Session types are a type discipline for describing and specifying communication behaviours of concurrent processes. Session subtyping, firstly introduced by Gay and Hole, is widely used for enlarging typability of session programs. This paper gives the complexity analysis of three algorithms for subtyping of synchronous binary session types. First, we analyse the complexity of the algorithm from the original paper, which is based on an inductive tree search. We then introduce its optimised version, which improves the complexity, but is still exponential against the size of the two types. Finally, we propose a new quadratic algorithm based on a graph search using the concept of XYZW-simulation, recently introduced by Silva et al.

中文翻译：

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二进制会话类型的三种子类型算法及其复杂度分析

会话类型是用于描述和指定并发进程的通信行为的类型规则。会话子类型化首先由 Gay 和 Hole 提出，广泛用于增强会话程序的可打字性。本文给出了同步二进制会话类型子类型化的三种算法的复杂度分析。首先，我们分析原始论文中基于归纳树搜索的算法的复杂性。然后，我们介绍其优化版本，该版本提高了复杂性，但相对于两种类型的大小仍然呈指数级增长。最后，我们提出了一种基于图搜索的新二次算法，使用 XYZW 模拟的概念，最近由 Silva 等人引入。