Tao R. Finite Automata and Application to Cryptography
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406 Index
period distribution polynomial, 251
permutation, 4
polynomial basis, 226, 229
polynomial coordinate, 226, 229
predecessor state, 11
pseudo-memory finite automata, 13
R
a
R
b
transformation sequence
– circular, 145
– elementary, 111, 133
– linear, 95, 100, 111
– natural expansion of, 148
– terminating, 133, 145
R
a
transformation, 78, 88, 133
– linear, 95, 100, 111
–modified,90
R
−1
a
R
−1
b
transformation sequence
– linear, 102
R
−1
a
transformation, 91
– linear, 102
R
b
transformation, 78, 88, 133
– linear, 95, 100, 111
–modified,90
R
−1
b
transformation, 92
– linear, 102
range, 3
rank spectrum, 340
relation, 2
restriction, 4
right part, 142
root basis, 233, 236, 239
root coordinate, 233, 236, 239
root state, 189
semi-input-memory finite automata, 13
sequence
– less than, 340
– translation of, 227
sequential mapping, 8
shift register, 225
– characteristic polynomial of, 225
– output polynomial of, 227
– second characteristic polynomial of,
227
state
– β-input set of, 50
– l-step, 165
– τ-match, 28
– l-step, 165
– compatible, 178
– equivalent, 9, 179
– match pair, 28, 35, 184, 185
– reachable, 184
– stronger than, 179, 185
subgraph, 6
subtree, 6
successor state, 11
surjection, 4
symmetric graph, 285
– edge, 285
– endpoint, 285
terminal vertex
–ofarc,5
–ofpath,5
transformation, 3
– c-dependent, 329
– c-independent, 329
– dependent degree of, 329
– dependent polynomial of, 329
– independent degree of, 329
– linearly dependent, 329
– linearly independent, 329
– truth table of, 331
translation, 227
– c-translation, 245
tree, 6
– x-branch, 66
– x-successor of, 42
– closed, 42, 45
– compatible, 41
– labelled, 6
– main branch, 71
– next maximal branch, 71
– strongly compatible, 41
– successor of, 45
type of derived permutation, 284
type of sequence, 284
undefined value, 3
valid partition, 161
value, 3
vertex, 5
–depthof,65
– input label sequence of, 41
– label of, 44
– output label sequence of, 41
word, 6
– ω-word, 6
– concatenation of, 6
– prefix of, 7
– stronger than, 178
– suffix of, 7
word length, 6
z-transformation, 23