14 papers
Conjectural Decidability of the Skolem Problem
Florian Luca, Joël Ouaknine, James Worrell
The Skolem Problem asks to determine whether a given integer linear recurrence sequence (LRS) has a zero term. This problem, whose decidability has been open for many decades, aris…
On Variable-Bounded Non-Linear Expansions of Presburger Arithmetic
Piotr Bacik, Joris Nieuwveld, Joël Ouaknine +3
We consider expansions of Presburger arithmetic with families of monadic polynomial predicates. (Examples of such predicates are the set of perfect squares, or the set of integers…
On the -adic Skolem Problem
Piotr Bacik, Joël Ouaknine, David Purser +1
The Skolem Problem asks to determine whether a given linear recurrence sequence (LRS) has a zero term. Showing decidability of this problem is equivalent to giving an effective pro…
The Value Problem for Weighted Timed Games with Two Clocks is Undecidable
Quentin Guilmant, Joël Ouaknine, Isa Vialard
The Value Problem for weighted timed games (WTGs) consists in determining, given a two-player weighted timed game with a reachability objective and a rational threshold, whether or…
Termination Analysis of Linear-Constraint Programs
Amir M. Ben-Amram, Samir Genaim, Joël Ouaknine +1
This paper provides an overview of techniques in termination analysis for programs with numerical variables and transitions defined by linear constraints. This subarea of program a…
On the Complexity of the Skolem Problem at Low Orders
Piotr Bacik, Joël Ouaknine, James Worrell
The Skolem Problem asks to determine whether a given linear recurrence sequence (LRS) over the integers has a zero term, that is, whether there e…