Abstract
In this paper we study the solvability of the equality negation task in a simple wait-free model where processes communicate by reading and writing shared variables or exchanging messages. In this task, two processes start with a private input value in the set \(\left\{ 0,1,2 \right\} \), and after communicating, each one must decide a binary output value, so that the outputs of the processes are the same if and only if the input values of the processes are different. This task is already known to be unsolvable; our goal here is to prove this result using the dynamic epistemic logic (DEL) approach introduced by Goubault, Ledent and Rajsbaum in GandALF 2018. We show that in fact, there is no epistemic logic formula that explains why the task is unsolvable. We fix this issue by extending the language of our DEL framework, which allows us to construct such a formula, and discuss its utility.
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Acknowledgements
The authors were supported by DGA project “Validation of Autonomous Drones and Swarms of Drones” and the academic chair “Complex Systems Engineering” of Ecole Polytechnique-ENSTA-Télécom-Thalès-Dassault-Naval Group-DGA-FX-FDO-Fondation ParisTech, by the UNAM-PAPIIT project IN109917 and IN106520, by the France-Mexico Binational SEP-CONACYT-ANUIES-ECOS grant M12M01, by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 787367 (PaVeS), as well as by the Austrian Science Fund (FWF) through Doctoral College LogiCS (W1255-N23).
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Goubault, É., Lazić, M., Ledent, J., Rajsbaum, S. (2020). A Dynamic Epistemic Logic Analysis of the Equality Negation Task. In: Soares Barbosa, L., Baltag, A. (eds) Dynamic Logic. New Trends and Applications. DALI 2019. Lecture Notes in Computer Science(), vol 12005. Springer, Cham. https://doi.org/10.1007/978-3-030-38808-9_4
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