
Algorithm, formal differentiation 23
Algorithm, graph 62—73
Algorithm, graph, computation of distance matrix 68
Algorithm, graph, decomposition type 63 72—73
Algorithm, graph, exchange (for minimal cost spanning tree) 69
Algorithm, graph, generating all spanning trees 72
Algorithm, graph, minimal cost spanning tree 69—70
Algorithm, graph, propagation type 63
Algorithm, graph, shortest path 63—64
Algorithm, graph, Warshall's 63 67
Algorithm, minimax evaluation of game tree 122
Algorithm, multiply-by-3-and-add-l 212
Algorithm, random number generator 144—145
Algorithm, sorting 75—83
Algorithm, sorting, bubble sort 77—78
Algorithm, sorting, insertion sorting 81
Algorithm, sorting, Quicksort 78
Algorithm, sorting, tournament-selection sort 81 95
Algorithm, syntax—directed 10 16 38
Algorithmic computation 236
Algorithmic meaning 19—24 29 41 see algorithmic"
Algorithmic semantics 20 41
Alpha-beta pruning 122—128 140
Ambiguity 4 11
Ambiguous grammar 39
Anderson, A.R. 244
Andree, R.V. 218
Apter, M.J. 244
Archimedes 198 222
Arithmetic 1 175 217
arithmetic expressions 1—42
Arithmetic expressions, class of all 2
Arithmetic expressions, definition 5
Arithmetic expressions, differentiation of 22
Arithmetic expressions, key operator in 41
Arithmetic expressions, language of 2—7
Arithmetic expressions, meaning of 7 see
Arithmetic expressions, Polish representation for 12
Arithmetic expressions, recognition of 39
Arithmetic expressions, reduction of 36
Arithmetic expressions, semantics 2—20
Arithmetic expressions, set of 10
Arithmetic expressions, syntax 36
Arithmetic, floating point 176 220
Arithmetical progression 205 222
Artificial intelligence, contribution of game playing programs 99
Ashton, W.D. 168
Association for Computing Machinery 98
Associative laws 31
Asymptotic error constant 181 184
Automata 232—236
Babington-Smith, B. 167
Backtrack 44—50 72 89 93 98 203
Backtrack, algorithm 44—47
Backtrack, applied to tilings 90
Backtrack, contrasted with heuristic tree search 98
Backup procedure 132—133 140
Backup procedure, comparison of several 140
Backup procedure, m and n 132
Backup procedure, minimax 124 132
Backus — Naur Form (Backus Normal Form) 36
Balanced incomplete block design 50—52
Balanced tree 83 85—86 96
Baumert, L. 89
Beckenbach, E.F. 88
Beckmann, P. 219
Berge, C. 90
Bernoulli, J. 154
Binary representation of numbers, applied to analysis of Nim 100
Binary search 82—84 95
Binary search tree 83—85
Binet's formula 188
Block designs 50—52 89
BNF see "Backus — Naur Form"
Bobrow, D.G. 231 244
Boorman, J.M. 192
Branch and bound algorithm 46
Bratley, P. 245
Brouncker, Lord William 200
Brown, G.W. 118 138
Brown, R. 158
Bubble sort 77—78
Buffon Needle Problem 153 170
Burks, A.W. 245
Calling the largest number 105—109 137 139
Calling the largest number and dynamic storage allocation 137
Calling the largest number, analysis of 106—109
Calling the largest number, variations on 139
Campbell, J.A. 137
Cantor, G. 239
Cayley, A. 72
Central-limit theorem 152
CHARACTER 2—5
character string 4 7 15 19 238
Chase, S.M. 137
Checker-playing program 99 136
Checking long computations 197 211
Chess 98 117—118 132 136
Chess automation 243
Chess-playing programs 136 225
Chi-square, applied to random number generator 149
Chi-square, statistic 148 169
Chi-square, test 146 222
Chomsky, N. 38
Church's thesis 236
Church, A. 236 245
CIR(e,T) (circuit function on spanning trees) 69—70 95
Circuit, in graph 68
Cohn, J.H.E. 219
Coin tosses 142 148
Combinatorial computing 43—96
Combinatorial mathematics 43 89
Combinatorial problems 43—44 47 191
Commutative laws 30
Complete tiled rectangle 61
complexity 232
Compound-interest law 195
Computability 236 245
Computable function 234 239
Computation of constants to high precision 191
Computer arithmetic 175 217
Computer chess tournament 98
Computer conversation 227—228
Connected component of a graph 66 69
Connectivity matrix 66—67 91 94
Constal, R. 192
Constant 4 191
Constraints in combinatorial problems 47
Context—free grammar 38
Convergence 138 179
Convergence, rate of 181 see
Conversational programs 226 246
Cost of spanning tree 69
| Crocker, S. 136
Csima, J. 89
Current flow in electrical network 56
Cutoff depth, criterion for halting variable-depth search 133
Cut—player 102 see
D<X,5>, formal derivative of an arithmetic expression 22 40
Dahse, Z. 200
Data structure 13 75
Davis, M. 245
de la Valine Poussin, C.J. 208
De Lagny, F. 200
Decision procedure 239
Decision theory 91
decision-making 97 137
Depth—first search 46 see
Derivation 1 5—8 11
Derivation tree (parsing tree) 7 39
Derivation, immediate 5
Derivative 22 195
Derivative of arithmetic expression, formal 22
Descendant, nodes in game tree 124 130
Descriptions of machines 234—235
Design of statistical experiments 50—51
Diagonalization 239 246
Dichampt, M. 201
Directed graph (digraph) 62
Dirichlet problem 159—160
Distance between pairs of nodes in a graph 67
Distance matrix 68 94
Distribution of primes, asymptotic 208 210
Distribution of random numbers 148 151 152 170
Distribution of random numbers, exponential 170
Distribution of random numbers, normal 152
Distribution of random numbers, Poisson 170
Distribution of random numbers, transformation of 151
Distribution of random numbers, uniform 151
Distributivity 32
Dobell, A.R. 167
DOCTOR 227
Dual graph 138
Duality, in graph theory 105 138
Dutka, J. 194 218 222
Dynamic storage allocation 137
Dynkin, E.B. 137
e 191 192 195 218 222
E(p,q), expected payoff in two-person zero-sum game 115—116
Eastlake, R. 136
Edge-disjoint spanning trees 139
Edges 62 65 73 135
Edges of a graph, directed 62
Effective numbering of procedures 240 242
Effectiveness 1 240
Eight-queens problem 44—48 92
Electrical networks 56—59 72 90 94
Electrical networks, correspondence with tiled rectangles 59
Electrical networks, current flow in 56
Electrical networks, Kirchhoff s First Law 58
Electrical networks, Ohm's Law 58
Electrical networks, planar 57
Electrical networks, resistance of branch 57
Electrical networks, solution of 58
Electrical networks, system of equations for 59
ELIZA 227—228 244
ENIAC 196 201
Equivalence of arithmetic expressions 18 35
Equivalence of procedures 241
Equivalence problem 241
Equivalence-preserving transformation 27—30
Eratosthenes, sieve of 203
Errors 175 187 189 211 217
Errors in long computer runs 211
Essential parentheses 26
Euclid 208
Euler's conjecture (on orthogonal latin squares) 55
Euler, L. 55 196 202
Evaluation of expressions 13
Evaluation of game tree, fixed—depth search 128 130
Evaluation of game tree, minimax 122
Evaluation of game tree, variable depth search 132—133
Evaluation of random number generators 146 149 167
Evaluation of random number generators, frequency test 146
Evaluation of random number generators, gap test 167
Evaluation of random number generators, poker test 150 170
Exchange algorithm (for min-cost spanning tree) 69 95
Exclusive-OR 100
Exhaustive search 98 128 202 see
expected payoff 116 119
Exponential distribution 170
exponentiation 39
Expression 1—10 16—24 see
Expression, interpretation 18—19
Expression, manipulation 10 21
Expression, rational 21
External sorting 76
Factor 6 26
Fibonacci numbers 86 187 206 219
Fibonacci squares 206 219 222
Fictitious play for evaluating game 118—121 137—139
Field axioms 30
FILE 73 76
Fillatoire 201
Finite affine plane 55 see
Finney, D.J. 89
Fixed—depth search, for evaluating game trees 130—131
Fletcher, J.G. 90
floating-point 175—176 178 217 220
Foliow-the-leader theory 168
Formal differentiation 22
Formal language 1—4 10 235
FORTRAN 21
Fox, J.H.Jr. 137
Frequency test for random numbers 146
Friedlander, G.G. 169
Froeberg, C.E. 217
Function 11 18—19
Function computed by a procedure 237 241
Functional equivalence 35
Functional semantics 18—20
Fundamental circuit matrix 95
Game 97
Game theory 98 111—119 137
Game tree 121—136 140
Game tree and number of strategies 140
Game tree, evaluation of 121—136
Game tree, heuristic search of 129—133
Game tree, illustrated for Nim 123
Game tree, labeling of nonterminal nodes 124
Game tree, levels of 122
Game tree, ordering of nodes 126
Game, calling largest number 105—109
Game, complete information in 105
Game, examples 99—111
Game, Game as model for decision and conflict situation 111
Game, game-playing programs 97 118
Game, Hex 109—111
Game, Nim 99—102
Game, position in 98 131—132
Game, Shannon switching 102
Game, two-person zero—sum 98 112—118
Game, value of 112—121 137
Game-playing program 98—99 118—122 129—130 140
Gap test, for random numbers 169
Gardelo, K. 169
Gardner, M. 90 137
Gauss's identity 202
Gauss, K.F. 202 208
Genuys, F. 201
Gillies, D.B. 196 210 218 219
Gilloud, J. 201
Gnugnoli, G. 168
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