What methods can be used to verify the CAP theorem in distributed systems?

The CAP theorem states that in a distributed system, it is impossible to guarantee all three properties simultaneously: Consistency, Availability, and Partition Tolerance. This theorem can be confirmed through the following methods:

1. Theoretical analysis — formal proof of the impossibility to ensure all three properties simultaneously in the presence of network partitions.

2. Experimental modeling — creating prototypes of distributed systems where, during network failures, it is observed that either consistency or availability must be sacrificed.

3. Analysis of real systems — studying the behavior of existing distributed databases and services (e.g., Cassandra, MongoDB, etcd), which choose different trade-offs among CAP properties.

4. Use of formal models and simulations — applying models such as TLA+ or Petri nets for formal analysis of system behavior during network partitions.

Thus, confirming the CAP theorem is achieved through a combination of theoretical proofs and practical experiments with distributed systems.