  Shared resources synchronization is a well studied problem, in both shared
memory environment or distributed memory environment. Many synchronization
mechanisms are proposed, with their own way to reach certain consistency level.
This thesis further found that there is no perfect synchronization mechanism.
Each of them has its properties at different level. For example, to enforce
strong consistency, writers may loose writing freedom or it would take more
time to coordinate. This thesis proposes a framework to generalize all
synchronization mechanism in a formal way for better reasoning on properties,
from the perspective of multi-writer to single-writer convergence. Therefore,
limitations prevent a synchronization mechanism from achieving every property
at its optimal level. CAP and ROLL were proposed in previous works to explain
such. CAP theorem states that it can only achieve two of Consistency,
Availability and Partition tolerance properties. ROLL Theorem uses a framework
to model leaderless SMR protocol and states quorum size and fault tolerance are
trading off. The thesis covers five properties in a more understandable way to
analyze trade-offs and explore new mechanisms.
