On the home-space problem for Petri nets and its Ackermannian complexity
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F24%3A73627226" target="_blank" >RIV/61989592:15310/24:73627226 - isvavai.cz</a>
Result on the web
<a href="https://lmcs.episciences.org/14926/pdf" target="_blank" >https://lmcs.episciences.org/14926/pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.46298/lmcs-20(4:23)2024" target="_blank" >10.46298/lmcs-20(4:23)2024</a>
Alternative languages
Result language
angličtina
Original language name
On the home-space problem for Petri nets and its Ackermannian complexity
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 semilinear set of configurations H we can effectively compute a semilinear set C of configurations, called a non-reachability core for H, such that for every set X the set H 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
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
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
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Logical Methods in Computer Science
ISSN
1860-5974
e-ISSN
1563-5104
Volume of the periodical
20
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
23
Pages from-to
"23-1"-"23-23"
UT code for WoS article
001378599000004
EID of the result in the Scopus database
2-s2.0-85212527833