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Gill A. — Applied Algebra for the Computer Sciences
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Название: Applied Algebra for the Computer SciencesАвтор: Gill A. Аннотация: The purpose of this book is to cover, in a mathematically precise manner, a variety of concepts, results, techniques, and applications of modern algebra that are of particular use to beginning students in the computer sciences. Abstract topics such as sets, relations, functions, Boolean algebras, groups, rings, and fields are interspersed in this book with computer-oriented applications such as combinational and sequential networks, formal languages, automata, and codes. The object of this interspersal is to provide the beginner with motivation for delving into abstract mathematics, and to lay the groundwork for a number of applied areas which, as a computer-sciences major, the student will pursue in the future.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1976Количество страниц: 445Добавлена в каталог: 12.11.2014Операции: Положить на полку |
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Falsity set 122 Fibonacci numbers 78 Field 296 Field, base 317 Field, extension 296 Field, Galois 323 Field, proper subfield 316 Field, skew 301 Field, splitting 321 Field, subfield 316 Final state 241 Finite algebraic system 94 Finite induction 71 72 Finite set 2 64 Finite-state automaton 240 260 Finite-state control 260 Finite-state machine 214 Forest 374 Formal language 232 Four-color conjecture 392 Full adder 180 Function 50 Function, Ackerman's 83 Function, boolean 173 Function, characteristic 68 Function, complementary transmission 201 Function, composite 54 Function, composition of 54 Function, computable 261 Function, dual transmission 202 Function, equality of 50 187 Function, extended next-state 218 241 Function, extension of 51 Function, idempotent 55 Function, identity 58 Function, inverse of 58 60 Function, linearly separable transmission 207 Function, minimization of transmission 199 Function, next state 215 241 Function, output 215 Function, Peano's successor 71 Function, recursive 251 Function, self-dual transmission 295 Function, single-valued 50 Function, symmetric 183 Function, synthesis of transmission 195 Function, well-defined 50 Functional completeness 205 Functional quasi-completeness 209 Gaal, L. 337 Galois field 323 Gate 183 Gate, and 184 Gate, comparator 226 Gate, exclusive OR 210 Gate, EXCOR 210 Gate, inhibitor 209 Gate, nand 206 Gate, nor 207 Gate, NOT 184 Gate, or 180 184 Gate, quasi-universal 209 Gate, standard 185 Gate, threshold 207 Gate, universal 206 Generalized Hamming code 359 Generated proposition 133 Generated set 7 82 Generating algorithm 233 Generator 267 274 292 Generator matrix 343 Geodesic 367 Gill, A. 227 325 359 Ginsburg, S. 263 Ginzburg, A. 263 Glb 143 Golomb, S. 359 Grammar 236 237 Graph 28 360 Graph, bipartite 382 Graph, complete 362 Graph, complete directed 398 Graph, connected 364 Graph, contractible 389 Graph, decision 406 Graph, directed 78 364 395 Graph, distance in 367 Graph, dual 392 Graph, Euler 369 Graph, Hamilton 371 Graph, isomorphism of 363 396 Graph, nondirected 395 Graph, nonplanar 387 Graph, planar 387 Graph, polygonal 391 Graph, regular 363 Graph, self-complementary 365 Graph, self-dual 392 Graph, subgraph 363 378 Gratzer, G. 178 Greatest common divisor 84 311 Greatest element 144 Greatest lower bound 143 Grossman, I. 415 Group 270 Group, abelian 271 Group, additive 271 298 Group, cyclic 274 Group, exponent of 278 Group, multiplicative 271 299 Group, order of 271 Group, permutation 272 Group, semigroup 266 Group, subgroup 279 281 Group, symmetric 272 Group, symmetries of the square 274 Half adder 180 Hall, M. 286 Halmos, P.R. 24 178 Halting problem for Turing machines 261 Hamilton cycle 371 Hamilton graph 371 Hamming code 353 Harary, F. 415 Harrison, M.A. 227 263 359 Hartmanis, J. 227 Hasse diagram 43 Hennie, F.C. 227 Herstein, I. 24 286 337 Hohn, F.E. 227 Homomorphic image 106 Homomorphism 106 Hopcroft, J.E. 263 Hypothesis 71 73 126 Ideal 292 Idempotent 99 267 Idempotent function 55 Idempotent laws 14 102 132 149 161 188 Identity 97 264 Identity function 58 Identity laws 13 97 99 131 161 188 267 271 288 296 327 Identity matrix 331 Identity permutation 61 Identity relation 28 Identity, additive 288 Identity, multiplicative 288 Identity, right 264 Image 50 295 Implication 125 Implication rules 136 Incident vertices 361 inclusion 3 Indeterminate 302 INDEX 285 Index set 4 Indirect proof 137 Induction 71 72 Induction hypothesis 71 73 Induction step 71 73 Induction variable 72 Infinite face 392 Infinite set 2 64 Information symbol 346 Inhibitor gate 209 Initial configuration 403 Initial state 215 241 260 Initial vertex 403 Injection 52 Input alphabet 214 240 Input head 260 Input symbol 214 240 Input tape 259 INTEGER 1 2 65 Integral domain 99 289 Intermediate configuration 403 Intersection 6 Inverse image 50 Inverse Laws 99 271 296 Inverse of element 97 270 inverse of function 60 Inverse of matrix 334 Inverse of proposition 130 Inverse, additive 297 Invertible element 97 270 Involution law 14 102 132 159 161 188 Irreducible polynomial 305 Irreflexivity 36 Isomorphism of algebras 107 Isomorphism of graphs 363 396 Iteration 231 Jealous husbands puzzle 414 Join 145 Junction 360 Kain, R.Y. 263 Kemeny, J.G. 90 141 Kernel 293 Koenigsberg bridge problem 370 Kohavi, Z. 228 Korfhage, R.R. 228 263 Kuratowski's theorem 390 Lagrange's theorem 285 Language 232 Language, ambiguous 235 Language, context sensitive 237 Language, context-free 237 Language, formal 232 Language, natural 232 Language, phrase-structure 236 Language, recursive 232 233 Language, regular 237 Lattice 145 Lattice of partitions 151 Lattice, complemented 159 Lattice, distributive 156 Lattice, modular 151 Laws of sets 13 14 Laws, absorption 14 104 132 149 161 188 Laws, associative 13 96 99 131 148 161 188 266 271 288 327 Laws, cancellation 99 275 288 Laws, commutative 13 96 99 131 148 161 188 267 271 288 Laws, complement 13 161 188 Laws, DeMorgan's 14 75 104 132 159 151 188 Laws, distributive 13 97 99 131 156 161 188 288 296 327 Laws, idempotent 14 102 132 149 161 188 Laws, identity 13 97 99 131 161 188 267 271 288 396 327 Laws, inverse 99 271 296 Laws, involution 14 102 132 159 161 188 Laws, negation 131 Laws, null 14 103 132 161 188 Laws, propositional 131 Leading coefficient 302 Leading term 302 Least common multiple 88 Least element 43 72 144 Least upper bound 143 Lederman, W. 286 Left congruence relation 116 Left coset 281 Left coset partition 284 Left identity 264 Left inverse of element 270 Left inverse of function 58 Left subtree 376 Left zero 265 Left-invertible element 270 Length of path 28 241 364 length of string 229 Lin, S. 359 Line 360 Linear binary code 343 Linear bounded automaton 260 Linear code 342 linear combination 329 Linear dependence 329 Linear independence 329 Linear ordering 43 Linearly separable transmission function 207 Ljapin, S. 286 Logic network 180 Loop 29 364 Lub 143 Machine, finite state 214 Machine, halting problem for Turing 261 MacLane, S. 24 48 90 178 286 337 Magnus, W. 415 Mapping 50 52 Marriage problem 383 Matching 383 Matrix 28 331 Maximal cycle 391 Maximal ideal 292 Maximal subgroup 279 Maximum likelihood decoding 341 Maxset 19 Maxset canonical form 20 Maxset normal form 20 Maxterm 174 191 Maxterm normal combinational network 196 Maxterm normal form 175 191 McCluskey, E.J. 228 McCoy, N.H. 337 Meet 145 Membership table 11 Memory 211 260 Message 338 339 Message set 339 Miller, R.E. 228 Minimal element 170 Minimization of transmission function 199 Minimum distance 341 Minimum polynomial 326 Minimum weight 348 Minset 16 Minset canonical form 18 Minset normal form 18 Minsky, M.L. 263 Minterm 174 191 Minterm normal combinational network 196 Minterm normal form 175 191 Mirkil, H. 90 141
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