FLPimpossibiliteten

FLPimpossibiliteten, also known as the Fischer–Lynch–Paterson impossibility result, is a fundamental concept in distributed computing and concurrency theory. It describes a theoretical limitation regarding the design of fault-tolerant distributed systems. The result was independently discovered by Leslie Lamport, Nancy Lynch, and Michael Fischer in 1980, though it is named after Fischer and Paterson, who published their findings first.

The theorem states that in an asynchronous distributed system where processes may fail by crashing (i.e., they stop responding but do not send incorrect messages), it is impossible to design a deterministic algorithm that satisfies all three of the following properties simultaneously:

1. **Termination**: The algorithm must eventually terminate for any valid input.

2. **Validity**: The algorithm must produce a correct output for any valid input.

3. **Agreement (or Consensus)**: All non-faulty processes must agree on the same output.

The impossibility arises because the system’s asynchrony means there is no bound on message delivery times or process speeds, making it impossible for processes to reliably detect failures or coordinate decisions without violating one of the three properties. This result highlights the challenges in achieving consensus in distributed environments where failures and delays are inevitable.

FLPimpossibiliteten has significant implications for distributed systems design, particularly in areas like blockchain, distributed databases, and consensus protocols. It underscores the need for alternative approaches, such as adding synchrony assumptions (e.g., bounded message delays) or relaxing some of the properties (e.g., allowing probabilistic termination). Despite its limitations, the theorem remains a cornerstone in understanding the trade-offs in distributed computing.