Parameterized systems consist of an arbitrary number of replicated agents with limited computational power, interacting to achieve common goals. They pervade computer science. Classical examples include families of digital circuits, distributed algorithms for leader election or byzantine agreement, routing algorithms, and multithreaded programs. Modern examples exhibit stochastic interaction between mobile agents, and include robot swarms, molecular computers, and cooperating ant colonies. A parameterized system is in fact an infinite collection of systems, one for each number of agents. Current verification technology of industrial strength can only check correctness of a few instances of this collection. For example, model checkers can automatically prove a distributed algorithm correct for a small number of processes, but not for any number.


While substantial progress has been made on the theory and applications of parameterized verification, in order to achieve large impact the field has to face three “grand challenges”:

  • Develop novel algorithms and tools for parametrized verification of classical parameterized systems that bypass the high complexity of current techniques.
  • Develop the first algorithms and tools for parameterized verification of modern stochastic parameterized systems.
  • Develop the first algorithms and tools for synthesis of correct-by-construction parameterized systems.

PaVeS addresses these challenges applying constraint-based technology, and recent breakthroughs in the theory of Petri nets and Vector Addition Systems.

For more information, please visit the PaVeS ERC project website.

Networks, computers, sensors, and actuators are being increasingly integrated into cyber-physical systems, i.e., software systems that interact with the physical world and must cope with its continuous behavior. An increasing number of cyber-physical systems operate in safety-critical domains, e.g., autonomous vehicles, robotic surgery, traffic control, human-robot collaboration, and smart grids. For this reason, their design and deployment should ideally be accompanied by a formal check of correct behavior. A fundamental challenge in the verification of cyber-physical systems is the fact that they are subject to change. The physical environment changes continuously, at runtime, and in ways that cannot be completely foreseen at the design stage. At the same time, the requirements may change. Sought-after aspects include more functionality, lower power consumption, or faster response. In many cases, the system should be migrated to a different hardware platform. To face this multi-level continuous change, we propose to


  1. develop verification and synthesis technology for robust system design, i.e., for the design of systems that maintain correct behavior under change
  2. develop verification and synthesis technology able to cope with frequent or even continuous change in the specification and the environment.

For more information please visit the ConVeY DFG Research Training Group ConVeY DFG Research Training Group website.