On Mobile Agent Verifiable Problems
Résumé
We consider decision problems that are solved in a distributed fashion by synchronous mobile agents operating in an unknown,
anonymous network. Each agent has a unique identifier and an input string and they have to decide collectively a property which
may involve their input strings, the graph on which they are operating, and their particular starting positions. Building on
recent work by Fraigniaud and Pelc [LATIN 2012, LNCS 7256, pp. 362-374], we introduce several natural new computability classes allowing for
a finer classification of problems below $\mathsf{co\text{-}MAV}$ or $\mathsf{MAV}$, the latter being the class of problems that are verifiable when the
agents
are provided with an appropriate certificate. We provide inclusion and separation results among all these classes. We also
determine their closure properties with
respect to set-theoretic operations. Our main technical tool, which is of independent interest, is a new meta-protocol
that enables
the execution of a possibly infinite number of mobile agent protocols essentially in parallel, similarly to the well-known
dovetailing technique from classical computability theory.
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