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We present the monitoring approach implemented in the latest version of <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\text {RVHyper}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n<mml:mtext>RVHyper<\/mml:mtext>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula>, a runtime verification tool for hyperproperties. The input to the tool are specifications given in the temporal logic <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\text {HyperLTL}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n<mml:mtext>HyperLTL<\/mml:mtext>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula>, which extends linear-time temporal logic\u00a0(LTL) with trace quantifiers and trace variables. <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\text {RVHyper}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n<mml:mtext>RVHyper<\/mml:mtext>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula> processes execution traces sequentially until a violation of the specification is detected. In this case, a counterexample, in the form of a set of traces, is returned. <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\text {RVHyper}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n<mml:mtext>RVHyper<\/mml:mtext>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula> employs a range of optimizations: a preprocessing analysis of the specification and a procedure that minimizes the traces that need to be stored during the monitoring process. In this article, we introduce a novel trace storage technique that arranges the traces in a tree-like structure to exploit partially equal traces. We evaluate <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\text {RVHyper}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n<mml:mtext>RVHyper<\/mml:mtext>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula> on existing benchmarks on secure information flow control, error correcting codes, and symmetry in hardware designs. As an example application outside of security, we show how <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\text {RVHyper}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n<mml:mtext>RVHyper<\/mml:mtext>\n<\/mml:math><\/jats:alternatives><\/jats:inline-formula> can be used to detect spurious dependencies in hardware designs.<\/jats:p>","DOI":"10.1007\/s10009-020-00552-5","type":"journal-article","created":{"date-parts":[[2020,2,20]],"date-time":"2020-02-20T13:03:34Z","timestamp":1582203814000},"page":"729-740","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Efficient monitoring of hyperproperties using prefix trees"],"prefix":"10.1007","volume":"22","author":[{"given":"Bernd","family":"Finkbeiner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christopher","family":"Hahn","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marvin","family":"Stenger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leander","family":"Tentrup","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,2,20]]},"reference":[{"key":"552_CR1","doi-asserted-by":"publisher","unstructured":"Agrawal, S., Bonakdarpour, B.: Runtime verification of k-safety hyperproperties in HyperLTL. 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