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On anti-occurrence of subsets of transitions in Petri net-based models of complex biological systems


[ 1 ] Instytut Informatyki, Wydział Informatyki i Telekomunikacji, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.3] Information and communication technology

Year of publication


Published in


Journal year: 2022 | Journal volume: vol. 222

Article type

scientific article

Publication language


  • Petri nets
  • biological systems
  • sets of transitions
  • computational complexity
  • exact algorithm

EN Background and Objective: In the last two decades there can be observed a rapid development of systems biology. The basis of systems methods is a formal model of an analyzed system. It can be created in a language of some branch of mathematics and recently Petri net-based biological models seem to be especially promising since they have a great expressive power. One of the methods of analysis of such models is based on transition invariants. They correspond to some subprocesses which do not change a state of the modeled biological system. During such analysis, a need arose to study the subsets of transitions, what leads to interesting combinatorial problems — which have been considered in theory and practice. Methods & Results: Two problems of anti-occurrence were considered. These problems concern a set of transitions which is not a subset of any of t-invariant supports or is not a subset of t-invariant supports from some collection of such supports. They are defined in a formal way, their computational complexity is analyzed and an exact algorithm is provided for one of them. Conclusions: A comprehensive analysis of complex biological phenomena is challenging. Finding elementary processes that do not affect subprocesses belonging to the entire studied biological system may be necessary for a complete understanding of such a model and it is possible thanks to the proposed algorithm.

Date of online publication


Pages (from - to)

104793-1 - 104793-13





Article Number: 104793

License type

CC BY (attribution alone)

Open Access Mode

czasopismo hybrydowe

Open Access Text Version

final published version

Date of Open Access to the publication

in press

Ministry points / journal


Impact Factor

1.957 [List 2021]

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