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This paper proposes an approach to the specification and model checking of a large, important class of distributed algorithms called control algorithms (CAs), which are superimposed on underlying distributed systems (UDSs). The approach is based on rewriting logic by moving from its object level to the meta-level. We introduce the idea of specifying CAs as meta-programs that take the specifications of UDSs and automatically generate the specifications of the UDSs on which the CAs are superimposed (UDS-CAs). Due to many options, such as network topologies, even fixing the number of each kind of entities, such as mobile support stations (MSSs) and mobile hosts (MHs) in a mobile checkpointing algorithm, there are many instances of a UDS. To address the problem, we generate all possible initial states of a UDS for a fixed number of each kind of entities such that some constraints, such as MSSs strongly connected with a wired network, are fulfilled and conduct model checking for each of the initial states. We demonstrate the usefulness by reporting on a case study where a counterexample is found for some specific initial states but not for the other initial states, detecting a subtle flaw lurking in a mobile checkpointing algorithm. [ABSTRACT FROM AUTHOR]