Towards Scalability in Nonstandard Static Analysis (
نویسندگان
چکیده
Interpretation with Infinitesimals∗ Towards Scalability in Nonstandard Static Analysis (Extended Abstract) Kengo Kido, Swarat Chaudhuri, and Ichiro Hasuo 1 University of Tokyo, Japan 2 JSPS Research Fellow 3 Rice University, USA Abstract Towards the goal of correctness and reliability of hybrid systems, we continue our nonstandard static analysis program (with Suenaga and Sekine) where hybrid dynamics is turned into purely discrete one with explicit use of infinitesimals. While our previous results have focused on deductive verification by program logics, the current work aims at automation and enhanced scalability by extending abstract interpretation—a technique known for its ample scalability and widespread use in various verification tools—with infinitesimals. Our theoretical results include soundness and termination via uniform widening operators; and our prototype implementation successfully verifies some benchmark examples.
منابع مشابه
Abstract Interpretation with Infinitesimals: Towards Scalability in Nonstandard Static Analysis
Interpretation with Infinitesimals Towards Scalability in Nonstandard Static Analysis Kengo Kido, Swarat Chaudhuri, and Ichiro Hasuo 1 University of Tokyo, Japan 2 Rice University, USA Abstract. Towards the goal of correctness and reliability of hybrid systems, we continue the nonstandard static analysis program where hybrid dynamics is turned into purely discrete one with explicit use of infin...
متن کاملAbstract Interpretation with Infinitesimals: Towards Scalability in Nonstandard Static Analysis (Extended Version)
Interpretation with Infinitesimals ? Towards Scalability in Nonstandard Static Analysis Kengo Kido, Swarat Chaudhuri, and Ichiro Hasuo 1 University of Tokyo, Japan 2 JSPS Research Fellow 3 Rice University, USA Abstract. We extend abstract interpretation for the purpose of verifying hybrid systems. Abstraction has been playing an important role in many verification methodologies for hybrid syste...
متن کاملA New Approach to Nonstandard Analysis
In this paper, we propose a new approach to nonstandard analysis without using the ultrafilters. This method is very simple in practice. Moreover, we construct explicitly the total order relation in the new field of the infinitesimal numbers. To illustrate the importance of this work, we suggest comparing a few applications of this approach with the former methods.
متن کاملExercises in Nonstandard Static Analysis of Hybrid Systems
In formal verification of hybrid systems, a big challenge is to incorporate continuous flow dynamics in a discrete framework. Our previous work proposed to use nonstandard analysis (NSA) as a vehicle from discrete to hybrid; and to verify hybrid systems using a Hoare logic. In this paper we aim to exemplify the potential of our approach, through transferring static analysis techniques to hybrid...
متن کاملNonstandard finite difference schemes for differential equations
In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...
متن کامل