Conventional automated test case generation techniques do not scale to modern software systems, as these systems have a large number of requirements that change frequently. In this paper, we present a scalable algorithm, AGenT, that generates test cases to cover maximal requirements. AGenT takes Expressive Decision Tables (EDT), specifying requirements of a system, as input and realises these as multiple Discrete Time Automata (DTAs). AGenT then generates test cases to cover each row of the tables. To improve scalability, it attempts to cover nearer rows (requiring fewer inputs) first, where distance is measured using a novel distance-to-match heuristic. It also maintains information about desirability and predictability of inputs so as to select promising inputs with a higher probability. Although the algorithm has been presented in the context of EDT, it operates on its DTA representation and hence can be applied to any system that is represented as a collection of DTAs like Statemate and Stateflow. In this paper, we describe AGenT in detail and present findings from two experiments that we conducted. We compared AGenT with state-of-the-art algorithms, DRAFT and a random test case generation algorithm, RTG. In the first experiment, AGenT took a maximum of 144 seconds to cover all rows whereas the other two algorithms timed out on many modules. In the second experiment, for a module with 701 rows, AGenT achieved 7% more coverage than DRAFT and 12% more than RTG.