Conway J.H. — Regular algebra and finite machines :: Электронная библиотека попечительского совета мехмата МГУ

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Conway J.H. — Regular algebra and finite machines

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Название: Regular algebra and finite machines

Автор: Conway J.H.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1971

Количество страниц: 147

Добавлена в каталог: 28.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Abstract family of language (AFL)      70
Accessible state      3
Acyclic algebra      104
Algebras, commutative      91
Algebras, conservative      104
Algebras, finite      100—102
Algebras, Gruska's algebra      85
Algebras, Kleene algebras      34
Algebras, radical algebras      88
Algebras, regulator algebras      71
Algebras, S-algebras      27 34 56
Algebras, X-algebras      34 100
Antiderivate      50
Antimachine      50
Applicator [ ]      56 85
Approximations      51—55
Automaton      1
Automaton, non-deterministic      31
Axioms      25 100
Biapplicator [[ ]]      85
Binary machine      3 41
Biproduct $\Omega$ : $\Psi$       57
Biregular operations +, :, **      57 60
Biregular operators      58 61
Biregulators      58
Biregulators in commutative cases      97
Biregulators, decision problems for      138
Biregulators, products of      57 62
Biregulators, table of      58
Bishuffle      59
Bistar $\Omega^{**}$       57
Biunit [1, 1]      57
Boiling process      113
Bomb      16
Bomb, combination lock bomb      18
Bomb, discriminant bomb      15
Bomb, transition matrix of      16
Boolean functions      44
Boolean functions in commutative case      96
Boolean functions, computation of      123
Bracket languages (a|b) etc.      126
Breadth b(E) of event      43
Canonical form for context-free language      127
Church's thesis      131
Classes of events and operators      65
Classes of events and operators, the class      82
Classical axioms C1-14      25 34—36
Classical axioms C1-14 for matrices      110
Classical axioms C1-14, insufficiency of      117
Classical equivalence      109
Classical events (C-events)      39
Classical events (C-events), derivatives of      109
Classical events (C-events), matrix star formula for      110
Combination lock      20
Combination lock bomb      18
Commutative algebra      91
Commutative biregulators      97
Commutative biregulators, open convex ditto      99
Commutative equations, minimal solutions      98
Commutative events      91
Companions of a language      85
Complement —E of event      44
Computational techniques      120
Concatenated power $E^{<n}$       25
Concave operator      72
Conservative algebra      104
Console      3
Constant part o[E]      41
Context-free languages      79
Contraction function $f_{-}$       62
Contraction operator $x_{-}$       59 61
Convex operator      72
Decision problems, insoluble      137
Decision procedures      33 53 123
Derivate      41
Derivate for classical events      109
Derivate, derivates for languages      86
Derivate, event derivate $\partial E/\partial G$       43
Derivate, input derivates $\partial E/\partial a$       41
Derivate, operator derivate $\partial E/\partial \Omega$       60
Derivate, right, or anti-derivate $\partial E/\partial G^{r}$       50
Derivate, word derivates $\partial E/\partial w$       41
Detonator      16
Diagram of machine (state diagram)      2
Direct sum      11
Discriminant bomb      15
Distinguishability      3
Distinguishing experiment      11
Divisibility of words      63
Dominating subfactorisation      47
Dual operator $^{\partial}\Omega$       59
Empty event 0      24
Empty word 1      3
Equality testing      123
Event      24
Event, breadth b(E) of event      43
Event, complement —E of event      44
Event, event classes      65
Event, event derivates      43
Event, factors of events      47
Event, length l(E) of event      43
Event, matrices of events      26
Event, regular event      26
Event, representable event      24
Event, reverse event $\leftarrow E$       44 60 66
Event, width w(E) of event      43
Event, X-events      39
Exact (n, m, p)-machine      8
Expansion function $f_{+}$       62
Expansion operator $a_{+}$       59 61
Experiment      3 7
Experiment, distinguishing experiment      11
Experiment, identifier experiment      12 15 19—20 23
Experiment, length of experiment      8 11
Explorer      20 23
Expression, regular      26 34
Expression, X-expressions      34
Factor matrix $|\overline{E}|$       48
Factor theorem for languages      86
Factorial function E! ( $E_{1}$ ,..., $E_{k}$ )      54
Factorisation      47
Factors      47
Factors, calculation with      123
Finite algebras      100—102
Free S-algebras      39 56
Free X-algebras      39
Full AFL      70
Function, regular      26
Function, S-function      65 81
Function, X-function      65
Grammar of language      79
Grammatically linear languages      84
Gruska's algebra      85
Gruska's theorem      84
Halting problem      131
Homomorphism      67
Homomorphism, unit-homomorphism      59 61
Identifier experiment      12 15 19—20 22
Inaccessibility      3
Indistinguishability      3
Inequalities $E \leqslant F$       27
Inequalities $E \leqslant F$ , testing for      123
Input (input letter)      1
Input (input letter), input derivate      41
Input (input letter), input vector      26
Insoluble problems      131
Insoluble problems for regular events and biregulators      138
Kleene algebras      34
Kleene's theorem      26
Languages (context-free)      79

Languages (context-free), bracket languages (a\b) etc.      126
Languages (context-free), canonical form for languages      127
Languages (context-free), class L of languages      82
Languages (context-free), companions of a language      85
Languages (context-free), computation with languages      126
Languages (context-free), derivatives of languages      86
Languages (context-free), factor theorem for languages      86
Languages (context-free), grammatically linear languages      84
Left factor      47
Length l(E) of event      43
Length l(E) of experiment      8 11
Letters, input and output      1
Letters, transient and terminal      79
Linear mechanism      30
Linear operator      56
Machines, (n, m, p)-machine      8
Machines, binary      3 41
Machines, construction from regular expressions      121
Machines, finite      1
Machines, infinite      127
Machines, Mealey machine      2
Machines, minimal machine      5—6
Machines, Moore machine      1
Machines, sequential machine      1
Machines, Turing machine      130
Machines, universal Turing machine      135
Matrix of events      26
Matrix of events, factor matrix $|\overline{E}|$       48
Matrix of events, of C-events      110
Matrix star formula Ml      28 40
Maximal solution of semilinear inequalities      127
Mechanism, linear      30
Mechanism, linear, general      45
Moore machine      1
Moore uncertainty principle      21
Moore's theorems      11 12
Non-deterministic automaton      31
Normal system      132
Normaliser $\mathscr{N}(E)$       55
Normaliser $\mathscr{N}(E)$ , computation of      124
o(E) = constant part of E      41
Occurrence      24
Open mapping conjecture      99
Open operator      72
Open operator, convex and commutative      99
Open operator, convex open operators      72
Operations, biregular +, :, **      57 60
Operations, Boolean      44
Operations, regular, +, ., *      25
Operations, S-operations $\sum$ , ., *      27
Operations, X-operations      34
Operators      56
Operators, biregular      58
Operators, classes of operators      65
Operators, concave operator      72
Operators, contraction operator $a_{-}$       59 61
Operators, convex operator      72 83
Operators, derivate $\partial /\partial \Omega$ = $^{\partial}\Omega$       59
Operators, dual operator $^{\partial}\Omega$       59
Operators, expansion operator $a_{+}$       59 61
Operators, inverse operator $\Omega^{-1}$       124
Operators, open operator      72
Operators, product $\Omega\Psi$ of operators      68
Operators, star $\Omega^{*}$ of operator      56 72
Operators, the operators $\circlearrowleft$       60 66
Output o( $\alpha$ ) of state      2
Output vector      26
Parikh's theorem      98
Pilling product theorem      68
Polynomial      65
Post Correspondence Problem      133
Problems, undecidable      131
Product of events      25
Product of events, biproduct $\Omega :\Psi$ of operators      57
Product of events, of operator classes      68
Product of events, of operators      68
Product of events, product of biregulators      62
Product of events, product of matrices      26
Production $u\rightarrow v$       79 132
Promotion lemma      113
Quotient by indistinguishability      4
Radical algebra      88
Redko theorem on axioms for regular algebra      104
Redko theorem on commutative algebra      93
Reduced form      12
Regular event      26
Regular event, commutative      91
Regular event, conservative      104
Regular expression      26 34
Regular expression, computation from machines      121—122
Regular expression, manipulation of      120
Regular function      26
Regular operations +, ., *      25
Regular operations +, ., * on operators      68
Regulator      57
Regulator, biregulator      58 61
Regulator, regulator algebra      71
Regulator, total regulator      57 63 71
Regulator, X-regulator      66
Representable event      24
Reverse $\leftarrow E$ of event      44 60 66
Right derivate      50
Right factor      47
Semilinear inequalities      127
Sequential machine      1
Shuffle       59
Solomaa's axiomatisation      107
Solution of equations      124
Square root $\surd E$       55
Standard algebra (=S-algebra)      27 34 56
Standard algebra (=S-algebra), S-functions      81
Standard algebra (=S-algebra), S-operations      27
Standard algebra (=S-algebra), S-operators      57
Star E* of event      25
Star E* of matrix      28 40
Star E* of operator      56 72
Star E*, bistar $\Omega^{**}$       56
Starth root      55
Starth root, computation of      124
State      1
State diagram      2
Subfactorization      47
Sum E + F of events      25
Sum E + F of operators      68
Sum E + F, infinite sum $\sum E_{t}$       25 34
Tautology      34
Total regulator      57 63 71
Transient and terminal letters      79
Transition function      2 29
Transition matrix of bomb      16
Transition matrix of machine      26
Truncation by inaccessibility      4
Turing machine      130
Turing machine, universal Turing machine      135
Uncertainty principle      21
Unit event 1      24
Unit event 1, biunit [1, 1]      57
Unit-homomorphism      59 67
Universal Turing machine      135
Vector, input or output      26
Width w(E) of event      43
Word      3
Word, divisibility of words      63
Word, empty word 1      3
Word, word derivate      41
X-algebra      34 40
X-event      39
X-expression      34
X-function      65
X-operations      34

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