Distributed verification using mobile agents

We study the problem of distributed verification in the mobile agent model. The problem of distributed verification in a network using local checking has been studied previously. In the local verification model, each node of the network must decide on a yes or no answer based on the knowledge of its immediate neighborhood and the global answer is obtained by a conjunction of the local answers. The efficiency of such a verification process is determined by the sizes of the proofs i.e. labels that must be assigned to the nodes to enable local verification of some global property. On the other hand, in the mobile agent model, verification is performed by an agent that is allowed to move from node to node of the graph, reading the labels of visited nodes in order to verify the required property. In this case, minimizing the memory of the agent is the primary objective. We study the space complexity of performing mobile verification in terms of memory of each agent as well as the number of agents required globally in networks of size n. In the case of a solitary agent, logarithmic memory is both necessary and sufficient for solving certain graph-based verification problems (even in the family of trees). For a team of at least two agents, the space complexity of most verification problems (including the well-studied MST verification) is reduced to O (log log n), while a team of at least three agents even with constant size memory each, is sufficient to solve all graph-based verification problems. We also study the effect of randomization and show that one agent with O (log log n) bits of memory and the ability to flip coins is as powerful as two deterministic agent having the similar memory limitations.