2381/28950 Nir Piterman Nir Piterman Alexey Bakhirkin Alexey Bakhirkin Josh Berdine Josh Berdine Backward analysis via over-approximate abstraction and under-approximate subtraction University of Leicester 2014 IR content 2014-06-26 14:09:45 Conference contribution https://figshare.le.ac.uk/articles/conference_contribution/Backward_analysis_via_over-approximate_abstraction_and_under-approximate_subtraction/10140362 We propose a novel approach for computing weakest liberal safe preconditions of programs. The standard approaches, which call for either under-approximation of a greatest fixed point, or complementation of a least fixed point, are often difficult to apply successfully. Our approach relies on a different decomposition of the weakest precondition of loops. We exchange the greatest fixed point for the computation of a least fixed point above a recurrent set, instead of the bottom element. Convergence is achieved using over-approximation, while in order to maintain soundness we use an under-approximating logical subtraction operation. Unlike general complementation, subtraction more easily allows for increased precision in case its arguments are related. The approach is not restricted to a specific abstract domain and we use it to analyze programs using the abstract domains of intervals and of 3-valued structures.