ForewordbyArtoSalomaa.
Preface
1. Introduction
1.1 Preliminaries
1.1.1 RelationsandFunctions
1.1.2 Graphs
1.2 DefinitionsofFiniteAutomata
1.2.1 FiniteAutomataasTransducers
1.2.2 SpecialFiniteAutomata
1.2.3 CompoundFiniteAutomata
1.2.4 FiniteAutomataasRecognizers
1.3 LinearFiniteAutomata
1.4 ConceptsonInvertibility
1.5 ErrorPropagationandFeedforwardInvertibility
1.6 LabelledTreesasStatesofFiniteAutomata
2. MutualInvertibilityandSearch
2.1 MinimalOutputWeightandInputSet
2.2 MutualInvertibilityofFiniteAutomata
2.3 FindInputbySearch
2.3.1 OnOutputSetandInputTree
2.3.2 ExhaustingSearch
2.3.3 StochasticSearch
3. RaRbTransformationMethod
3.1 SufficientConditionsandInversion
3.2 GenerationofFiniteAutomatawithInvertibility
3.3 InvertibilityofQuasi-LinearFiniteAutomata
3.3.1 DecisionCriteria
3.3.2 StructureProblem
4. RelationsBetweenTransformations
4.1 RelationsBetweenRaRbTransformations
4.2 CompositionofRaRbTransformations
4.3 ReducedEchelonMatrix
4.4 CanonicalDiagonalMatrixPolynomial
4.4.1 RaRbTransformationsoverMatrixPolynomial
4.4.2 RelationsBetweenRaRbTransformationandCanonicalDiagonalForm
4.4.3 RelationsofRight-Parts
4.4.4 ExistenceofTerminatingRaRbTransformationSequence
5. StructureofFeedforwardInverses
5.1 ADecisionCriterion..
5.2 DelayFree
5.3 OneStepDelay
5.4 TwoStepDelay
6. SomeTopicsonStructureProblem
6.1 SomeVariantsofFiniteAutomata
6.1.1 PartialFiniteAutomata
6.1.2 NondeterministicFiniteAutomata
6.2 InversesofaFiniteAutomaton
6.3 OriginalInversesofaFiniteAutomaton
6.4 WeakInversesofaFiniteAutomaton
6.5 OriginalWeakInversesofaFiniteAutomaton
6.6 WeakInverseswithBoundedErrorPropagationofaFiniteAutomaton
7. LinearAutonomousFiniteAutomata
7.1 BinomialCoefficient
7.2 RootRepresentation
7.3 TranslationandPeriod
7.3.1 ShiftRegisters
7.3.2 FiniteAutomata
7.4 Linearization
7.5 Decimation
8. OneKeyCryptosystemsandLatinArrays
8.1 CanonicalFormforFiniteAutomatonOneKeyCryptosystems
8.2 LatinArrays
8.2.1 Definitions
8.2.2 On(n，k，r)-LatinArrays
8.2.3 Invariant
8.2.4 AutotopismGroup
8.2.5 TheCasen=2，3
8.2.6 TheCasen=4，k≤4
8.3 LinearlyIndependentLatinArrays
8.3.1 LatinArraysofInvertibleFunctions
8.3.2 GenerationofLinearlyIndependentPermutations
9. FiniteAutomatonPublicKeyCryptosystems
9.1 TheoreticalFundamentals
9.2 BasicAlgorithm
9.3 AnExampleofFAPKC
9.4 OnWeakKeys
9.4.1 LinearRaRbTransformationTest
9.4.2 OnAttackbyReducedEchelonMatrix
9.4.3 OnAttackbyCanonicalDiagonalMatrixPolynomial
9.5 Security
9.5.1 InversionbyaGeneralMethod
9.5.2 InversionbyDecomposingFiniteAutomata
9.5.3 ChosenPlaintextAttack
9.5.4 ExhaustingSearchandStochasticSearch
9.6 GeneralizedAlgorithms
9.6.1 SomeTheoreticalResults
9.6.2 TwoAlgorithms
References
Index
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