130 research outputs found
The Additive Ordered Structure of Natural Numbers with a Beatty Sequence
We have provided a pure model-theoretic proof for the decidability of the
additive structure of the natural numbers together with a function {f} sending
{x} to {[\phi x]} with {\phi} the golden ratio.Comment: 14 page
Flat Model Checking for Counting LTL Using Quantifier-Free Presburger Arithmetic
This paper presents an approximation approach to verifying counter systems
with respect to properties formulated in an expressive counting extension of
linear temporal logic. It can express, e.g., that the number of
acknowledgements never exceeds the number of requests to a service, by counting
specific positions along a run and imposing arithmetic constraints. The
addressed problem is undecidable and therefore solved on flat
under-approximations of a system. This provides a flexibly adjustable trade-off
between exhaustiveness and computational effort, similar to bounded model
checking. Recent techniques and results for model-checking frequency properties
over flat Kripke structures are lifted and employed to construct a parametrised
encoding of the (approximated) problem in quantifier-free Presburger
arithmetic. A prototype implementation based on the z3 SMT solver demonstrates
the effectiveness of the approach based on problems from the RERS Challange
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