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Abstract Interpretation over Zones without Widening

32 pagesPublished: June 22, 2012

Abstract

We present a practical algorithm for computing least
solutions of systems of (fixpoint-)equations over the integers with,
besides other monotone operators,
addition, multiplication by positive constants, maximum, and minimum.
The algorithm is based on max-strategy iteration.
Its worst-case running-time (w.r.t. a uniform cost measure)
is independent of the sizes of occurring numbers.
We apply this
algorithm to compute the abstract semantics of
programs over integer intervals as well as over integer zones.

Keyphrases: abstract interpretation, fixpoint equation systems, interval analysis, static program analysis, Strategy Improvement Algorithms, timed automata, verification, Zones

In: Andrei Voronkov, Laura Kovács and Nikolaj Bjorner (editors). WING 2010. Workshop on Invariant Generation 2010, vol 1, pages 12--43

Links:
BibTeX entry
@inproceedings{WING2010:Abstract_Interpretation_over_Zones,
  author    = {Thomas Martin Gawlitza and Helmut Seidl},
  title     = {Abstract Interpretation over Zones without Widening},
  booktitle = {WING 2010. Workshop on Invariant Generation 2010},
  editor    = {Andrei Voronkov and Laura Kovacs and Nikolaj Bjorner},
  series    = {EPiC Series in Computing},
  volume    = {1},
  pages     = {12--43},
  year      = {2012},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/qQzK},
  doi       = {10.29007/qqdg}}

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