Combining Forward and Backward Abstract Interpretation of Horn Clauses

Abstract : Alternation of forward and backward analyses is a standard technique in abstract interpretation of programs, which is in particular useful when we wish to prove unreachability of some undesired program states. The current state-of-the-art technique for combining forward (bottom-up, in logic programming terms) and backward (top-down) abstract interpretation of Horn clauses is query-answer transformation. It transforms a system of Horn clauses, such that standard forward analysis can propagate constraints both forward, and backward from a goal. Query-answer transformation is effective, but has issues that we wish to address. For that, we introduce a new backward collecting semantics, which is suitable for alternating forward and backward abstract interpretation of Horn clauses. We show how the alternation can be used to prove unreachability of the goal and how every subsequent run of an analysis yields a refined model of the system. Experimentally, we observe that combining forward and backward analyses is important for analysing systems that encode questions about reachability in C programs. In particular, the combination that follows our new semantics improves the precision of our own abstract interpreter, including when compared to a forward analysis of a query-answer-transformed system.
Liste complète des métadonnées

Cited literature [37 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01551447
Contributor : Alexey Bakhirkin <>
Submitted on : Wednesday, July 26, 2017 - 8:09:35 PM
Last modification on : Friday, July 6, 2018 - 10:08:02 AM

Files

sas17.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01551447, version 2
  • ARXIV : 1707.01277

Collections

Citation

Alexey Bakhirkin, David Monniaux. Combining Forward and Backward Abstract Interpretation of Horn Clauses. 24th International Static Analysis Symposium (SAS), Francesco Ranzato; Patrick Cousot, Aug 2017, New York City, United States. ⟨hal-01551447v2⟩

Share

Metrics

Record views

140

Files downloads

97