Resourceful Reachability as HORN-LA

Berdine, Josh; Bjørner, Nikolaj; Ishtiaq, Samin; Kriener, Jael; Wintersteiger, Christoph M.

doi:10.1007/978-3-642-45221-5_10

Cited by 4 publications

(2 citation statements)

References 9 publications

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“…This is the case, e.g., when checking abstract counterexamples for concrete feasibility [3] A Proofs Lemma 1. For a statement C and a set of states S Â U, wp.C; S / D U X pre+fail.C; U X S /.…”

Section: Discussionmentioning

confidence: 99%

Backward Analysis via over-Approximate Abstraction and under-Approximate Subtraction

2014

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Abstract. We propose a novel approach for computing weakest liberal safe preconditions of programs. The standard approaches, which call for either underapproximation 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.

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Section: Discussionmentioning

confidence: 99%

Backward Analysis via over-Approximate Abstraction and under-Approximate Subtraction

2014

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“…In practice, we have so far obtained satisfactory results only with finding recurrent sets of individual loops. There also exists work on showing feasibility of abstract counterexamples (including, for non-numeric abstract domains [9]), and techniques from that area would also be applicable to show reachability of a recurrent set.…”

Section: Introductionmentioning

confidence: 99%

Finding Recurrent Sets with Backward Analysis and Trace Partitioning

Bakhirkin

Piterman

2016

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract.We propose an abstract-interpretation-based analysis for recurrent sets. A recurrent set is a set of states from which the execution of a program cannot or might not (as in our case) escape. A recurrent set is a part of a program's nontermination proof (that needs to be complemented by reachability analysis). We find recurrent sets by performing a potentially over-approximate backward analysis that produces an initial candidate. We then perform over-approximate forward analysis on the candidate to check and refine it and ensure soundness. In practice, the analysis relies on trace partitioning that predicts future paths through the program that non-terminating executions will take. Using our technique, we were able to find recurrent sets in many benchmarks found in the literature including some that, to our knowledge, cannot be handled by existing tools. In addition, we note that typically, analyses that search for recurrent sets are applied to linear under-approximations of programs or employ some form of non-approximate numeric reasoning. In contrast, our analysis uses standard abstract-interpretation techniques and is potentially applicable to a larger class of abstract domains (and therefore -programs).

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