一阶递归函数终止准则的形式化验证

IF 0.9 3区计算机科学 Q4 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Journal of Automated Reasoning Pub Date : 2023-11-29 DOI:10.1007/s10817-023-09669-z

Cesar A. Muñoz, Mauricio Ayala-Rincón, Mariano M. Moscato, Aaron M. Dutle, Anthony J. Narkawicz, Ariane Alves Almeida, Andréia B. Avelar da Silva, Thiago M. Ferreira Ramos

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引用次数: 1

摘要

本文给出了一阶递归函数终止准则的形式化。形式化是在原型验证系统(Prototype Verification System, PVS)中开发的，包括语义终止、图灵终止、大小变化原理、调用上下文图和矩阵加权图的规范和等价证明。这些终止标准是在一个计算模型上定义的，该模型由一种称为PVS0的基本函数语言组成，它是递归一阶函数的嵌入。通过这种嵌入，可以将PVS中检查递归函数终止的固有机制很好地扩展为调用上下文图等半自动终止准则。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Formal Verification of Termination Criteria for First-Order Recursive Functions

This paper presents a formalization of several termination criteria for first-order recursive functions. The formalization, which is developed in the Prototype Verification System (PVS), includes the specification and proof of equivalence of semantic termination, Turing termination, size change principle, calling context graphs, and matrix-weighted graphs. These termination criteria are defined on a computational model that consists of a basic functional language called PVS0, which is an embedding of recursive first-order functions. Through this embedding, the native mechanism for checking termination of recursive functions in PVS could be soundly extended with semi-automatic termination criteria such as calling contexts graphs.

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来源期刊

Journal of Automated Reasoning 工程技术-计算机：人工智能

CiteScore

3.60

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Automated Reasoning is an interdisciplinary journal that maintains a balance between theory, implementation and application. The spectrum of material published ranges from the presentation of a new inference rule with proof of its logical properties to a detailed account of a computer program designed to solve various problems in industry. The main fields covered are automated theorem proving, logic programming, expert systems, program synthesis and validation, artificial intelligence, computational logic, robotics, and various industrial applications. The papers share the common feature of focusing on several aspects of automated reasoning, a field whose objective is the design and implementation of a computer program that serves as an assistant in solving problems and in answering questions that require reasoning. The Journal of Automated Reasoning provides a forum and a means for exchanging information for those interested purely in theory, those interested primarily in implementation, and those interested in specific research and industrial applications.