递归函数的π可定义性及其实现研究

π-Definability of Recursive Functions and Implementation Research

并发计算模型是计算机科学研究的重要问题之一．π演算作为一个并发计算模型,是一种重要的移动进程演算,其中 的进程通过发送通信链接互相交互．与传统的进程代数如CCS相比,π演算有着更为良好的代数性质和表达能力．正如λ演算 能够描述所有的可计算函数,π演算也有同样的能力．本文提出了一个方法,据此可以把自然数和函数描述为进程,从而证明了 π演算有足够的能力描述所有的可计算函数,同时还说明了与λ演算相比,π演算有着更高的计算效率．

Concurrent computation model is one of the most important problems in theoretical computer science. The π-calculus is an important mobile process algebra where processes interact by sending communication links to each other. Comparing with the classical process calculi, such as CCS, π-calculus has better algebra properties and more expressive power. Just as λ-calculus allows you to construct and reason about every possible computable function, there were high hopes that π-calculus would play similar role for concurrency. This paper is about the way we model objects and data types as π-calculus agents. And despite the fact that we＇ve explicitly ignored the internal functionality of processes, it turns out that process algebra is powerful enough to model the whole recursive functions and has more higher efficiency for computation .