Lab for Automated Reasoning and Analysis LARA

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

sav07_lecture_11 [2007/04/25 18:17] (current)
vkuncak created
Line 1: Line 1:
 +====== Lecture 11 ======
 +
 +===== Modular analysis of procedures =====
 +
 +Inlining specifications. ​ Last part of [[SAV07 Homework 4]].
 +
 +Postconditions that refer to values of variables in the precondition.
 +
 +The meaning of modifies clauses.
 +
 +===== ASTREE Static Analyzer =====
 +
 +=== The Octagon Abstract Domain ===
 +
 +[[http://​www.di.ens.fr/​~mine/​publi/​article-mine-HOSC06.pdf|Link to paper]]
 +
 +
 +=== A Static Analyzer for Large Safety-Critical Software ===
 +
 +[[http://​www.di.ens.fr/​~cousot/​COUSOTpapers/​PLDI03.shtml|Link to paper]]
 +
 +Section 5.4: A remark on notation:
 +  * if $\rho$ denotes the state and $S$ is a deterministic statement, then $[\![S]\!]^s(\rho)$ represents the new state after executing the statement; the relation corresponding to statement semantics would be $\{(S,​[\![S]\!]^s(\rho)) \mid \rho \mbox{ is a state, mapping variables to their values \}$.
 +  * this function is extended to map sets of states to sets of states, which gives function mapping $E$ to $[\![S]\!]^c(E)$ and is what we called strongest postcondition $sp(S,E)$.
 +  * this is abstracted to abstract domain
 +
 +Domains used
 +  * octagons (see above paper)
 +  * ellipsoid
 +
 +Widening with tresholds.
 +
 +Sound approximation of real numbers with floating point calculations.
 +
 +Improving precision
 +  * trace partitioning:​ recover some of the path sensitivity of weakest preconditions
 +  * decision trees
 +  * loop unrolling
 +  * procedures are inlined
 +
 +Packing: computing relationships between groups of variables and not all variables
 +  * for octagons
 +  * for decision trees
 +
 +Results
 +  * the absence of false alarms is remarkable, result of heavy tuning of the analysis to given progrma
 +  * main loop invariant is 4.5MB
 +
 +=== Combination of Abstractions in the ASTRÉE Static Analyzer ===
 +
 +  * [[http://​www.di.ens.fr/​~cousot/​COUSOTpapers/​ASIAN06.shtml|Link to paper]]
 +
 +Note Section 4.1 on how many of the standard assumptions of the domain do not hold any more for such a complex analyzer.
 +
 +Consider Example 3 of non-monotonicity in the presence of widening. ​ The reason that the result is less precise starting from [0,0] interval for y instead of [0,9] is because widening to [0,​$+\infty$] is applied before the fixepoint interval [0,9] is reached.
 +
 +Section 5 deals with communicating information between different domains. ​ The functions that are defined are mostly various form of approximating conjunction (intersection of sets of states). ​ There are many such functions because arguments and results can belong to different domains.
  
 
sav07_lecture_11.txt · Last modified: 2007/04/25 18:17 by vkuncak
 
© EPFL 2018 - Legal notice