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Conference Papers Year : 2019

The Parametric Complexity of Lossy Counter Machines

Abstract

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

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Sylvain Schmitz. The Parametric Complexity of Lossy Counter Machines. ICALP 2019, Jul 2019, Patras, Greece. pp.129:1--129:15, ⟨10.4230/LIPIcs.ICALP.2019.129⟩. ⟨hal-02020728v2⟩
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