On robustness for the skolem and positivity problems
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 …
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 …
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 …
automata over the min-plus semiring, the max-plus semiring and the semiring of natural …
Identity testing for radical expressions
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 …
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 …
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 plethora of applications such as the verification of probabilistic systems, model checking …
A universal Skolem set of positive lower density
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 …
(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 …
plethora of applications such as the verification of probabilistic systems, model checking …
On robustness for the skolem, positivity and ultimate positivity problems
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 …
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 …
Automata (PFA) and characterise the complexity of these problems in terms of the degree of …