On robustness for the skolem and positivity problems

S Akshay, H Bazille, B Genest… - STACS 2022-39th …, 2022 - hal.science
The Skolem problem is a long-standing open problem in linear dynamical systems: can a
linear recurrence sequence (LRS) ever reach 0 from a given initial configuration? Similarly …

A robust class of linear recurrence sequences

C Barloy, N Fijalkow, N Lhote, F Mazowiecki - Information and Computation, 2022 - Elsevier
We introduce a subclass of linear recurrence sequences which we call poly-rational
sequences because they are denoted by rational expressions closed under sum and …

[PDF][PDF] Pumping lemmas for weighted automata

A Chattopadhyay, F Mazowiecki… - Logical Methods in …, 2021 - lmcs.episciences.org
We present pumping lemmas for five classes of functions definable by fragments of weighted
automata over the min-plus semiring, the max-plus semiring and the semiring of natural …

Identity testing for radical expressions

N Balaji, K Nosan, M Shirmohammadi… - Proceedings of the 37th …, 2022 - dl.acm.org
We study the Radical Identity Testing problem (RIT): Given an algebraic circuit representing
a polynomial and nonnegative integers a1,…, ak and d1,…, dk, written in binary, test …

On eventual non-negativity and positivity for the weighted sum of powers of matrices

S Akshay, S Chakraborty, D Pal - International Joint Conference on …, 2022 - Springer
The long run behaviour of linear dynamical systems is often studied by looking at eventual
properties of matrices and recurrences that underlie the system. A basic problem in this …

Robust Positivity Problems for Linear Recurrence Sequences: The Frontiers of Decidability for Explicitly Given Neighbourhoods

M Vahanwala - 43rd IARCS Annual Conference on Foundations …, 2023 - drops.dagstuhl.de
Abstract Linear Recurrence Sequences (LRS) are a fundamental mathematical primitive for
a plethora of applications such as the verification of probabilistic systems, model checking …

A universal Skolem set of positive lower density

F Luca, J Ouaknine, J Worrell - 2022 - ora.ox.ac.uk
The Skolem Problem asks to decide whether a given integer linear recurrence sequence
(LRS) has a zero term. Decidability of this problem has been open for many decades, with …

Robust positivity problems for linear recurrence sequences

M Vahanwala - arXiv preprint arXiv:2305.04870, 2023 - arxiv.org
Linear Recurrence Sequences (LRS) are a fundamental mathematical primitive for a
plethora of applications such as the verification of probabilistic systems, model checking …

On robustness for the skolem, positivity and ultimate positivity problems

S Akshay, H Bazille, B Genest… - Logical Methods in …, 2024 - lmcs.episciences.org
The Skolem problem is a long-standing open problem in linear dynamical systems: can a
linear recurrence sequence (LRS) ever reach 0 from a given initial configuration? Similarly …

[PDF][PDF] Decision questions for probabilistic automata on small alphabets

PC Bell, P Semukhin - Logical Methods in Computer Science, 2023 - lmcs.episciences.org
We study the emptiness and λ-reachability problems for unary and binary Probabilistic Finite
Automata (PFA) and characterise the complexity of these problems in terms of the degree of …