Divyesh Unadkat

Supratik Chakraborty, Ashutosh Gupta, Divyesh Unadkat

We present a novel verification technique to prove interesting properties of a class of array programs with a symbolic parameter N denoting the size of arrays. The technique relies on constructing two slightly different versions of the same program. It infers difference relations between the corresponding variables at key control points of the joint control-flow graph of the two program versions. The desired post-condition is then proved by inducting on the program parameter $N$, wherein the difference invariants are crucially used in the inductive step. This contrasts with classical techniques that rely on finding potentially complex loop invaraints for each loop in the program. Our synergistic combination of inductive reasoning and finding simple difference invariants helps prove properties of programs that cannot be proved even by the winner of Arrays sub-category from SV-COMP 2021. We have implemented a prototype tool called diffy to demonstrate these ideas. We present results comparing the performance of diffy with that of state-of-the-art tools.

Supratik Chakraborty, Ashutosh Gupta, Divyesh Unadkat

We present a full-program induction technique for proving (a sub-class of) quantified as well as quantifier-free properties of programs manipulating arrays of parametric size N. Instead of inducting over individual loops, our technique inducts over the entire program (possibly containing multiple loops) directly via the program parameter N. Significantly, this does not require generation or use of loop-specific invariants. We have developed a prototype tool Vajra to assess the efficacy of our technique. We demonstrate the performance of Vajra vis-a-vis several state-of-the-art tools on a set of array manipulating benchmarks.

Supratik Chakraborty, Ashutosh Gupta, Divyesh Unadkat

Formally verifying properties of programs that manipulate arrays in loops is computationally challenging. In this paper, we focus on a useful class of such programs, and present a novel property-driven verification method that first infers array access patterns in loops using simple heuristics, and then uses this information to compositionally prove universally quantified assertions about arrays. Specifically, we identify tiles of array accesses patterns in a loop, and use the tiling information to reduce the problem of checking a quantified assertion at the end of a loop to an inductive argument that checks only a slice of the assertion for a single iteration of the loop body. We show that this method can be extended to programs with sequentially composed loops and nested loops as well. We have implemented our method in a tool called Tiler. Initial experiments show that Tiler outperforms several state-of-the-art tools on a suite of interesting benchmarks.