
On Positivity and Minimality for SecondOrder Holonomic Sequences
An infinite sequence ⟨u_n⟩_n∈ℕ of real numbers is holonomic (also known ...
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Linear Complexity of Geometric Sequences Defined by Cyclotomic Classes and Balanced Binary Sequences Constructed by the Geometric Sequences
Pseudorandom number generators are required to generate pseudorandom num...
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Algebrabased Loop Synthesis
We present an algorithm for synthesizing program loops satisfying a give...
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Extremal values of semiregular continuants and codings of interval exchange transformations
Given a set A consisting of positive integers a_1<a_2<⋯<a_k and a kterm...
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Tropical recurrent sequences
Tropical recurrent sequences are introduced satisfying a given vector (b...
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A Timecop's Chase Around the Table
We consider the cops and robber game variant consisting of one cop and o...
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Variation diminishing linear timeinvariant systems
This paper studies the variation diminishing property of kpositive syst...
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Deciding ωRegular Properties on Linear Recurrence Sequences
We consider the problem of deciding ωregular properties on infinite traces produced by linear loops. Here we think of a given loop as producing a single infinite trace that encodes information about the signs of program variables at each time step. Formally, our main result is a procedure that inputs a prefixindependent ωregular property and a sequence of numbers satisfying a linear recurrence, and determines whether the sign description of the sequence (obtained by replacing each positive entry with "+", each negative entry with "", and each zero entry with "0") satisfies the given property. Our procedure requires that the recurrence be simple, , that the update matrix of the underlying loop be diagonalisable. This assumption is instrumental in proving our key technical lemma: namely that the sign description of a simple linear recurrence sequence is almost periodic in the sense of Muchnik, Semënov, and Ushakov. To complement this lemma, we give an example of a linear recurrence sequence whose sign description fails to be almost periodic. Generalising from sign descriptions, we also consider the verification of properties involving semialgebraic predicates on program variables.
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