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
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] Pum** lemmas for weighted automata
We present pum** 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 …
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 …
On eventual non-negativity and positivity for the weighted sum of powers of matrices
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 …
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
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 …