{"title":"Syntax directed analysis of liveness properties of while programs","authors":"Krzysztof R. Apt, Carole Delporte-Gallet","doi":"10.1016/S0019-9958(86)80037-7","DOIUrl":null,"url":null,"abstract":"<div><p>A syntax directed proof system which allows to prove <em>liveness</em> properties of <strong>while</strong>-programs is introduced. The proof system is proved to be arithmetically sound and complete in the sense of <span>Harel (“Lecture Notes in Comput. Sci. Vol. 68,” Springer-Verlag, Berlin/New York, 1979)</span>. The results of the paper generalize a corresponding result <span>Pneuli (“Prc. 18th Sympos. FOCS” IEEE, Providence, R. I., 1977)</span> proves for unstructured programs. The proof system decomposes into two parts. The first part allows to prove simple <em>safety</em> properties. These properties are used as axioms in the second proof system which deals with <em>liveness</em> properties. The completeness proof is constructive and provides a heuristic for proving specific liveness properties.</p></div>","PeriodicalId":38164,"journal":{"name":"信息与控制","volume":"68 1","pages":"Pages 223-253"},"PeriodicalIF":0.0000,"publicationDate":"1986-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0019-9958(86)80037-7","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"信息与控制","FirstCategoryId":"1093","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019995886800377","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 3
Abstract
A syntax directed proof system which allows to prove liveness properties of while-programs is introduced. The proof system is proved to be arithmetically sound and complete in the sense of Harel (“Lecture Notes in Comput. Sci. Vol. 68,” Springer-Verlag, Berlin/New York, 1979). The results of the paper generalize a corresponding result Pneuli (“Prc. 18th Sympos. FOCS” IEEE, Providence, R. I., 1977) proves for unstructured programs. The proof system decomposes into two parts. The first part allows to prove simple safety properties. These properties are used as axioms in the second proof system which deals with liveness properties. The completeness proof is constructive and provides a heuristic for proving specific liveness properties.
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