J. Esparza, P. Lammich, René Neumann, T. Nipkow, A. Schimpf, J. Smaus
{"title":"A Fully Verified Executable LTL Model Checker","authors":"J. Esparza, P. Lammich, René Neumann, T. Nipkow, A. Schimpf, J. Smaus","doi":"10.1007/978-3-642-39799-8_31","DOIUrl":"https://doi.org/10.1007/978-3-642-39799-8_31","url":null,"abstract":"","PeriodicalId":280633,"journal":{"name":"Arch. Formal Proofs","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131386059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Bytecode Logic for JML and Types","authors":"Lennart Beringer, M. Hofmann","doi":"10.1007/11924661_24","DOIUrl":"https://doi.org/10.1007/11924661_24","url":null,"abstract":"","PeriodicalId":280633,"journal":{"name":"Arch. Formal Proofs","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2006-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116607181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Intersecting Chords Theorem","authors":"Lukas Bulwahn","doi":"10.3840/002781","DOIUrl":"https://doi.org/10.3840/002781","url":null,"abstract":"This entry provides a geometric proof of the intersecting chords theorem. The theorem states that when two chords intersect each other inside a circle, the products of their segments are equal. After a short review of existing proofs in the literature [1, 3–5], I decided to use a proof approach that employs reasoning about lengths of line segments, the orthogonality of two lines and Pythagoras Law. Hence, one can understand the formalized proof easily with the knowledge of a few general geometric facts that are commonly taught in high-school. Thistheorem is the 55th theorem of the Top 100 Theorems list.","PeriodicalId":280633,"journal":{"name":"Arch. Formal Proofs","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114273386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Formalization of Randomized Approximation Algorithms for Frequency Moments","authors":"Emin Karayel","doi":"10.4230/LIPIcs.ITP.2022.21","DOIUrl":"https://doi.org/10.4230/LIPIcs.ITP.2022.21","url":null,"abstract":"In 1999 Alon et al. introduced the still active research topic of approximating the frequency moments of a data stream using randomized algorithms with minimal space usage. This includes the problem of estimating the cardinality of the stream elements – the zeroth frequency moment. Higher-order frequency moments provide information about the skew of the data stream which is, for example, critical information for parallel processing. (The k -th frequency moment of a data stream is the sum of the k -th powers of the occurrence counts of each element in the stream.) They introduce both lower bounds and upper bounds on the space complexity of the problems, which were later improved by newer publications. The algorithms have guaranteed success probabilities and accuracies without making any assumptions on the input distribution. They are an interesting use case for formal verification because their correctness proofs require a large body of deep results from algebra, analysis and probability theory. This work reports on the formal verification of three algorithms for the approximation of F 0 , F 2 and F k for k ≥ 3. The results include the identification of significantly simpler algorithms with the same runtime and space complexities as the previously known ones as well as the development of several reusable components, such as a formalization of universal hash families, amplification methods for randomized algorithms, a model for one-pass data stream algorithms or a generic flexible encoding library for the verification of space complexities.","PeriodicalId":280633,"journal":{"name":"Arch. Formal Proofs","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123733149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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