The Parametric Complexity of Lossy Counter Machines

Sylvain Schmitz (1, 2)

1 LSV - Laboratoire Spécification et Vérification [Cachan]
2 IUF - Institut universitaire de France

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.

Keywords: counter machine; well-structured system; well-quasi-order; antichain; fast-growing complexity

Domains: Logic in Computer Science [cs.LO]

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⟩