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Model checking multi-level and recursive nets

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Abstract

With the increasing complexity of the problems and systems arising nowadays, the use of multi-level models is becoming more frequent in practice. However, there are still few reports in the literature concerning methods for analyzing such models without flattening the multi-level structure. For instance, several variants of multi-level Petri nets have been applied for modeling interaction protocols and mobility in multi-agent systems and coordination of cross-organizational workflows. But there are few automated tools for analyzing the behavior of these nets. In this paper we explain how to detect faults in models based on a representative class of multi-level nets: the nested Petri nets. We translate a nested net into a verifiable model that preserves its modular structure, a PROMELA program. This allows the use of SPIN model checker to verify properties related to termination, boundedness and reachability.

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Notes

  1. See the complete grammar at http://spinroot.com/spin/Man/grammar.html.

  2. The skip statement is equivalent to the constant 1, i.e., it is always executable.

  3. The rendezvous communication in PROMELA is not suitable for simulating the synchronizations in a NPN. A rendezvous statement can only be executed if a matching statement can be performed immediately; otherwise the process is blocked. This would prevent a net token from firing any other transition until the synchronization could be completed.

  4. In case \(np=onp\), transpNetTok is not required. Besides, if t is unlabeled the entire code can be omitted. Also note that net-typed variables do not need a representation in the translation.

  5. An inhibitor arc is enabled when the input place is empty.

  6. Any sequence \(A_k\) may contain regions with priorities 4 or 5, not both.

  7. See http://www.dropbox.com/s/uloj2xmgwomimqv/exNPNMASimpExt.pml?dl=0.

  8. See http://www.dropbox.com/s/28j8x7fhyx7ucdg/npn2cpn.rar?dl=0 for the models.

  9. Error: value (256->0 (8)) truncated in assignment.

  10. See http://www.dropbox.com/s/n7y5ib76ym9x59p/exNPNMASsmall.pml?dl=0.

  11. The first verification of the model may use the standard PROMELA receive statement, instead of the non-deterministic version.

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Acknowledgments

We are grateful to Gerard J. Holzmann for his prompt replies to several questions concerning the use of process priorities in SPIN. We also thank the anonymous reviewers for their comments and suggestions that helped to improve the presentation of this paper.

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Authors and Affiliations

  1. Center for Mathematics, Computation and Cognition, Federal University of ABC, Santo André, Brazil

    Mirtha Lina Fernández Venero

  2. Department of Computer Science, University of São Paulo, São Paulo, Brazil

    Flávio Soares Corrêa da Silva

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  1. Mirtha Lina Fernández Venero
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Correspondence to Mirtha Lina Fernández Venero.

Additional information

Communicated by Esther Guerra and Wil M. P. van der Aalst.

This is an extended and complete version of a preliminary work presented in [62].

Appendices

Appendix 1: The code for dealing with channels representing net-typed places

The next embedded C code is used to count the number of request messages at a net place channel whose second field coincides with a given label. A similar C code can be used to compute the number of occurrences a given token at a channel representing a basic colored place(numTok). A call to the function numMsg should have the form numMsg(qptr(PProcName->c-1),i) where c is a channel and i is an integer. The prefix PProcName-> (e.g., Pinit-> ) is required to refer a local channel inside a c_expr. The prefix now. must be used instead for a global channel.

figure l

The inline definition recMsg below is used for receiving a request message from a channel in a non-deterministic way (denoted in Sect. 3 by the operator ?*). The definitions transpNetTok and consNetTok implement the operations for moving and removing all request messages of a given net token process at a net place, respectively. All net token processes at a place are terminated using consNetsAtPlace.

figure m

Appendix 2: PROMELA program for the NPN in Fig. 2

This appendix includes the PROMELA translation for the net components in Fig. 2, Sect. 2.2. The proctype definition corresponding to the Agent element net uses input parameters for na, nr and nc. Besides, the place p2 is unfolded into three uncolored places p2a, p2r and p2c [61]. Some non-shared places of \({ SN}\) have been declared as global variables because they are used to specify the LTL property p in Sect. 5.1. The complete model can be found at http://www.dropbox.com/s/et6mhll7ze17j6t/exNPNMAS.pml?dl=0.

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Appendix 3: Outline for the translation of the NPN in Fig. 8

This section outlines the proctype definitions corresponding to the net components of the NPN in Fig. 8, Sect. 5.2. We have omitted several branches in the loops that are similar to those provided in this and previous examples. Here we note that the labels in \(L_v^+\) are not required by the translation. Hence, in the model the labels in \(L_v^-\) are numbered from 1 to 10 and MaxL is defined as 15. See the entire model at http://www.dropbox.com/s/dhxo1bg2d196lf0/prosecutionEx.rar?dl=0. The logic program implementing the object net can be found at http://edoc.sub.uni-hamburg.de/informatik/volltexte/2009/60/.

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Fernández Venero, M.L., Corrêa da Silva, F.S. Model checking multi-level and recursive nets. Softw Syst Model 16, 1117–1144 (2017). https://doi.org/10.1007/s10270-015-0509-6

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