Skolem meets schanuel
The celebrated Skolem-Mahler-Lech Theorem states that the set of zeros of a linear
recurrence sequence is the union of a finite set and finitely many arithmetic progressions …
recurrence sequence is the union of a finite set and finitely many arithmetic progressions …
Does a program yield the right distribution? Verifying probabilistic programs via generating functions
We study discrete probabilistic programs with potentially unbounded looping behaviors over
an infinite state space. We present, to the best of our knowledge, the first decidability result …
an infinite state space. We present, to the best of our knowledge, the first decidability result …
On the skolem problem and the skolem conjecture
It is a longstanding open problem whether there is an algorithm to decide the Skolem
Problem for linear recurrence sequences (LRS) over the integers, namely whether a given …
Problem for linear recurrence sequences (LRS) over the integers, namely whether a given …
Equivalence and similarity refutation for probabilistic programs
We consider the problems of statically refuting equivalence and similarity of output
distributions defined by a pair of probabilistic programs. Equivalence and similarity are two …
distributions defined by a pair of probabilistic programs. Equivalence and similarity are two …
Skolem Meets Bateman-Horn
The Skolem Problem asks to determine whether a given integer linear recurrence sequence
has a zero term. This problem arises across a wide range of topics in computer science …
has a zero term. This problem arises across a wide range of topics in computer science …
Completing the picture for the Skolem Problem on order-4 linear recurrence sequences
P Bacik - arXiv preprint arXiv:2409.01221, 2024 - arxiv.org
For almost a century, the decidability of the Skolem Problem-that is, the problem of finding
whether a given linear recurrence sequence (LRS) has a zero term-has remained open. A …
whether a given linear recurrence sequence (LRS) has a zero term-has remained open. A …
Computing zeta functions of large polynomial systems over finite fields
We improve the algorithms of Lauder-Wan [11] and Harvey [8] to compute the zeta function
of a system of m polynomial equations in n variables, over the q element finite field F q, for …
of a system of m polynomial equations in n variables, over the q element finite field F q, for …