Selfless Interpolation for Infinite-State Model Checking

Schindler, Tanja; Jovanović, Dejan

doi:10.1007/978-3-319-73721-8_23

Cited by 7 publications

(16 citation statements)

References 35 publications

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“…However, those interpolants are still restricted to single inequalities. The work most closely related to ours is [36] where the authors independently recognized the weakness of interpolation based on Farkas coefficients. They introduce a new interpolation procedure that gives guarantees of convergence of a special sequence of interpolation problems often occurring in model checking problems.…”

Section: Introductionmentioning

confidence: 87%

“…We used the same benchmarks as in [36]. They consist of several problem sets related to fault-tolerant algorithms (om, ttesynchro, ttastartup, unifapprox, azadmanesh, approxagree, hacms, misc), benchmarks from software model checking (cav12, ctigar), benchmark suite of kind model checker (lustre), simple concurrent programs (conc), and problems modeling a lock-free hash table (lfht).…”

Section: Methodsmentioning

confidence: 99%

“…We call the resulting interpolant the Farkas interpolant. While a single inequality is desirable in some cases, it prevents IC3-style algorithms from converging in other ones [36]. We present how methods from linear algebra can be applied on a Farkas interpolant to obtain decomposed interpolants that do not consist of a single inequality and guarantee the convergence of the model-checking algorithm for some of the cases where Farkas interpolants do not converge.…”

Section: Introductionmentioning

confidence: 99%

“…They introduce a new interpolation procedure that gives guarantees of convergence of a special sequence of interpolation problems often occurring in model checking problems. However, this interpolation algorithm is based on a different decision procedure, called conflict resolution [26], which, based on the results reported in [36], is not as efficient as the Simplex-based decision procedure. In contrast, we show how the original approach based on the Simplex-based decision procedure and Farkas coefficients can be modified to produce interpolants not restricted to the single-inequality form, while additionally obtaining strength guarantees with respect to the original Farkas interpolants.…”

Section: Introductionmentioning

confidence: 99%

“…The reason for producing such a series is that both tools rely on Farkas interpolants that always consist of a single inequality. Instead of generalizing the Farkas interpolants, an approach advocated in this work, interpolation based on a different decision procedure was proposed for sally in [36], whereas SeaHorn [18] with Spacer as its underlying reasoning engine solves this issue with abstract interpretation.…”

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confidence: 99%

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Decomposing Farkas Interpolants

Blicha

Hyvärinen

Kofroň

et al. 2019

Tools and Algorithms for the Construction and Analysis of Systems

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Modern verification commonly models software with Boolean logic and a system of linear inequalities over reals and overapproximates the reachable states of the model with Craig interpolation to obtain, for example, candidates for inductive invariants. Interpolants for the linear system can be efficiently constructed from a Simplex refutation by applying the Farkas' lemma. However, Farkas interpolants do not always suit the verification task and in the worst case they may even be the cause of divergence of the verification algorithm. This work introduces the decomposed interpolants, a fundamental extension of the Farkas interpolants obtained by identifying and separating independent components from the interpolant structure using methods from linear algebra. We integrate our approach to the model checker Sally and show experimentally that a portfolio of decomposed interpolants results in immediate convergence on instances where state-of-the-art approaches diverge. Being based on the efficient Simplex method, the approach is very competitive also outside these diverging cases.

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Section: Introductionmentioning

confidence: 87%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Decomposing Farkas Interpolants

Blicha

Hyvärinen

Kofroň

et al. 2019

Tools and Algorithms for the Construction and Analysis of Systems

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Global Guidance for Local Generalization in Model Checking

Krishnan

Chen

Shoham

et al. 2020

Computer Aided Verification

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SMT-based model checkers, especially IC3-style ones, are currently the most effective techniques for verification of infinite state systems. They infer global inductive invariants via local reasoning about a single step of the transition relation of a system, while employing SMTbased procedures, such as interpolation, to mitigate the limitations of local reasoning and allow for better generalization. Unfortunately, these mitigations intertwine model checking with heuristics of the underlying SMT-solver, negatively affecting stability of model checking. In this paper, we propose to tackle the limitations of locality in a systematic manner. We introduce explicit global guidance into the local reasoning performed by IC3-style algorithms. To this end, we extend the SMT-IC3 paradigm with three novel rules, designed to mitigate fundamental sources of failure that stem from locality. We instantiate these rules for the theory of Linear Integer Arithmetic and implement them on top of Spacer solver in Z3. Our empirical results show that GSpacer, Spacer extended with global guidance, is significantly more effective than both Spacer and sole global reasoning, and, furthermore, is insensitive to interpolation.

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Interpolation and Model Checking for Nonlinear Arithmetic

Jovanović

Dutertre

2021

Lecture Notes in Computer Science

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We present a new model-based interpolation procedure for satisfiability modulo theories (SMT). The procedure uses a new mode of interaction with the SMT solver that we call solving modulo a model. This either extends a given partial model into a full model for a set of assertions or returns an explanation (a model interpolant) when no solution exists. This mode of interaction fits well into the model-constructing satisfiability (MCSAT) framework of SMT. We use it to develop an interpolation procedure for any MCSAT-supported theory. In particular, this method leads to an effective interpolation procedure for nonlinear real arithmetic. We evaluate the new procedure by integrating it into a model checker and comparing it with state-of-art model-checking tools for nonlinear arithmetic.

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Selfless Interpolation for Infinite-State Model Checking

Cited by 7 publications

References 35 publications

Decomposing Farkas Interpolants

Decomposing Farkas Interpolants

Global Guidance for Local Generalization in Model Checking

Interpolation and Model Checking for Nonlinear Arithmetic

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