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
{"title":"一阶递归函数终止准则的形式化验证","authors":"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","doi":"10.1007/s10817-023-09669-z","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":15082,"journal":{"name":"Journal of Automated Reasoning","volume":"10 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Formal Verification of Termination Criteria for First-Order Recursive Functions\",\"authors\":\"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\",\"doi\":\"10.1007/s10817-023-09669-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>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.</p>\",\"PeriodicalId\":15082,\"journal\":{\"name\":\"Journal of Automated Reasoning\",\"volume\":\"10 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-11-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Automated Reasoning\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.1007/s10817-023-09669-z\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Automated Reasoning","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s10817-023-09669-z","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
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.
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.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
