Abstract. We consider programmable matter consisting of simple computational elements, called particles, that can establish and release bonds and can actively move in a self-organized way, and we investigate the feasibility of solving fundamental problems relevant for programmable matter. As a suitable model for such self-organizing particle systems, we will use a generalization of the geometric amoebot model first proposed in SPAA 2014. Based on the geometric model, we present efficient localcontrol algorithms for leader election and line formation requiring only particles with constant size memory, and we also discuss the limitations of solving these problems within the general amoebot model.

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Allowing read operations to return stale data with low probability has been proposed as a means to increase availability in quorums systems. Existing solutions that allow stale reads cannot tolerate an adversarial scheduler that can maliciously delay messages between servers and clients in the system and for such a scheduler existing solutions cannot enforce a bound on the staleness of data read. This paper considers the possibility of increasing system availability while at the same time tolerating a malicious scheduler and guaranteeing an upper bound on the staleness of data. We characterize the conditions under which this increase is possible and show that it depends on the ratio of the write frequency to the servers' failure frequency. For environments with a relatively large failure frequency compared to write frequency, we propose K-quorums that can provide higher availability than the strict quorum systems and also guarantee bounded staleness. We also propose a definition of k-atomicity and present a protocol to implement a k-atomic register using k-quorums.

We study ways to restrict or prevent the damage that can be caused in a peer-to-peer network by corrupt entities creating multiple pseudonyms. We show that it is possible to remotely issue certificates that can be used to test the distinctness of identities. Our certification protocols are based on geometric techniques that establish location information in a fault-tolerant and distributed fashion. They do not rely on a centralized certifying authority or infrastructure that has direct knowledge of entities in the system, and work in Euclidean or spherical geometry of arbitrary dimension. They tolerate corrupt entities, including corrupt certifiers, collusion by either certification applicants or certifiers, and either a broadcast or point-to-point message model.

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Quorum systems have been used to implement many coordination problems in distributed systems such as mutual exclusion, data replication, distributed consensus, and commit protocols. Malkhi and Reiter recently proposed quorum systems that can tolerate Byzantine failures; they called these systems Byzantine quorum systems and gave some examples of such quorum systems. In this paper, we propose a new definition of Byzantine quorums that is appropriate for synchronous systems. We show how these quorums can be used for data replication and propose a general construction of synchronous Byzantine quorums using standard quorum systems. We prove tight lower bounds on the load of synchronous Byzantine quorums for various patterns of failures and we present synchronous Byzantine quorums that have optimal loads that match the lower bounds for two failure patterns.

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