Mobile robot networks emerged in the past few years as a promising distributed computing model. Existing work in the literature typically ensures the correctness of mobile robot protocols via ad hoc handwritten proofs, which, in the case of asynchronous execution models, are both cumbersome and error-prone.In this paper, we propose the first formal model and general verification (by model-checking) methodology for mobile robot protocols operating in a discrete space (that is, the set of possible robot positions is finite). Our contribution is threefold. First, we formally model using synchronized automata a network of mobile robots operating under various synchrony (or asynchrony) assumptions. Then, we use this formal model as input model for the DiVinE model-checker and prove the equivalence of the two models. Third, we verify using DiVinE two known protocols for variants of the ring exploration in an asynchronous setting (exploration with stop and perpetual exclusive exploration).The exploration with stop we verify was manually proved correct only when the number of robots is k > 17, and n (the ring size) and k are co-prime. As the necessity of this bound was not proved in the original paper, our methodology demonstrates that for several instances of k and n not covered in the original paper, the algorithm remains correct. In the case of the perpetual exclusive exploration protocol, our methodology exhibits a counter-example in the completely asynchronous setting where safety is violated, which is used to correct the original protocol.

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International audienceIn this paper, we study the exclusive perpetual exploration problem with mobile anonymous and oblivious robots in a discrete space. Our results hold for the most generic settings: robots are asynchronous and are not given any sense of direction, so the left and right sense (i.e. chirality) is decided by the adversary that schedules robots for execution, and may change between invocations of a particular robots (as robots are oblivious). We investigate both the minimal and the maximal number of robots that are necessary and sufficient to solve the exclusive perpetual exploration problem. On the minimal side, we prove that three deterministic robots are necessary and sufficient, provided that the size n of the ring is at least 10, and show that no protocol with three robots can exclusively perpetually explore a ring of size less than 10. On the maximal side, we prove that k = n − 5 robots are necessary and sufficient to exclusively perpetually explore a ring of size n when n is co-prime with k

Abstract. In this paper, we investigate the exclusive perpetual exploration of grid shaped networks using anonymous, oblivious and fully asynchronous robots. Our results hold for robots without sense of direction (i.e. they do not agree on a common North, nor do they agree on a common left and right ; furthermore, the "North" and "left" of each robot is decided by an adversary that schedules robots for execution, and may change between invocations of particular robots). We focus on the minimal number of robots that are necessary and sufficient to solve the problem in general grids. In more details, we prove that three deterministic robots are necessary and sufficient, provided that the size of the grid is n × m with 3 ≤ n ≤ m or n = 2 and m ≥ 4. Perhaps surprisingly, and unlike results for the exploration with stop problem (where grids are "easier" to explore and stop than rings with respect to the number of robots), exclusive perpetual exploration requires as many robots in the ring as in the grid. Furthermore, we propose a classification of configurations such that the space of configurations to be checked is drastically reduced. This pre-processing lays the bases for the automated verification of our algorithm for general grids as it permits to avoid combinatorial explosion.

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Self-stabilizing systems have the ability to converge to a correct behavior when started in any configuration. Most of the work done so far in the self-stabilization area assumed either communication via shared memory or via FIFO channels.This paper is the first to lay the bases for the design of self-stabilizing message passing algorithms over unreliable non-FIFO channels. We propose an optimal stabilizing data-link layer that emulates a reliable FIFO communication channel over unreliable capacity bounded non-FIFO channels.

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This paper is the first to specify blockchains as a composition of abstract data types all together with a hierarchy of consistency criteria that formally characterizes the histories admissible for distributed programs that use them. The paper presents as well some results on implementability of the presented abstractions and a mapping of representative existing blockchains from both academia and industry in our framework.