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Constrained Dynamic Tree Networks

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11123)

Abstract

We generalise Constrained Dynamic Pushdown Networks, introduced by Bouajjani et al., to Constrained Dynamic Tree Networks. In this model, we have trees of processes which may monitor their children. We allow the processes to be defined by any computation model for which the alternating reachability problem is decidable. We address the problem of symbolic reachability analysis for this model. More precisely, we consider the problem of computing an effective representation of their reachability sets using finite state automata. We show that backwards reachability sets starting from regular sets of configurations are always regular. We provide an algorithm for computing backwards reachability sets using tree automata.

Keywords

  • Model-checking
  • Dynamic networks
  • Concurrency
  • Pushdown systems
  • Alternation
  • Higher-order
  • Collapsible pushdown systems

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  • DOI: 10.1007/978-3-030-00250-3_4
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Notes

  1. 1.

    If it is not the case, we create a copy of these states on which we conserve all the transition as an “internal state”, and remove the incoming transitions to these states.

  2. 2.

    If so, for a state \(s_r\), we create a new final state \(s\) and add the transition \(s_r\xrightarrow {\mathrm {Id}} s\), and remove \(s_r\) from the set of final states.

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Acknowledgement

We thank the anonymous reviewers for their remarks. This work was supported by the Engineering and Physical Sciences Research Council [EP/K009907/1].

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Correspondence to Matthew Hague .

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Hague, M., Penelle, V. (2018). Constrained Dynamic Tree Networks. In: Potapov, I., Reynier, PA. (eds) Reachability Problems. RP 2018. Lecture Notes in Computer Science(), vol 11123. Springer, Cham. https://doi.org/10.1007/978-3-030-00250-3_4

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  • DOI: https://doi.org/10.1007/978-3-030-00250-3_4

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