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Adaptive and Bio-semantics of Continuous Petri Nets : Choosing the Appropriate Interpretation

Herajy M., Heiner M.

Fundamenta Informaticae

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2018

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Vol. 160, nr 1/2

53--80

EN

Continuous Petri nets (CPN) provide a graphical tool to model and analyse the deterministic dynamic behaviour of biological reaction networks. They can be considered as an alternative to the traditional ODE representation of biological models, enjoying a visual depiction of reaction networks. A model constructed as CPN can take advantages of quantitative (e.g., transient and steady state analysis) as well as qualitative (e.g., structural analysis) techniques. However, there are different semantics of CPN due to varying interpretations of transition rates. Choosing an appropriate semantics and corresponding simulator is not a straightforward procedure for the modelling of certain biological systems. In this paper, we compare two widely used semantics of CPN: adaptive semantics and bio-semantics. In the adaptive case, the enabling of continuous transitions may vary and the ODEs are correspondingly adjusted during model execution in order to avoid negative markings, while continuous transitions are always enabled in the bio-semantics and ODEs are never altered during the whole simulation period. We discuss the implementation complexity of both approaches in the context of systems biology and present two case studies to illustrate the best utilisation and individual strength of the two interpretations.

2

Complexity Analysis of Continuous Petri Nets

Fraca E., Haddad S.

Fundamenta Informaticae

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2015

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Vol. 137, nr 1

1--28

EN

At the end of the eighties, continuous Petri nets were introduced for: (1) alleviating the combinatory explosion triggered by discrete Petri nets (i.e. usual Petri nets) and, (2) modelling the behaviour of physical systems whose state is composed of continuous variables. Since then several works have established that the computational complexity of deciding some standard behavioural properties of Petri nets is reduced in this framework. Here we first establish the decidability of additional properties like coverability, boundedness and reachability set inclusion. We also design new decision procedures for reachability and lim-reachability problems with a better computational complexity. Finally we provide lower bounds characterising the exact complexity class of the reachability, the coverability, the boundedness, the deadlock freeness and the liveness problems. A small case study is introduced and analysed with these new procedures.

3

A Novel Continuous Model to Approximate Time Petri Nets: Modelling and Analysis

Gu T., Dong R.

International Journal of Applied Mathematics and Computer Science

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2005

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Vol. 15, no 1

141-150

EN

In order to approximate discrete-event systems in which there exist considerable states and events, David and Alla define a continuous Petri net (CPN). So far, CPNs have been a useful tool not only for approximating discrete-event systems but also for modelling continuous processes. Due to different ways of calculating instantaneous firing speeds of transitions, various continuous Petri net models, such as the CCPN (constant speed CPN), VCPN (variable speed CPN) and the ACPN (asymptotic CPN), have been proposed, where the continuous flow is specified uniquely by maximal firing speeds. However, in applications such as chemical processes there exist situations where the continuous flow must be above some minimal speed or in the range of minimal and maximal speeds. In this paper, from the point of view of approximating a time Petri net, the CPN is augmented with maximal and minimal firing speeds, and a novel continuous model, i.e., the Interval speed CPN (ICPN) is defined. The enabling and firing semantics of transitions of the ICPN are discussed, and the facilitating of continuous transitions is classified into three levels: 0-level, 1-level and 2-level. Some policies to resolve the conflicts and algorithms to undertake the behavioural analysis for the ICPN are developed. In addition, a chemical process example is presented.