Abstract Interpretation with Infinitesimals

Towards Scalability in Nonstandard Static Analysis
  • Kengo Kido
  • Swarat Chaudhuri
  • Ichiro Hasuo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9583)


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 \(\mathtt {dt}\) 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.


Widening Operator Convex Polyhedron Abstract Interpretation Iteration Sequence Hybrid Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.University of TokyoTokyoJapan
  2. 2.JSPS Research FellowTokyoJapan
  3. 3.Rice UniversityHoustonUSA

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