Abstract
Reconfigurable broadcast networks (RBN) are a model of distributed computation in which agents can broadcast messages to other agents using some underlying communication topology which can change arbitrarily over the course of executions. In this paper, we conduct parameterized analysis of RBN. We consider cubes, (infinite) sets of configurations in the form of lower and upper bounds on the number of agents in each state, and we show that we can evaluate boolean combinations over cubes and reachability sets of cubes in PSPACE. In particular, reachability from a cube to another cube is a PSPACE-complete problem.
To prove the upper bound for this parameterized analysis, we prove some structural properties about the reachability sets and the symbolic graph abstraction of RBN, which might be of independent interest. We justify this claim by providing two applications of these results. First, we show that the almost-sure coverability problem is PSPACE-complete for RBN, thereby closing a complexity gap from a previous paper [3]. Second, we define a computation model using RBN, à la population protocols, called RBN protocols. We characterize precisely the set of predicates that can be computed by such protocols.
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 787367 (PaVeS).
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Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. Distributed Comput. 18(4), 235–253 (2006). https://doi.org/10.1007/s00446-005-0138-3
Angluin, D., Aspnes, J., Eisenstat, D., Ruppert, E.: The computational power of population protocols. Distributed Comput. 20(4), 279–304 (2007). https://doi.org/10.1007/s00446-007-0040-2
Balasubramanian, A.R., Weil-Kennedy, C.: Reconfigurable broadcast networks and asynchronous shared-memory systems are equivalent. In: Ganty, P., Bresolin, D. (eds.) Proceedings 12th International Symposium on Games, Automata, Logics, and Formal Verification, GandALF 2021, Padua, Italy, 20-22 September 2021. EPTCS, vol. 346, pp. 18–34 (2021). https://doi.org/10.4204/EPTCS.346.2
Bertrand, N., Fournier, P.: Parameterized verification of many identical probabilistic timed processes. In: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS. pp. 501–513 (2013). https://doi.org/10.4230/LIPIcs.FSTTCS.2013.501
Bertrand, N., Fournier, P., Sangnier, A.: Playing with probabilities in reconfigurable broadcast networks. In: Foundations of Software Science and Computation Structures - 17th International Conference, FOSSACS. pp. 134–148 (2014). https://doi.org/10.1007/978-3-642-54830-7_9
Bouyer, P., Markey, N., Randour, M., Sangnier, A., Stan, D.: Reachability in networks of register protocols under stochastic schedulers. In: Chatzigiannakis, I., Mitzenmacher, M., Rabani, Y., Sangiorgi, D. (eds.) 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, July 11-15, 2016, Rome, Italy. LIPIcs, vol. 55, pp. 106:1–106:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016). https://doi.org/10.4230/LIPIcs.ICALP.2016.106
Chini, P., Meyer, R., Saivasan, P.: Liveness in broadcast networks. In: Atig, M.F., Schwarzmann, A.A. (eds.) Networked Systems - 7th International Conference, NETYS 2019, Marrakech, Morocco, June 19-21, 2019, Revised Selected Papers. Lecture Notes in Computer Science, vol. 11704, pp. 52–66. Springer (2019). https://doi.org/10.1007/978-3-030-31277-0_4
Delzanno, G., Sangnier, A., Traverso, R., Zavattaro, G.: On the complexity of parameterized reachability in reconfigurable broadcast networks. In: D’Souza, D., Kavitha, T., Radhakrishnan, J. (eds.) IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2012, December 15-17, 2012, Hyderabad, India. LIPIcs, vol. 18, pp. 289–300. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012), https://doi.org/10.4230/LIPIcs.FSTTCS.2012.289
Delzanno, G., Sangnier, A., Traverso, R., Zavattaro, G.: On the complexity of parameterized reachability in reconfigurable broadcast networks. Long version (2012), https://www.irif.fr/~sangnier/publis/DSTZ-FSTTCS12-long.pdf
Delzanno, G., Sangnier, A., Zavattaro, G.: Parameterized verification of ad hoc networks. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010 - Concurrency Theory, 21th International Conference, CONCUR 2010, Paris, France, August 31-September 3, 2010. Proceedings. Lecture Notes in Computer Science, vol. 6269, pp. 313–327. Springer (2010). https://doi.org/10.1007/978-3-642-15375-4_22
Esparza, J., Ganty, P., Majumdar, R., Weil-Kennedy, C.: Verification of immediate observation population protocols. In: CONCUR. LIPIcs, vol. 118, pp. 31:1–31:16. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2018). https://doi.org/10.4230/LIPIcs.CONCUR.2018.31
Esparza, J., Jaax, S., Raskin, M.A., Weil-Kennedy, C.: The complexity of verifying population protocols. Distributed Comput. 34(2), 133–177 (2021). https://doi.org/10.1007/s00446-021-00390-x
Esparza, J., Raskin, M.A., Weil-Kennedy, C.: Parameterized analysis of immediate observation petri nets. In: Donatelli, S., Haar, S. (eds.) Application and Theory of Petri Nets and Concurrency - 40th International Conference, PETRI NETS 2019, Aachen, Germany, June 23-28, 2019, Proceedings. Lecture Notes in Computer Science, vol. 11522, pp. 365–385. Springer (2019). https://doi.org/10.1007/978-3-030-21571-2_20
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Balasubramanian, A.R., Guillou, L., Weil-Kennedy, C. (2022). Parameterized Analysis of Reconfigurable Broadcast Networks. In: Bouyer, P., Schröder, L. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2022. Lecture Notes in Computer Science, vol 13242. Springer, Cham. https://doi.org/10.1007/978-3-030-99253-8_4
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