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On Presburger arithmetic extended with non-unary counting quantifiers

Peter Habermehl ; Dietrich Kuske.

We consider a first-order logic for the integers with addition. This logic extends classical first-order logic by modulo-counting, threshold-counting and exact-counting quantifiers, all applied to tuples of variables (here, residues are given as terms while moduli and thresholds are given&nbsp;[&hellip;]

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Infinite and Bi-infinite Words with Decidable Monadic Theories

Dietrich Kuske ; Jiamou Liu ; Anastasia Moskvina.

We study word structures of the form $(D,<,P)$ where $D$ is either $\mathbb{N}$ or $\mathbb{Z}$, $<$ is the natural linear ordering on $D$ and $P\subseteq D$ is a predicate on $D$. In particular we show: (a) The set of recursive $\omega$-words with decidable monadic second order theories is&nbsp;[&hellip;]

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Propositional Dynamic Logic for Message-Passing Systems

Benedikt Bollig ; Dietrich Kuske ; Ingmar Meinecke.

We examine a bidirectional propositional dynamic logic (PDL) for finite and infinite message sequence charts (MSCs) extending LTL and TLC-. By this kind of multi-modal logic we can express properties both in the entire future and in the past of an event. Path expressions strengthen the classical&nbsp;[&hellip;]

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