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**Published in:** LIPIcs, Volume 125, 22nd International Conference on Principles of Distributed Systems (OPODIS 2018)

What can be computed by a network of n randomized finite state machines communicating under the stone age model (Emek & Wattenhofer, PODC 2013)? The inherent linear upper bound on the total space of the network implies that its global computational power is not larger than that of a randomized linear space Turing machine, but is this tight? We answer this question affirmatively for bounded degree networks by introducing a stone age algorithm (operating under the most restrictive form of the model) that given a designated I/O node, constructs a tour in the network that enables the simulation of the Turing machine's tape. To construct the tour with high probability, we first show how to 2-hop color the network concurrently with building a spanning tree.

Yehuda Afek, Yuval Emek, and Noa Kolikant. The Synergy of Finite State Machines. In 22nd International Conference on Principles of Distributed Systems (OPODIS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 125, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{afek_et_al:LIPIcs.OPODIS.2018.22, author = {Afek, Yehuda and Emek, Yuval and Kolikant, Noa}, title = {{The Synergy of Finite State Machines}}, booktitle = {22nd International Conference on Principles of Distributed Systems (OPODIS 2018)}, pages = {22:1--22:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-098-9}, ISSN = {1868-8969}, year = {2019}, volume = {125}, editor = {Cao, Jiannong and Ellen, Faith and Rodrigues, Luis and Ferreira, Bernardo}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2018.22}, URN = {urn:nbn:de:0030-drops-100825}, doi = {10.4230/LIPIcs.OPODIS.2018.22}, annote = {Keywords: finite state machines, stone-age model, beeping communication scheme, distributed network computability} }

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**Published in:** LIPIcs, Volume 121, 32nd International Symposium on Distributed Computing (DISC 2018)

This paper studies a variant of the leader election problem under the stone age model (Emek and Wattenhofer, PODC 2013) that considers a network of n randomized finite automata with very weak communication capabilities (a multi-frequency asynchronous generalization of the beeping model's communication scheme). Since solving the classic leader election problem is impossible even in more powerful models, we consider a relaxed variant, referred to as k-leader selection, in which a leader should be selected out of at most k initial candidates. Our main contribution is an algorithm that solves k-leader selection for bounded k in the aforementioned stone age model. On (general topology) graphs of diameter D, this algorithm runs in O~(D) time and succeeds with high probability. The assumption that k is bounded turns out to be unavoidable: we prove that if k = omega (1), then no algorithm in this model can solve k-leader selection with a (positive) constant probability.

Yehuda Afek, Yuval Emek, and Noa Kolikant. Selecting a Leader in a Network of Finite State Machines. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 4:1-4:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{afek_et_al:LIPIcs.DISC.2018.4, author = {Afek, Yehuda and Emek, Yuval and Kolikant, Noa}, title = {{Selecting a Leader in a Network of Finite State Machines}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {4:1--4:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-092-7}, ISSN = {1868-8969}, year = {2018}, volume = {121}, editor = {Schmid, Ulrich and Widder, Josef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.4}, URN = {urn:nbn:de:0030-drops-97933}, doi = {10.4230/LIPIcs.DISC.2018.4}, annote = {Keywords: stone age model, beeping communication scheme, leader election, k-leader selection, randomized finite state machines, asynchronous scheduler} }

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Brief Announcement

**Published in:** LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

What can be computed by a network of n randomized finite state machines communicating under the stone age model (a generalization of the beeping model’s communication scheme)? The inherent linear upper bound on the total space of the network implies that its global computational power is not larger than that of a randomized linear space Turing machine, but is this tight? The reported reseach answers this question affirmatively for bounded degree networks by introducing a stone age algorithm (operating under the most restrictive form of the model) that given a designated I/O node, constructs a tour in the network that enables the simulation of the Turing machine’s tape. To construct the tour, it is first shown how to 2-hop color the network concurrently with building a spanning tree with high probability.

Yehuda Afek, Yuval Emek, and Noa Kolikant. Brief Announcement: The Synergy of Finite State Machines. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 42:1-42:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{afek_et_al:LIPIcs.DISC.2017.42, author = {Afek, Yehuda and Emek, Yuval and Kolikant, Noa}, title = {{Brief Announcement: The Synergy of Finite State Machines}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {42:1--42:3}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.42}, URN = {urn:nbn:de:0030-drops-80072}, doi = {10.4230/LIPIcs.DISC.2017.42}, annote = {Keywords: beeping communication, finite state machine, stone age model, distributed network complexity} }

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