0000000000987952
AUTHOR
Inese Berzina
Bounded Bi-ideals and Linear Recurrence
Bounded bi-ideals are a subclass of uniformly recurrent words. We introduce the notion of completely bounded bi-ideals by imposing a restriction on their generating base sequences. We prove that a bounded bi-ideal is linearly recurrent if and only if it is completely bounded.
On a Non-periodic Shrinking Generator
We present a new non-periodic random number generator based on the shrinking generator. The A-sequence is still generated using a LFSR, but the S-sequence is replaced by a finitely generated bi-ideal - a non-periodic sequence. The resulting pseudo-random sequence performs well in statistical tests. We show a method for the construction of an infinite number of finitely generated bi-ideals from a given A-sequence, such that the resulting sequence of the shrinking generator is nonperiodic. Further we prove the existence of what we call universal finitely generated bi-ideals that produce non-periodic words when used as the S-sequence of a shrinking generator for all non-trivial periodic A-sequ…