caa a22 4500 445842814 CHVBK 20180317145350.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s11047-010-9211-3 doi (NATIONALLICENCE)springer-10.1007/s11047-010-9211-3 Popova-Zeugmann Louchka Department of Computer Science, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany aut Quantitative evaluation of time-dependent Petri nets and applications to biochemical networks [Elektronische Daten] [Louchka Popova-Zeugmann] Time Petri nets (TPN) are a well-known extension of standard Petri nets, where each transition gets a continuous time interval, specifying the range of the transition's firing time. In contrast, Timed Petri nets are a different time-dependent extension where a time duration is associated with each transition. We sketch a locally defined transformation from a Timed into a Time Petri net. Additionally, we consider time-dependent Petri nets, where the firing of each transition lasts a certain time which is limited by both a lower and an upper bound. These nets can also be transformed locally into TPN and are used in this paper for modelling and analysing biochemical systems, and we present algorithms allowing their quantitative analyses. We consider algorithms which work for arbitrary systems, i.e., bounded as well as unbounded ones, and algorithms, which are suitable for bounded systems only. The crucial point is the state space reduction, which exploits basically two ideas: parametric state description and discretisation of the state space. Altogether, we introduce eight problems, characterised by their input/ output relation. A sketch of the solution idea as well as possible application scenarios to evaluate biochemical systems are given, too. Springer Science+Business Media B.V., 2010 Time Petri nets nationallicence Timed Petri Nets nationallicence Biochemical Networks nationallicence Time Distances nationallicence Natural Computing Springer Netherlands 10/3(2011-09-01), 1017-1043 1567-7818 10:3<1017 2011 10 11047 https://doi.org/10.1007/s11047-010-9211-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11047-010-9211-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Popova-Zeugmann Louchka Department of Computer Science, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany aut NATIONALLICENCE 773 0- Natural Computing Springer Netherlands 10/3(2011-09-01), 1017-1043 1567-7818 10:3<1017 2011 10 11047 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer