The Semilinear Home-Space Problem Is Ackermann-Complete for Petri Nets
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
The Semilinear Home-Space Problem Is Ackermann-Complete for Petri Nets
Original language description
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.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Leibniz International Proceedings in Informatics (LIPIcs)
ISBN
978-3-95977-299-0
ISSN
1868-8969
e-ISSN
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Number of pages
17
Pages from-to
"36-1"-"36-17"
Publisher name
Dagstuhl Publishing
Place of publication
Wadern
Event location
Antwerp
Event date
Sep 18, 2023
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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