Constraint Specialisation in Horn Clause Verification

Kafle, Bishoksan; Gallagher, John P.

doi:10.1145/2678015.2682544

Cited by 19 publications

(26 citation statements)

References 35 publications

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“…For the safety check (the procedure SAFE in Algorithm 1) we use the verification procedure described in [18] which uses abstract interpretation over the domain of convex polyhedra, with a timeout of 5 minutes. The symbol "-" in Table 1 denotes that we were unable to solve these problems within the given time.…”

Section: Resultsmentioning

confidence: 99%

“…The oracle is sound: if SAFE(P) returns safe (unsafe) then P is safe (unsafe). SAFE could be any existing automatic Horn clause solver [12,19,18,17,6]. When it cannot verify a program within a given time limit, the unknown answer is emitted.…”

Section: Procedures For Verificationmentioning

confidence: 99%

“…We prove each such set of clauses using abstract interpretation [4] over the domain of convex polyhedra [5] as described in [18]. Finally, the preliminary results in a set of Horn clause verification benchmarks show that this is a useful program transformation.…”

Section: Introductionmentioning

confidence: 99%

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Decomposition by tree dimension in Horn clause verification

Kafle

Gallagher

Ganty

2015

Electron. Proc. Theor. Comput. Sci.

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In this paper we investigate the use of the concept of tree dimension in Horn clause analysis and verification. The dimension of a tree is a measure of its non-linearity -for example a list of any length has dimension zero while a complete binary tree has dimension equal to its height. We apply this concept to trees corresponding to Horn clause derivations. A given set of Horn clauses P can be transformed into a new set of clauses P ≤k , whose derivation trees are the subset of P's derivation trees with dimension at most k. Similarly, a set of clauses P >k can be obtained from P whose derivation trees have dimension at least k + 1. In order to prove some property of all derivations of P, we systematically apply these transformations, for various values of k, to decompose the proof into separate proofs for P ≤k and P >k (which could be executed in parallel). We show some preliminary results indicating that decomposition by tree dimension is a potentially useful proof technique. We also investigate the use of existing automatic proof tools to prove some interesting properties about dimension(s) of feasible derivation trees of a given program.

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Section: Resultsmentioning

confidence: 99%

Section: Procedures For Verificationmentioning

confidence: 99%

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Decomposition by tree dimension in Horn clause verification

Kafle

Gallagher

Ganty

2015

Electron. Proc. Theor. Comput. Sci.

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“…The CHC Specialization strategy we consider in this paper is a variant of specialization techniques for (constraint) logic programs which have been proposed to support program verification [1,11,13,15,24,28,29,34,37]. However, these techniques are focused on the verification of partial or total correctness of single programs, and not on the relational verification.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Predicate Pairing with Abstraction for Relational Verification

Angelis

Fioravanti

Pettorossi

et al. 2018

Logic-Based Program Synthesis and Transformation

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Relational verification is a technique that aims at proving properties that relate two different program fragments, or two different program runs. It has been shown that constrained Horn clauses (CHCs) can effectively be used for relational verification by applying a CHC transformation, called predicate pairing, which allows the CHC solver to infer relations among arguments of different predicates. In this paper we study how the effects of the predicate pairing transformation can be enhanced by using various abstract domains based on linear arithmetic (i.e., the domain of convex polyhedra and some of its subdomains) during the transformation. After presenting an algorithm for predicate pairing with abstraction, we report on the experiments we have performed on over a hundred relational verification problems by using various abstract domains. The experiments have been performed by using the VeriMAP transformation and verification system, together with the Parma Polyhedra Library (PPL) and the Z3 solver for CHCs.

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“…Horn Clauses, as an intermediate language, have become a popular formalism for verification [5,15], attracting both the logic programming and software verification communities [4]. As a result of these, several verification techniques and tools have been developed for CHCs, among others, [17,16,26,11,27,24,23]. To the best of our knowledge, the use of automata based approach for abstraction-refinement of Horn clauses is relatively new [27,33], though the original framework proposed for imperative programs goes back to [19,20].…”

Section: Related Workmentioning

confidence: 99%

Interpolant Tree Automata and their Application in Horn Clause Verification

Kafle

Gallagher

2016

Electron. Proc. Theor. Comput. Sci.

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This paper investigates the combination of abstract interpretation over the domain of convex polyhedra with interpolant tree automata, in an abstraction-refinement scheme for Horn clause verification. These techniques have been previously applied separately, but are combined in a new way in this paper. The role of an interpolant tree automaton is to provide a generalisation of a spurious counterexample during refinement, capturing a possibly infinite set of spurious counterexample traces. In our approach these traces are then eliminated using a transformation of the Horn clauses. We compare this approach with two other methods; one of them uses interpolant tree automata in an algorithm for trace abstraction and refinement, while the other uses abstract interpretation over the domain of convex polyhedra without the generalisation step. Evaluation of the results of experiments on a number of Horn clause verification problems indicates that the combination of interpolant tree automaton with abstract interpretation gives some increase in the power of the verification tool, while sometimes incurring a performance overhead.

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Constraint Specialisation in Horn Clause Verification

Cited by 19 publications

References 35 publications

Decomposition by tree dimension in Horn clause verification

Decomposition by tree dimension in Horn clause verification

Predicate Pairing with Abstraction for Relational Verification

Interpolant Tree Automata and their Application in Horn Clause Verification

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