arXiv:2611.13067v1 Announce Type: new Abstract: Multi-agent systems increasingly operate in dynamic environments and execute complex tasks that require coordination, posing significant computational challenges. Counting tasks, which require a minimum number of agents to satisfy a given condition, arise naturally in such systems. Examples include surveillance tasks, where at least m drones must continuously monitor a critical area, and emergency-response tasks, where at least m robots must converge to an incident location. The identities of the agents assigned to these tasks may change dynamically depending on their states, input bounds, and individual objectives. In this work, we propose a control barrier function (CBF)-based framework for enforcing counting invariance and counting convergence tasks, without explicitly assigning agents or enumerating all possible subteams. We develop a recursion-based method for constructing differentiable CBFs for counting tasks. The resulting CBF constraints are incorporated into quadratic programs, enabling online controller synthesis. Numerical experiments demonstrate scalability to large multi-agent systems, while a multi-drone emergency-response case study illustrates the satisfaction of counting tasks.