In networked systems supporting mobile agents, a particularly dangerous security threat facing the agents is the presence of a black hole (Bh): a network host that destroys any incoming agent without leaving any trace. The problem, called Black hole search (Bhs), of efficiently determining the location of such a dangerous host has been extensively studied under a variety of different assumptions. In spite of their differences, the existing results share the same assumption that all the searching agents are reliable.In this paper, we start the investigation of the Bhs problem when some of the searching agents are faulty in a malicious way. More precisely, we consider that up to f of the k searching agents are Byzantine: they may behave in an arbitrary manner, actively misleading other agents; furthermore, they are in collusion with the black hole, and immune to its destructive power.We study under what conditions the Bhs problem can be solved in a synchronous network of arbitrary topology in spite of the malicious agents, examining the impact on complexity of two factors: the a-priori topological knowledge held by the agents, and the communication mechanism available to them.We prove that, with prior knowledge about the graph topology (i.e., a network map), Bhs can be solved by k ≥ 2f +2 agents in O(n + f) synchronous rounds both with whiteboards and with just local communication, where n is the number of nodes in the network.Without any knowledge about the topological structure, using whiteboard communication Bhs can be solved by k ≥ (f+1)(∆+ 1) agents in O(m+f) rounds; instead, using local communication, Bhs can be solved by k ≥ (f + 1)(∆ + 1) + 3f + 1 agents in O(m • n + f) rounds, where m is the number of links of the network and ∆ is the maximum degree of the network.In all cases, as we show, the bound on the total number k of agents is asymptotically optimal.

Programmable Matter (PM) has been widely investigated in recent years. It refers to some kind of substance with the ability to change its physical properties (e.g., shape or color) in a programmable way. In this paper, we refer to the SILBOT model, where the particles live and move on a triangular grid, are asynchronous in their computations and movements, and do not possess any direct means of communication (silent) or memory of past events (oblivious). Within SILBOT , we aim at studying Spanning problems, i.e., problems where the particles are required to suitably span all over the grid. We first address the Line Formation problem where the particles are required to end up in a configuration where they all lie on a line, i.e., they are aligned and connected. Secondly, we deal with the more general Scattering problem: starting from any initial configuration, we aim at reaching a final one where no particles occupy neighboring nodes. Furthermore, we investigate configurations where some nodes of the grid can be occupied by unmovable elements (i.e., obstacles) from both theoretical and experimental view points.

By Programmable Matter (PM) is usually meant a system of weak and self-organizing computational entities, called particles, which can be programmed via distributed algorithms to collectively achieve some global tasks. We consider the SILBOT model where particles are modeled as finite state automata, living and operating in the cells of a hexagonal grid. Particles are all identical, executing the same deterministic algorithm which is based on local observation of the surroundings, up to two hops. Particles are asynchronous, without any direct means of communication and disoriented but sharing a common handedness, i.e., chirality is assumed. Within such a basic model, we consider a foundational primitive for PM, that is Coating: a set of n particles must move so as to ensure the closed surrounding of an object occupying some connected cells of the grid. We present an optimal deterministic distributed algorithm - along with the correctness proof, that in Θ(n²) rounds solves the Coating problem, where a round concerns the minimal time window within which each particle is activated at least once.

Programmable Matter (PM) has been widely investigated in recent years. One reference model is certainly Amoebot, with its recent canonical version (DISC 2021). Along this line, with the aim of simplification and to address concurrency, the SILBOT model has been introduced (AAMAS 2020). Within SILBOT, we consider the Line formation primitive in which particles are required to end up in a configuration where they are all aligned and connected. We propose a simple and elegant distributed algorithm, optimal in terms of number of movements.