A Generalization of Cobham’s Theorem for Regular Sequences
نویسندگان
چکیده
A sequence is said to be k-automatic if the n term of this sequence is generated by a finite state machine with n in base k as input. A result due to Cobham states that if a sequence is both kand `-automatic and k and ` are multiplicatively independent, then the sequence is eventually periodic. Allouche and Shallit defined (R, k)-regular sequences as a natural generalization of k-automatic sequences for a given ring R. In this paper we prove the following generalization of Cobham’s theorem: If a sequence is (R, k)and (R, `)-regular and k and ` are multiplicatively independent, then the sequence satisfies a linear recurrence over R.
منابع مشابه
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تاریخ انتشار 2007