Pi Calculus
1. Overview
- for the study of concurrent systems.
- allows for the description, analysis, and verification of interacting systems.
- Core Concepts:
- Processes: The fundamental units of Pi Calculus that engage in interactions.
- Channels: The conduits for communication between processes.
- Mobility: The notion that the connection structure among processes can change over time.
- Names: Used in Pi Calculus to represent channels and can be communicated between processes, enabling dynamic topology.
- Operations:
- Prefix:
(x).P describes a process P that waits to receive input on channel x before proceeding.
- Output:
x<y>.P describes a process P that sends y over channel x and then behaves as P.
- Parallel Composition:
P | Q represents the parallel execution of processes P and Q.
- Restriction:
νx.P restricts the scope of the channel x to the process P, meaning x is private to P.
- Replication:
!P indicates an unbounded number of copies of process P running in parallel.
- Applications:
- Used in modeling and verifying protocols for communication networks.
- Helps in analyzing the correctness of distributed systems and their ability to handle concurrency.
- Provides foundational structures for programming languages designed for concurrent computations.
- Related Concepts:
- Calculus of Communicating Systems (CCS): An earlier model of concurrency developed by Milner.
- Mobile processes: A shift from static to dynamic process structures, where the communication links between processes can change, a concept captured by Pi Calculus.
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