Extending VIAP to Handle Array Programs

Rajkhowa, Pritom; Lin, Fangzhen

doi:10.1007/978-3-030-03592-1_3

Cited by 11 publications

(33 citation statements)

References 15 publications

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“…We have compared our tool with Spacer (Z3 v4.8.3) [26], that implements a recent QUIC3 [22] algorithm, Booster (v0.2) [2], VIAP (v1.0) [35], and Veri-Abs (v1.3.10) [11]. The last two tools performed well in the ReachSafety Array subcategory at SVCOMP 2019 4 .…”

Section: Discussionmentioning

confidence: 99%

“…It may even be possible to get rid of such loops altogether, by accelerating (computing transitive closures of) transition relations involving array updates in that loop [7]. Along similar lines, VIAP [35] resorts to reasoning with recurrences instead of loops. It translates the input program, including loops, to a set of first-order axioms, and checks if they derive the property.…”

Section: Related Workmentioning

confidence: 99%

“…While a detailed discussion of the related work comes later in the paper (Sect. 6), it is noteworthy that being syntax-guided crucially helps us overcome several limitations of other techniques to verify array-handling programs [2,9,11,35]. Most of them avoid inferring quantified invariants explicitly and thus do not produce checkable proofs.…”

Section: Introductionmentioning

confidence: 99%

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Quantified Invariants via Syntax-Guided Synthesis

Fedyukovich

Prabhu

Madhukar

et al. 2019

Computer Aided Verification

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Programs with arrays are ubiquitous. Automated reasoning about arrays necessitates discovering properties about ranges of elements at certain program points. Such properties are formally specified by universally quantified formulas, which are difficult to find, and difficult to prove inductive. In this paper, we propose an algorithm based on an enumerative search that discovers quantified invariants in stages. First, by exploiting the program syntax, it identifies ranges of elements accessed in each loop. Second, it identifies potentially useful facts about individual elements and generalizes them to hypotheses about entire ranges. Finally, by applying recent advances of SMT solving, the algorithm filters out wrong hypotheses. The combination of properties is often enough to prove that the program meets a safety specification. The algorithm has been implemented in a solver for Constrained Horn Clauses, Freq-Horn, and extended to deal with multiple (possibly nested) loops. We show that FreqHorn advances state-of-the-art on a wide range of public array-handling programs.

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Section: Discussionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantified Invariants via Syntax-Guided Synthesis

Fedyukovich

Prabhu

Madhukar

et al. 2019

Computer Aided Verification

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“…However, it is often difficult to automatically infer such invariants, especially when programs have loops that are sequentially composed and/or nested within each other, and have complex control flows. This has spurred recent interest in mathematical induction-based techniques for verifying parametric properties of array manipulating programs [11,12,42,44]. While induction-based techniques are efficient and quite powerful, their Achilles heel is the automation of the inductive argument.…”

Section: Introductionmentioning

confidence: 99%

Diffy: Inductive Reasoning of Array Programs Using Difference Invariants

Chakraborty

Gupta

Unadkat

2021

Computer Aided Verification

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We present a novel verification technique to prove properties of a class of array programs with a symbolic parameter N denoting the size of arrays. The technique relies on constructing two slightly different versions of the same program. It infers difference relations between the corresponding variables at key control points of the joint control-flow graph of the two program versions. The desired post-condition is then proved by inducting on the program parameter N, wherein the difference invariants are crucially used in the inductive step. This contrasts with classical techniques that rely on finding potentially complex loop invaraints for each loop in the program. Our synergistic combination of inductive reasoning and finding simple difference invariants helps prove properties of programs that cannot be proved even by the winner of Arrays sub-category in SV-COMP 2021. We have implemented a prototype tool called Diffy to demonstrate these ideas. We present results comparing the performance of Diffy with that of state-of-the-art tools.

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“…Specifically, (i) we do not require explicit or implicit loop-specific invariants to be provided by the user or generated by a solver (viz. by constrained Horn clause solvers [20,14,9] or recurrence solvers [25,16]), (ii) we induct on the full program (possibly containing multiple loops) with parameter N and not on iterations of individual loops in the program, and (iii) we perform non-trivial correctby-construction code transformations, whenever feasible, to simplify the inductive step of reasoning. The combination of these factors often reduces reasoning about a program with multiple loops to reasoning about one with fewer (sometimes even none) and "simpler" loops, thereby simplifying proof goals.…”

Section: Introductionmentioning

confidence: 99%

Verifying Array Manipulating Programs with Full-Program Induction

Chakraborty

Gupta

Unadkat

2020

Tools and Algorithms for the Construction and Analysis of Systems

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We present a full-program induction technique for proving (a sub-class of) quantified as well as quantifier-free properties of programs manipulating arrays of parametric size N . Instead of inducting over individual loops, our technique inducts over the entire program (possibly containing multiple loops) directly via the program parameter N . Significantly, this does not require generation or use of loop-specific invariants. We have developed a prototype tool Vajra to assess the efficacy of our technique. We demonstrate the performance of Vajra vis-a-vis several state-of-the-art tools on a set of array manipulating benchmarks. // assume(true) 1. for (int t1=0; t1

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Extending VIAP to Handle Array Programs

Cited by 11 publications

References 15 publications

Quantified Invariants via Syntax-Guided Synthesis

Quantified Invariants via Syntax-Guided Synthesis

Diffy: Inductive Reasoning of Array Programs Using Difference Invariants

Verifying Array Manipulating Programs with Full-Program Induction

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