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Pré-Publication, Document De Travail Année : 2019

The Parametric Complexity of Lossy Counter Machines

Résumé

The reachability problem in lossy counter machines is the best-known ACKERMANN-complete problem and has been used to establish most of the ACKERMANN-hardness statements in the literature. This hides however a complexity gap when the number of counters is fixed. We close this gap and prove Fd-completeness for machines with d counters, which provides the first known uncontrived problems complete for the fast-growing complexity classes at levels 3 < d < ω. We develop for this an approach through antichain factorisations of bad sequences and analysing the length of controlled antichains.
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Dates et versions

hal-02020728 , version 1 (15-02-2019)
hal-02020728 , version 2 (21-04-2019)

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  • HAL Id : hal-02020728 , version 1

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Sylvain Schmitz. The Parametric Complexity of Lossy Counter Machines. 2019. ⟨hal-02020728v1⟩
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