EN FR
EN FR
Bilateral Contracts and Grants with Industry
Bibliography
Bilateral Contracts and Grants with Industry
Bibliography


Section: New Results

Numeric Invariant Inference

A Numeric Abstract Domain to Infer Octagonal Constraints with Absolute Value

Participants : Liqian Chen [National Laboratory for Parallel and Distributed Processing, National University of Defense Technology, Changsha, P.R.China] , Jiangchao Liu, Antoine Miné, Deepak Kapur [University of New Mexico, USA] , Ji Wang [National Laboratory for Parallel and Distributed Processing, National University of Defense Technology, Changsha, P.R.China] .

The octagon abstract domain, devoted to discovering octagonal constraints (also called Unit Two Variable Per Inequality or UTVPI constraints) of a program, is one of the most commonly used numerical abstractions in practice, due to its quadratic memory complexity and cubic time complexity. However, the octagon domain itself is restricted to express convex sets and has limitations in handling non-convex properties which are sometimes required for proving some numerical properties in a program. In [12] , we intend to extend the octagon abstract domain with absolute value, to infer certain non-convex properties by exploiting the absolute value function. More precisely, the new domain can infer relations of the form {±X±Yc,±X±|Y|d,±|X|±|Y|e}. We provide algorithms for domain operations such that the new domain still enjoys the same asymptotic complexity as the octagon domain. Moreover, we present an approach to support strict inequalities over rational or real-valued variables in this domain, which also fits for the octagon domain. Experimental results of our prototype are encouraging; The new domain is scalable and able to find non-convex invariants of interest in practice but without too much overhead (compared with that using octagons).

A Method to Infer Inductive Numeric Invariants Inspired from Constraint Programming.

Participant : Antoine Miné.

In [29] , we suggest the idea of using algorithms inspired by Constraint Programming in order to infer inductive invariants on numeric programs. Similarly to Constraint Programming solvers on continuous domains, our algorithm approximates the problem from above, using decreasing iterations that may split, discard, and tighten axis-aligned boxes. If successful, the algorithm outputs a set of boxes that includes the initial states and is a post-fixpoint of the abstract semantic function of interest. Our work is very preliminary; many improvements still need to be performed to determine if the method is usable in practice, and in which contexts. Nevertheless, we show that a naive proof-of-concept implementation of our algorithm is already capable of inferring non-trivial inductive invariants that would otherwise require the use of relational or even non-linear abstract domains when using more traditional abstract interpretation iteration methods.