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P2 Stream Differential Equations: Specification Formats and Solution Methods

流微分方程:规格格式与求解方法
LMCS vol.Volume 13, Issue 12017匹配度 1/10 · 该论文属于形式语义/余代数理论,讨论流微分方程的规格格式与求解方法,与用户关注的 AI与PL交叉、静态分析、浮点程序分析、贝叶斯程序分析均无直接关联。引用 13 inbox
Helle Hvid Hansen, Clemens Kupke, Jan Rutten
crossref: 2026-09-10

AI 速览

一句话:综述流微分方程的多种规格格式、求解方法及其可定义流类,并阐明语法解法与抽象 GSOS 的联系。

流(无限序列)类型简单却理论丰富。流微分方程是一种用余归纳方式指定流及流运算的方法,过去二十年积累了众多结果。本文对此进行综述:重点分类不同格式的流微分方程,梳理其求解方法,以及各类格式所能定义的流类;并详细讨论所谓的语法求解方法与抽象 GSOS 之间的关系。该工作为理解流规范语言的表达力、解的存在唯一性与余代数语义提供了统一视角。

问题
如何系统理解流微分方程的不同规格格式、求解方法及其可定义流类,并厘清语法解法与抽象 GSOS 的联系。
方法
以综述形式汇总并分类文献结果,对规格格式和求解方法进行比较,并分析其余代数与 GSOS 语义。
评估
通过理论分类与结果对比而非实证实验,给出不同格式可定义流类的刻画及方法间关系。
原文摘要(Abstract)

Streams, or infinite sequences, are infinite objects of a very simple type, yet they have a rich theory partly due to their ubiquity in mathematics and computer science. Stream differential equations are a coinductive method for specifying streams and stream operations, and their theory has been developed in many papers over the past two decades. In this paper we present a survey of the many results in this area. Our focus is on the classification of different formats of stream differential equations, their solution methods, and the classes of streams they can define. Moreover, we describe in detail the connection between the so-called syntactic solution method and abstract GSOS.

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BibTeX
@article{paperbot207,
  title = {Stream Differential Equations: Specification Formats and Solution Methods},
  author = {Helle Hvid Hansen and Clemens Kupke and Jan Rutten},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 13, Issue 1},
  year = {2017},
  doi = {10.23638/lmcs-13(1:3)2017}
}