{"id":158398,"date":"2009-10-19T00:00:00","date_gmt":"2009-10-19T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/the-reachability-bound-problem\/"},"modified":"2018-10-16T19:58:38","modified_gmt":"2018-10-17T02:58:38","slug":"the-reachability-bound-problem","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/the-reachability-bound-problem\/","title":{"rendered":"The Reachability-Bound Problem"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We define the &#8220;reachability-bound problem&#8221; to be the problem of finding a symbolic worst-case bound on the number of times a given control location inside a procedure is visited in terms of the inputs to that procedure. This has applications in bounding resources consumed by a program such as time, memory, network-traffic, power, as well as estimating quantitative properties (as opposed to boolean properties) of data in programs, such as amount of information leakage or uncertainty propagation.<\/p>\n<p>Our approach to solving the reachability-bound problem brings together two very different techniques for reasoning about loops in an effective manner. One of these techniques is an abstract-interpretation based iterative technique for computing precise disjunctive invariants (to summarize nested loops). The other technique is a non-iterative proof-rules based technique (for loop bound computation) that takes over the role of doing inductive reasoning, while deriving its power from use of SMT solvers to reason about abstract loop-free fragments.<\/p>\n<p>Our solution to the reachability-bound problem allows us to compute precise symbolic bounds for several loops in .Net base-class libraries for which earlier techniques fail. We also illustrate the precision of our algorithm for disjunctive invariant computation (which has a more general applicability beyond the reachability-bound problem) on a set of benchmark examples.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We define the &#8220;reachability-bound problem&#8221; to be the problem of finding a symbolic worst-case bound on the number of times a given control location inside a procedure is visited in terms of the inputs to that procedure. 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