Positivity of third order linear recurrence sequences
نویسندگان
چکیده
منابع مشابه
Positivity Problems for Low-Order Linear Recurrence Sequences
We consider two decision problems for linear recurrence sequences (LRS) over the integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the Ultimate Positivity Problem (are all but finitely many terms of a given LRS positive?). We show decidability of both problems for LRS of order 5 or less, with complexity in the Counting Hierarchy for Positivity, and in polynomi...
متن کاملPositivity of second order linear recurrent sequences
We give an elementary proof for the Positivity Problem for second order recurrent sequences: it is decidable whether or not a recurrent sequence defined by un = aun−1 + bun−2 has only nonnegative terms.
متن کاملEffective Positivity Problems for Simple Linear Recurrence Sequences
We consider two computational problems for linear recurrence sequences (LRS) over the integers, namely the Positivity Problem (determine whether all terms of a given LRS are positive) and the effective Ultimate Positivity Problem (determine whether all but finitely many terms of a given LRS are positive, and if so, compute an index threshold beyond which all terms are positive). We show that, f...
متن کاملUltimate Positivity is Decidable for Simple Linear Recurrence Sequences
We consider the decidability and complexity of the Ultimate Positivity Problem, which asks whether all but finitely many terms of a given rational linear recurrence sequence (LRS) are positive. Using lower bounds in Diophantine approximation concerning sums of S-units, we show that for simple LRS (those whose characteristic polynomial has no repeated roots) the Ultimate Positivity Problem is de...
متن کاملOn the Positivity Problem for Simple Linear Recurrence Sequences,
Given a linear recurrence sequence (LRS) over the integers, the Positivity Problem asks whether all terms of the sequence are positive. We show that, for simple LRS (those whose characteristic polynomial has no repeated roots) of order 9 or less, Positivity is decidable, with complexity in the Counting Hierarchy.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2009
ISSN: 0166-218X
DOI: 10.1016/j.dam.2009.06.021