{"id":164120,"date":"2013-03-01T00:00:00","date_gmt":"2013-03-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/a-data-driven-approach-for-algebraic-loop-invariants-2\/"},"modified":"2018-10-16T20:08:38","modified_gmt":"2018-10-17T03:08:38","slug":"a-data-driven-approach-for-algebraic-loop-invariants-2","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/a-data-driven-approach-for-algebraic-loop-invariants-2\/","title":{"rendered":"A Data Driven Approach for Algebraic Loop Invariants"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We describe a Guess-and-Check algorithm for computing algebraic equation invariants of the form wedge <i>i f<\/i>i(x<sub>1<\/sub>, &#8230; , x<sub>n<\/sub>) = 0, where each f<sub>i<\/sub> is a polynomial over the variables x<sub>1<\/sub>, &#8230; , x<sub>n<\/sub> of the program. The Guess phase is data driven and derives a candidate invariant from data generated from concrete executions of the program. This candidate invariant is subsequently validated in a Check phase by an off-the-shelf SMT solver. Iterating between the two phases leads to a sound algorithm. Moreover, we are able to prove a bound on the number of decision procedure queries which Guess-and-Check requires to obtain a sound invariant. We show how Guess-and-Check can be extended to generate arbitrary boolean combinations of linear equalities as invariants, which enables us to generate expressive invariants to be consumed by tools that cannot handle non-linear arithmetic. We have evaluated our technique on a number of benchmark programs from recent papers on invariant generation. Our results are encouraging \u2013 we are able to effifficiently compute algebraic invariants in all cases, with only a few tests.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We describe a Guess-and-Check algorithm for computing algebraic equation invariants of the form wedge i fi(x1, &#8230; , xn) = 0, where each fi is a polynomial over the variables x1, &#8230; , xn of the program. The Guess phase is data driven and derives a candidate invariant from data generated from concrete executions of [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13560],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-164120","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-programming-languages-software-engineering","msr-locale-en_us"],"msr_publishername":"Lecture Notes in Computer Science","msr_edition":"European Symposium on Programming 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