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Eilenberg S. — Automata, languages, and machines. Volume A
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Название: Automata, languages, and machines. Volume AАвтор: Eilenberg S. Аннотация: The last twenty years have brought forth a body of research known under the names of the theory of automata and the theory of formal languages. Both topics are closely related and form a distinct part of what is rather nebulously described as "computer science." They are made up of a body of mathematical objects, theorems, and methods of proof that are essentially algebraic, bordering on logic. Many of the published results show motivations specific to the interests of their authors and these were frequently very varied—to mention a few: logic, linguistics, theory of communication, programming, electronic circuits, and even models for neurophysiology.
Язык: Рубрика: Computer science /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1974Количество страниц: 469Добавлена в каталог: 15.11.2013Операции: Положить на полку |
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135 394 107 126 31 2-category 352 Accessible linear sequential machine 417 Accessible part of an automaton 22 Accessible sequential machine 333 Accessible state 22 Accessible subset construction 34 Action monoid of an automaton 61 Action of a 31 Algebra over 159 Algebra over 162 Alphabet 5 Analytic 196 Automaton 12 Automaton, accessible 14 Automaton, accessible part of 22 Automaton, action monoid of 61 Automaton, behavior of 14 Automaton, coaccessible 23 Automaton, coaccessible part of 23 Automaton, complete 30 Automaton, completion of 31 Automaton, deterministic 30 Automaton, generalized 191 Automaton, graph of 26 Automaton, minimal 43 Automaton, normalized 138 Automaton, of type ( 72 Automaton, push-down 286 Automaton, reduced 46 Automaton, stack 287 Automaton, trim 23 Automaton, two-way 283 Automaton, unambiguous 147 Base 5 88 Base, maximal 88 Behavior of a machine 267 Behavior of an automaton 14 Bernoulli distribution 223 Berstel’s theorem 215 Bijective interpretation 115 Bimachine 320 Bimachine, complete 320 Bimachine, generalized 320 Bimachine, result of 321 Canonical projection 241 Category 6 Category, composition in 7 Category, large 8 Category, morphisms in 7 Category, object of 6 Category, small 8 Cayley — Hamilton theorem 434 Chabert’s theorem 439 Characteristic equation 434 Closure 379 Coaccessible state, part of an automaton 23 Cobham’s theorem 109 Coding 117 Complete automaton 30 Complete minimal automaton 47 Complete recurrence polynomial 432 Complete semiring 125 Complete sequential machine 298 Complete subset 47 Completely integrally closed ring 438 Completion of a deterministic automaton 31 Composition of linear sequential machines 424 Composition of relations 2 Composition of sequential machines 350 Congruence in a monoid 9 Congruence right 60 Cross-section 256 Denominator 204 431 Denominator, lowest 431 Dense subset 94 Deterministic automaton 30 Deterministic machine 288 Differential 314 Distance function 359 Division theorem 150 Domain of a relation 3 Dual 415 EDGE 12 Edge, label of 12 Equality theorem 143 Equivalence relation 8 Equivalent types 268 Expansion of real numbers 363 Feller’s Tauberian theorem 214 Fine morphism 6 Free monoid, base of 5 Function 3 Function, bijective 3 Function, generalized sequential 299 Function, injective 3 Function, linear sequential 411 Function, sequential 298 360 Function, surjective 3 Generalized automaton 191 Generating function 196 Generic sequence 395 Ginsburg — Rose theorem 317 Graph of a relation 2 Graph of an automaton 26 Hadamard product 197 Height 162 169 Hilbert curve 376 Hurwitz product 197 Initial state 12 Input alphabet 267 Input code 267 Integral closure 437 Integrally closed ring 431 Internal shuffle product 20 Interpretation, bijective 115 Interpretation, Polish 116 Interpretation, reversed 115 Interpretation, reversed bijective 116 Interpretation, Russian 116 Interpretation, standard 104 Inverse relation 2 Kalman — Rouchaleau — Wyman theorem 439 Kleene’s Theorem 175 Left multiplication 34 Left shift 417 Length-preserving relation 254 Limit theorem 220 Linear sequential machine 409 Linear sequential machine, accessible 417 Linear sequential machine, direct product of 411 Linear sequential machine, finite 411 Linear sequential machine, minimal 417 Linear sequential machine, reduced 417 Linear sequential machine, result of 409 Local set 27 Locally finite family 127 Locally finite monoid 170 Locally finite semigroup 170 Machine, deterministic 288 Machine, of type 266 Machine, Turing 288 Maximal base 88 Maximal base, prefix 92 Mealy machine 299 Minimal automaton 43 Minimal linear sequential machine 417 Minimal sequential machine 338 Modules 31 Monoid 3 Monoid, morphism of 4 Monoid, syntactic 62 Moore machine 299 312 Multiplication, left 34 Multiplication, right 35 Multiplicative dependence 109 Multiplicative relation 164 Multiplicity 120 126 Natural factorization mapping 9 Next-state function 297 Non-singular subset 188 Normalization procedure 139 Normalized automaton 138 Null path 13 Output alphabet 267 Output code 267 Output extended 297 Output function 297 Output module 298 Output module, generalized 299 Palindrome 56 Parallel composition 422 Parallel product 354 Partial function 3 Path in an automaton 13 Path in an automaton, label of 13 Path in an automaton, length of 13 Path in an automaton, successful 14 Peano curve 371 Period 100 Period of an analytic function 209 Polish interpretation 116 Positive rational function 282 Positive semiring 125 Post Correspondence Problem 159 Prefix 78 Prefix, maximal 92 Primary module 428 Proper state mapping 39 Purely singular subset 189 Push-down automaton 286 Quotient criterion 55 Rational 163 Rational closure 163 Rational expression 167 Rational formal power series 204 Rational operation 161 Rational relation 236 Rationally closed subset 161 Recognizable 139 Recognizable power series 199 Recognizable subset 14 Recurrence formula 205 Recurrence polynomial 432 Recurrent stats 97 Reduced automaton 46 Reduced linear sequential machine 417 Reduced output module 338 Relation 2 Relation, composition of 2 Relation, computed by a machine 267 Relation, domain of 2 Relation, equivalence 8 Relation, graph of 2 Relation, inverse of 2 Relation, length-preserving 254 Relation, multiplicative 164 Relation, positive rational 282 Relation, rational 236 Remak — Krull — Schmidt theorem 427 Replacement procedure 273 Restriction mapping 40 Result of a bimachine 321 Result of a linear sequential machine 409 Result of a sequential machine 298 Reversal function 18 Reversal of an automaton 18 Reversed interpretation 115 Right congruence 60 Right multiplication 34 Right shift 406 Russian interpretation 116 Sch 230 Semigroup 6 Semiring 122 Semiring, complete 125 Semiring, positive 125 Sequential machine 296 Sequential machine, accessible 333 Sequential machine, complete 298 Sequential machine, generalized 299 Sequential machine, minimal 417 Sequential machine, result of 298 Sequential machine, state-dependent 312 Series composition 425 Shuffle product 19 Shuffle product, internal 20 Sigma$-module, action of 31 Sigma$-module, complete 31 Singleton 127 Skolem — Mahler — Lech Theorem 206 Stack automaton 287 Standard interpretation 104 Standard pair representation 105 State 12 State relation 411 State, accessible 22 State, coaccessible 23 State, initial 12 State, recurent 97 State, terminal 12 State-mapping, complete 412 State-mapping, of automata 38 State-mapping, of linear sequential machines 412 State-mapping, of sequential machines 330 State-mapping, proper 38 stem 100 Strong minimization problem 343 Subalgebra 160 Subcategory 7 Subcategory, full 7 Subdivision property 71 Submonoid 4 Subset construction 33 Subset construction, accessible 34 Substitution 173 Subtraction theorem 153 Successful path 14 Support 127 Syntactic monoid 62 Syntactic morphism 62 Synthesis problem 348 Terminal state 12 Terminal subset of a machine 268 Thue sequence 399 Transducer 273 Transducer, accelerated 276 Transition matrix 14 Trim automaton 23 Trivial path 13 Turing machine 288 Two-way automaton 283 Type of a machine 266 Ultimately periodic sequence 362 Ultimately periodic set 101 Unambiguous automaton 147
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