The Semilinear Home-Space Problem Is Ackermann-Complete for Petri Nets
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F23%3A73620756" target="_blank" >RIV/61989592:15310/23:73620756 - isvavai.cz</a>
Výsledek na webu
<a href="https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.36" target="_blank" >https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2023.36</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.CONCUR.2023.36" target="_blank" >10.4230/LIPIcs.CONCUR.2023.36</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
The Semilinear Home-Space Problem Is Ackermann-Complete for Petri Nets
Popis výsledku v původním jazyce
A set of configurations H is a home-space for a set of configurations X of a Petri net if every configuration reachable from (any configuration in) X can reach (some configuration in) H. The semilinear home-space problem for Petri nets asks, given a Petri net and semilinear sets of configurations X, H, if H is a home-space for X. In 1989, David de Frutos Escrig and Colette Johnen proved that the problem is decidable when X is a singleton and H is a finite union of linear sets with the same periods. In this paper, we show that the general (semilinear) problem is decidable. This result is obtained by proving a duality between the reachability problem and the non-home-space problem. In particular, we prove that for any Petri net and any linear set of configurations L we can effectively compute a semilinear set C of configurations, called a non-reachability core for L, such that for every set X the set L is not a home-space for X if, and only if, C is reachable from X. We show that the established relation to the reachability problem yields the Ackermann-completeness of the (semilinear) home-space problem. For this we also show that, given a Petri net with an initial marking, the set of minimal reachable markings can be constructed in Ackermannian time.
Název v anglickém jazyce
The Semilinear Home-Space Problem Is Ackermann-Complete for Petri Nets
Popis výsledku anglicky
A set of configurations H is a home-space for a set of configurations X of a Petri net if every configuration reachable from (any configuration in) X can reach (some configuration in) H. The semilinear home-space problem for Petri nets asks, given a Petri net and semilinear sets of configurations X, H, if H is a home-space for X. In 1989, David de Frutos Escrig and Colette Johnen proved that the problem is decidable when X is a singleton and H is a finite union of linear sets with the same periods. In this paper, we show that the general (semilinear) problem is decidable. This result is obtained by proving a duality between the reachability problem and the non-home-space problem. In particular, we prove that for any Petri net and any linear set of configurations L we can effectively compute a semilinear set C of configurations, called a non-reachability core for L, such that for every set X the set L is not a home-space for X if, and only if, C is reachable from X. We show that the established relation to the reachability problem yields the Ackermann-completeness of the (semilinear) home-space problem. For this we also show that, given a Petri net with an initial marking, the set of minimal reachable markings can be constructed in Ackermannian time.
Klasifikace
Druh
D - Stať ve sborníku
CEP obor
—
OECD FORD obor
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2023
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název statě ve sborníku
Leibniz International Proceedings in Informatics (LIPIcs)
ISBN
978-3-95977-299-0
ISSN
1868-8969
e-ISSN
—
Počet stran výsledku
17
Strana od-do
"36-1"-"36-17"
Název nakladatele
Dagstuhl Publishing
Místo vydání
Wadern
Místo konání akce
Antwerp
Datum konání akce
18. 9. 2023
Typ akce podle státní příslušnosti
WRD - Celosvětová akce
Kód UT WoS článku
—