Description of membrane systems with time Petri nets: promoters/inhibitors, membrane dissolution, and priorities
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Description of membrane systems with time Petri nets: promoters/ inhibitors, membrane dissolution, and priorities Péter Battyányi1 · György Vaszil1 Received: 21 June 2020 / Accepted: 9 October 2020 © The Author(s) 2020
Abstract We continue the investigations of the connection between membrane systems and time Petri nets by extending the examined class of systems from simple symbol-object membrane systems to more complex cases: rules with promoters/inhibitors, membrane dissolution, and priority relation on the rules. By constructing the simulating time Petri net, we retain one of the main characteristics of the Petri net model; namely, the firings of the transitions can take place in any order, and there is no need to introduce maximal parallelism in the Petri net semantics. Instead, we substantially exploit the gain in computational strength obtained by the introduction of the timing feature for Petri nets. Keywords Petri nets · Promoters and inhibitors · Priorities · Membrane dissolution
1 Introduction Several models have emerged in the past decades to model distributed systems with interactive, parallel components. One of them was developed by Petri [16], and since then, the Petri nets have become the underlying system of a vast field of research with a considerable practical interest, see [3, 15, 19] for more information. The theory of membrane systems was established by Păun [12], and it has proved to be a very convenient and many-sided model of distributed systems with concurrent processes, see [13, 14]. Here, we continue the investigations concerning the relationship of these two computational models. Place/transition Petri nets are bipartite graphs, the conditions of the events of a distributed system are represented by places, and directed arcs connect the places to the transitions which model the events. The conditions for the events are The preliminary version of this paper was presented at CMC20, the 20th Conference on Membrane Computing, August 5–8, 2019, in Curtea de Argeş, Romania. * György Vaszil [email protected] Péter Battyányi [email protected] 1
Department of Computer Science, Faculty of Informatics, University of Debrecen, Kassai út 26, Debrecen 4028, Hungary
expressed by tokens: an event can take place, i.e., a transition can fire, if there are enough tokens in the places at the source ends of the incoming arcs of a transition. These places are called preconditions. The outgoing edges of a transition represent the post-condition of the events. Firing of a transition means removing tokens from the preconditions and adding them to the post-conditions. The number of tokens moved in this way is prescribed by the multiplicities of the incoming and outgoing arcs. Membrane systems are models of distributed, synchronized computational systems ordered in a tree-like structure. The building blocks are compartments which contain multisets of objects. The multisets evolve in each compartment in a parallel manner, and the compartments, in each computational ste
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