PPT-2 Invariants

Props A chocolate bar 5 paper cups Invariants An invariant is something that does not change Other names you may be more familiar with are laws patterns Invariants in Maths and Science 1. William Harris. , . Akash. . Lal. , . Aditya. . Nori. Sriram. . Rajamani. 1. 1. 2. 2. 2. 2. Termination bugs are a real problem in systems . and application code.. “Gecko . mediaplayer. hangs the browser”. With Liquid . Types. Ranjit. . Jhala. , UC San Diego. (with Pat . Rondon. , Ming Kawaguchi). Part I. First-Order Verification. Part II. Higher-Order Verification. char* . rev_copy. (. char* . a, . int. Rahul Sharma and Alex Aiken (Stanford University). 1. Randomized Search. x. = . i. ;. y = j;. while . y!=0 . do. . x = x-1;. . y = y-1;. if( . i. ==j ). assert x==0. No!. Yes!.  . 2. Invariants. Invariant . Inference. Invariants. Dictionary Meaning:. A function, quantity, or . property. which remains unchanged. Property (in our context): a predicate that holds for some, all, or no states. Pranav. . Garg. University of . illinois. at . urbana-champaign. Joint work with:. . P. . madhusudan. (. uiuc. ),. . christof. . loding. (RWTH . AAchen. ). . daniel. . neider. (RWTH Aachen). Proseminar „Programmanalyse. ”, Prof. Dr. Heike . Wehrheim. Universit. ät Paderborn, WS 2011. /2012. Anton . Tonkushin. Static debugging. Array indexing outside of its proper bounds. Division by zero. Jordi Cortadella. Department of Computer Science. Invariants. Invariants help to …. Define how variables must be initialized before a loop. Define the necessary condition to reach the post-condition . using. Model Checking and Abstract Interpretation. Anvesh Komuravelli, CMU. Joint work with Ken McMillan. The Problem. Array-Manipulating Program . P. + Assertions. Automatic analysis for. assertion failures. EEN 417. Fall 2013. When is a Design of a System . “. Correct. ”. ?. A design is correct when it meets its specification (requirements) in its operating environment. “. A design without specification cannot be right or wrong, it can only be surprising!. in . Flowpipe. Construction . using Pseudo-Invariants. Stanley . Bak. United States Air Force Research Lab. Information Directorate – Rome, NY. Cyber-Physical Systems. Include computational (discrete) components, and physical-world (continuous) aspects. Debugging. Debugging is a . fact of life. . . Arise for many reasons (. typing mistakes, conceptual errors. ). . What can we do to make it easier?. Some IDEs have . tools. . . We can use . Logging. and . Mooly. . Sagiv. http://www.cs.tau.ac.il/~msagiv/courses/pa16.html. Formalities. Prerequisites: Compilers or Programming Languages. Course Grade. 10 % Lecture Summary (. latex+examples. within one week). SDN Data & Control Planes:. Header Space Analysis. SDN Stack. State layers . hold a . representation . of the . network’s configuration. . Code layers implement. logic . to maintain the . mapping between . Ahmed . Khurshid. , . Wenxuan. Zhou, Matthew Caesar, P. Brighten Godfrey. University of Illinois. Presented by Ofri Ziv. November 2013. Outline. Motivation. Design. Evaluation. Example. Conclusion. Motivation.