Tree Automata-Based Refinement with Application to Horn Clause Verification

Kafle, Bishoksan; Gallagher, John P.

doi:10.1007/978-3-662-46081-8_12

Cited by 9 publications

(13 citation statements)

References 29 publications

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“…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%

“…In practice we use some injective renaming function from states to predicates in the constructed program. Further discussion of the mappings between CHCs and FTAs can be found in [19]. By construction, the derivations of chc id (A ) (for the accepting predicates) correspond to the elements of L (A ).…”

Section: Trace Automata For Chcsmentioning

confidence: 99%

“…Details on difference construction can be found in [19]. We construct the difference of two FTAs by (1) standardising apart the predicate names; (2) forming the union of the two FTAs; (3) determinising the union; (4) removing from the determinised FTA all states (and transitions that contain them) that contain an accepting state of the second FTA.…”

Section: Assignment Of Identifiers In the At-most-k-dimension Programmentioning

confidence: 99%

“…After assigning identifiers to each of the clauses in Fib ≤0 , we can construct an FTA corresponding to it using Definition 4, and obtain the FTA shown in Figure 6: as before we represent a predicate p ≤k by p[k] and a predicate p =k by p(k). We can generate a new program from this DFTA together with the original program Fib following the approach taken in [19] obtaining the program in Figure 8. It should be noted that the derivation trees rooted at false have dimension at-least 1.…”

Section: Examplementioning

confidence: 99%

“…false :-K > 2, mc91(X,Y,K). The clauses together with the integrity constraint are given to an automatic solver for Horn clauses [12,19], which are able to prove the safety of the clauses and thus establish the upper bound of 2.…”

Section: Program Instrumentation With Dimensionmentioning

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: Procedures For Verificationmentioning

confidence: 99%

Section: Trace Automata For Chcsmentioning

confidence: 99%

Section: Assignment Of Identifiers In the At-most-k-dimension Programmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Section: Program Instrumentation With Dimensionmentioning

confidence: 99%

See 3 more Smart Citations

Decomposition by tree dimension in Horn clause verification

Kafle

Gallagher

Ganty

2015

Electron. Proc. Theor. Comput. Sci.

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Combining Forward and Backward Abstract Interpretation of Horn Clauses

Bakhirkin

Monniaux

2017

Static Analysis

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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-ofthe-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. Queryanswer 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.

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