Conference Papers Year : 2022

What’s decidable about linear loops?

Abstract

We consider the MSO model-checking problem for simple linear loops, or equivalently discrete-time linear dynamical systems, with semialgebraic predicates (i.e., Boolean combinations of polynomial inequalities on the variables). We place no restrictions on the number of program variables, or equivalently the ambient dimension. We establish decidability of the model-checking problem provided that each semialgebraic predicate either has intrinsic dimension at most 1, or is contained within some three-dimensional subspace. We also note that lifting either of these restrictions and retaining decidability would necessarily require major breakthroughs in number theory.
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Dates and versions

hal-03789796 , version 1 (27-09-2022)

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Toghrul Karimov, Engel Lefaucheux, Joel Ouaknine, David Purser, Anton Varonka, et al.. What’s decidable about linear loops?. 49th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL 2022), Jan 2022, Philadelphia, United States. pp.1 - 25, ⟨10.1145/3498727⟩. ⟨hal-03789796⟩
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