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For (finite-state) hardware, temporal hyperproperties are supported by model checking algorithms, and tools for general temporal logics like HyperLTL exist. For (infinite-state) software, the analysis of temporal hyperproperties has, so far, been limited to<jats:italic>k<\/jats:italic>-safety properties, i.e., properties that stipulate the absence of a bad interaction between any<jats:italic>k<\/jats:italic>traces. In this paper, we present an automated method for the verification of<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\forall ^k\\exists ^l$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:msup><mml:mo>\u2200<\/mml:mo><mml:mi>k<\/mml:mi><\/mml:msup><mml:msup><mml:mo>\u2203<\/mml:mo><mml:mi>l<\/mml:mi><\/mml:msup><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-safety properties in infinite-state systems. A<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\forall ^k\\exists ^l$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:msup><mml:mo>\u2200<\/mml:mo><mml:mi>k<\/mml:mi><\/mml:msup><mml:msup><mml:mo>\u2203<\/mml:mo><mml:mi>l<\/mml:mi><\/mml:msup><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>-safety property stipulates that for any<jats:italic>k<\/jats:italic>traces, there<jats:italic>exist<\/jats:italic><jats:italic>l<\/jats:italic>traces such that the resulting<jats:inline-formula><jats:alternatives><jats:tex-math>$$k+l$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>k<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>l<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>traces do not interact badly. This combination of universal and existential quantification enables us to express many properties beyond<jats:italic>k<\/jats:italic>-safety, including, for example, generalized non-interference or program refinement. Our method is based on a strategy-based instantiation of existential trace quantification combined with a program reduction, both in the context of a fixed predicate abstraction. Notably, our framework allows for mutual dependence of strategy and reduction.<\/jats:p>","DOI":"10.1007\/978-3-031-13185-1_17","type":"book-chapter","created":{"date-parts":[[2022,8,6]],"date-time":"2022-08-06T19:29:09Z","timestamp":1659814149000},"page":"341-362","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["Software Verification of\u00a0Hyperproperties Beyond k-Safety"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6234-5651","authenticated-orcid":false,"given":"Raven","family":"Beutner","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4280-8441","authenticated-orcid":false,"given":"Bernd","family":"Finkbeiner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,8,7]]},"reference":[{"issue":"2","key":"17_CR1","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1016\/0304-3975(91)90224-P","volume":"82","author":"M Abadi","year":"1991","unstructured":"Abadi, M., Lamport, L.: The existence of refinement mappings. 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