The prescription of sets of trajectories for controlled finite deterministic automaton G is formulated via the notion of the class of specifications denoted, both individually and collectively, by SPEC. Next, the formulation and (language) specification of structures for interacting automata are developed within the Multi-Agent (MA) product framework, and specifications are defined in terms of SPECs. Necessary and sufficient conditions for the synthesis of MA supervisors are given and an associated MA product of specificatins is introduced.