{"id":186691,"date":"2011-08-12T00:00:00","date_gmt":"2011-08-19T14:26:38","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/theories-solvers-and-static-analysis-by-abstract-interpretation\/"},"modified":"2016-08-22T11:31:03","modified_gmt":"2016-08-22T18:31:03","slug":"theories-solvers-and-static-analysis-by-abstract-interpretation","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/theories-solvers-and-static-analysis-by-abstract-interpretation\/","title":{"rendered":"Theories, Solvers and Static Analysis by Abstract Interpretation"},"content":{"rendered":"<div class=\"asset-content\">\n<p>The algebraic\/model theoretic design of static analyzers uses abstract domains based on representations of properties and pre-calculated property transformers. It is very efficient. The logical\/proof theoretic approach uses SMT solvers\/theorem provers and computation of property transformers on-the-fly. It is very expressive. We propose to unify both approaches, so that they can be combined to reach the sweet spot best adapted to a specific application domain in the precision\/cost spectrum. We first give a new formalization of the proof theoretic approach in the abstract interpretation framework, introducing a semantics based on multiple interpretations to deal with the soundness of such approaches. Then we describe how to combine them with any other abstract interpretation-based analysis using an iterated reduction to combine abstractions. The key observation is that the Nelson-Oppen procedure which decides satisfiability in a combination of logical theories by exchanging equalities and disequalities computes a reduced product (after the state is enhanced with some new \u201cobservations\u201d corresponding to alien terms). By abandoning restrictions ensuring completeness (such as disjointness, convexity, stably-infiniteness, or shininess, etc) we can even broaden the application scope of logical abstractions for static analysis (which is incomplete anyway). Joint work with Laurent Mauborgne (IMDEA, Madrid)<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The algebraic\/model theoretic design of static analyzers uses abstract domains based on representations of properties and pre-calculated property transformers. It is very efficient. The logical\/proof theoretic approach uses SMT solvers\/theorem provers and computation of property transformers on-the-fly. It is very expressive. We propose to unify both approaches, so that they can be combined to reach [&hellip;]<\/p>\n","protected":false},"featured_media":196334,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-186691","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/H99CMUFPv0U","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/186691"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/186691\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/196334"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=186691"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=186691"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=186691"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=186691"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=186691"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=186691"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=186691"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}