  We develop a logic-based framework for formal specification and algorithmic
verification of homogeneous and dynamic concurrent multi-agent transition
systems (HDMAS). Homogeneity means that all agents have the same available
actions at any given state and the actions have the same effects regardless of
which agents perform them. The state transitions are therefore determined only
by the vector of numbers of agents performing each action and are specified
symbolically, by means of conditions on these numbers definable in Presburger
arithmetic. The agents are divided into controllable (by the system
supervisor/controller) and uncontrollable, representing the environment or
adversary. Dynamicity means that the numbers of controllable and uncontrollable
agents may vary throughout the system evolution, possibly at every transition.
  As a language for formal specification we use a suitably extended version of
Alternating-time Temporal Logic (ATL), where one can specify properties of the
type "a coalition of (at least) $n$ controllable agents can ensure against (at
most) $m$ uncontrollable agents that any possible evolution of the system
satisfies a given objective $\varphi$", where $\varphi$ is specified again as a
formula of that language and each of $n$ and $m$ is either a fixed number or a
variable that can be quantified over.
  We provide formal semantics to our logic $\mathcal{L}_{HDMAS}$ and define
normal form of its formulae. We then prove that every formula in
$\mathcal{L}_{HDMAS}$ is equivalent in the finite to one in a normal form and
develop an algorithm for global model checking of formulae in normal form in
finite HDMAS models, which invokes model checking truth of Presburger formulae.
We establish worst case complexity estimates for the model checking algorithm
and illustrate it on a running example.
