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.
Document type :
Conference papers
Complete list of metadatas

Cited literature [50 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02020728
Contributor : Sylvain Schmitz <>
Submitted on : Sunday, April 21, 2019 - 6:14:02 PM
Last modification on : Friday, July 5, 2019 - 12:04:05 PM

File

main.pdf
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution - ShareAlike 4.0 International License

Identifiers

Citation

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⟩

Share

Metrics

Record views

54

Files downloads

68