  Verification techniques express program states as logical formulas over
program variables. For example, symbolic execution and abstract interpretation
encode program states as a set of integer inequalities. However, for real-world
programs these formulas tend to become large, which affects scalability of
analyses. To address this problem, researchers developed complementary
approaches which either remove redundant inequalities or extract a subset of
inequalities sufficient for specific reasoning. For arbitrary integer
inequalities, such reduction approaches either have high complexities or
over-approximate. However, efficiency and precision of these approaches can be
improved for a restricted type of logical formulas used in relational numerical
abstract domains. While previous work investigated custom efficient redundant
inequality elimination for Zones states, our work examines custom semantic
slicing algorithms that identify a minimal set of changed inequalities in Zones
states.
  The client application of the minimal changes in Zones is an empirical study
on comparison between invariants computed by data-flow analysis using Zones,
Intervals and Predicates numerical domains. In particular, evaluations compare
how our proposed algorithms affect the precision of comparing Zones vs.
Intervals and Zones vs. Predicates abstract domains. The results show our
techniques reduce the number of variables by more than 70% and the number of
inequalities by 30%, compared to full states. The approach refines the
granularity of comparison between domains, reducing incomparable invariants
between Zones and Predicates from 52% to 4%, and increases equality of
Intervals and Zones, invariants from 27% to 71%. The techniques improve the
comparison efficiency by reducing total runtime for all subject comparisons for
Zones and Predicates from over 4 minutes to a few seconds.
