Abstract Interpretation with Infinitesimals: Towards Scalability in Nonstandard Static Analysis (Extended Version)

We extend abstract interpretation for the purpose of verifying hybrid systems. Abstraction has been playing an important role in many verification methodologies for hybrid systems, but some special care is needed for abstraction of continuous dynamics defined by ODEs. We apply Cousot and Cousot's framework of abstract interpretation to hybrid systems, almost as it is, by regarding continuous dynamics as an infinite iteration of infinitesimal discrete jumps. This extension follows the recent line of work by Suenaga, Hasuo and Sekine, where deductive verification is extended for hybrid systems by 1) introducing a constant dt for an infinitesimal value; and 2) employing Robinson's nonstandard analysis (NSA) to define mathematically rigorous semantics. Our theoretical results include soundness and termination via uniform widening operators; and our prototype implementation successfully verifies some benchmark examples.Comment: 28 pages, an extended version of a paper accepted in 17th International Conference on Verification, Model Checking, and Abstract Interpretation (VMCAI 2016

Deterministic Parallel Fixpoint Computation

Abstract interpretation is a general framework for expressing static program analyses. It reduces the problem of extracting properties of a program to computing an approximation of the least fixpoint of a system of equations. The de facto approach for computing this approximation uses a sequential algorithm based on weak topological order (WTO). This paper presents a deterministic parallel algorithm for fixpoint computation by introducing the notion of weak partial order (WPO). We present an algorithm for constructing a WPO in almost-linear time. Finally, we describe PIKOS, our deterministic parallel abstract interpreter, which extends the sequential abstract interpreter IKOS. We evaluate the performance and scalability of PIKOS on a suite of 1017 C programs. When using 4 cores, PIKOS achieves an average speedup of 2.06x over IKOS, with a maximum speedup of 3.63x. When using 16 cores, PIKOS achieves a maximum speedup of 10.97x.Comment: Published in POPL 2020. Code is available at https://github.com/95616ARG/pikos_popl202