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Rich Sequences and Decidability of Arithmetic Theories
Toghrul Karimov, Joris Nieuwveld, Joël Ouaknine
We develop a new framework for proving the undecidability of first-order theories of structures of the form , ,…
On existential Büchi arithmetic in two coprime bases
Joris Nieuwveld
For multiplicatively independent natural numbers and , Villemaire showed in 1992 that the first-order theory of Presburger arithmetic expanded with both Büchi predicates $V_…
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 Expansions of Monadic Second-Order Logic with Dynamical Predicates
Joris Nieuwveld, Joël Ouaknine
Expansions of the monadic second-order (MSO) theory of the structure have been a fertile and active area of research ever since the publication of…
On the Decidability of Presburger Arithmetic Expanded with Powers
Toghrul Karimov, Florian Luca, Joris Nieuwveld +2
We prove that for any integers , the existential fragment of the first-order theory of the structure …
Model Checking Markov Chains as Distribution Transformers
Rajab Aghamov, Christel Baier, Toghrul Karimov +4
The conventional perspective on Markov chains considers decision problems concerning the probabilities of temporal properties being satisfied by traces of visited states. However,…
On the Decidability of Monadic Theories of Arithmetic Predicates
Valérie Berthé, Toghrul Karimov, Joris Nieuwveld +3
We investigate the decidability of the monadic second-order (MSO) theory of the structure , for various unary predicates $P_1,\ldots,P…
Skolem Meets Schanuel
Yuri Bilu, Florian Luca, Joris Nieuwveld +3
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. The c…