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Eilenberg S. — Automata, languages, and machines. Volume A
Eilenberg S. — Automata, languages, and machines. Volume A

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Название: Automata, languages, and machines. Volume A

Автор: 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: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 469

Добавлена в каталог: 15.11.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$K$-$\Sigma$-automaton      135
$k$-recognizable sequence      394
$k$-recognizable set      107
$k$-subset      126
$\Sigma$-module      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 $\Sigma$-module      31
Algebra over $K$      159
Algebra over $K$, unitary      162
Alphabet      5
Analytic $K$-subset      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 ($p$, $r$)      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 $\Phi$      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 $K$-subset      163
Rational closure      163
Rational expression      167
Rational formal power series      204
Rational operation      161
Rational relation      236
Rationally closed subset      161
Recognizable $K$-subset      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$\ddot{u}$tzenberger’s theorem      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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