K-induction without unrolling

Gurfinkel, Arie; Ivrii, Alexander

doi:10.23919/fmcad.2017.8102253

Cited by 13 publications

(17 citation statements)

References 8 publications

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“…The closest related work is KIC3 [16]. It modifies the counter example queue management strategy in IC3 to utilize k-induction during blocking.…”

Section: Related Work Kavy Builds On Top Of the Ideas Of Ic3mentioning

confidence: 99%

“…Notwithstanding all of its advantages, strong induction has been mostly displaced by more recent SMC techniques such as Interpolation [25], Property Directed Reachability [3,7,13,15], and their combinations [29]. In SMC kinduction is equivalent to induction: any k-inductive property P can be strengthened to an inductive property Q [6,16]. Even though in the worst case Q is exponentially larger than P [6], this is rarely observed in practice [26].…”

Section: Introductionmentioning

confidence: 99%

“…Even though in the worst case Q is exponentially larger than P [6], this is rarely observed in practice [26]. Furthermore, the SAT queries get very hard as k increases and usually succeed only for rather small values of k. A recent work [16] shows that strong induction can be integrated in Pdr. However, [16] argues that k-induction is hard to control in the context of Pdr since choosing a proper value of k is difficult.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, the SAT queries get very hard as k increases and usually succeed only for rather small values of k. A recent work [16] shows that strong induction can be integrated in Pdr. However, [16] argues that k-induction is hard to control in the context of Pdr since choosing a proper value of k is difficult. A wrong choice leads to a form of state enumeration.…”

Section: Introductionmentioning

confidence: 99%

“…A wrong choice leads to a form of state enumeration. In [16], k is fixed to 5, and regular induction is used as soon as 5-induction fails.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Interpolating Strong Induction

Krishnan

Vizel

Gurfinkel

2019

Computer Aided Verification

Self Cite

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The principle of strong induction, also known as k-induction is one of the first techniques for unbounded SAT-based Model Checking (SMC). While elegant and simple to apply, properties as such are rarely k-inductive and when they can be strengthened, there is no effective strategy to guess the depth of induction. It has been mostly displaced by techniques that compute inductive strengthenings based on interpolation and property directed reachability (Pdr). In this paper, we present kAvy, an SMC algorithm that effectively uses k-induction to guide interpolation and Pdr-style inductive generalization. Unlike pure k-induction, kAvy uses Pdr-style generalization to compute and strengthen an inductive trace. Unlike pure Pdr, kAvy uses relative k-induction to construct an inductive invariant. The depth of induction is adjusted dynamically by minimizing a proof of unsatisfiability. We have implemented kAvy within the Avy Model Checker and evaluated it on HWMCC instances. Our results show that kAvy is more effective than both Avy and Pdr, and that using k-induction leads to faster running time and solving more instances. Further, on a class of benchmarks, called shift, kAvy is orders of magnitude faster than Avy, Pdr and k-induction.

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“…The closest related work is KIC3 [16]. It modifies the counter example queue management strategy in IC3 to utilize k-induction during blocking.…”

Section: Related Work Kavy Builds On Top Of the Ideas Of Ic3mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…A wrong choice leads to a form of state enumeration. In [16], k is fixed to 5, and regular induction is used as soon as 5-induction fails.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Interpolating Strong Induction

Krishnan

Vizel

Gurfinkel

2019

Computer Aided Verification

Self Cite

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A Cooperative Parallelization Approach for Property-Directed k-Induction

Blicha

Hyvärinen

Marescotti

et al. 2020

Lecture Notes in Computer Science

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Non-well-founded Deduction for Induction and Coinduction

Cohen

2021

Automated Deduction – CADE 28

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Induction and coinduction are both used extensively within mathematics and computer science. Algebraic formulations of these principles make the duality between them apparent, but do not account well for the way they are commonly used in deduction. Generally, the formalization of these reasoning methods employs inference rules that express a general explicit (co)induction scheme. Non-well-founded proof theory provides an alternative, more robust approach for formalizing implicit (co)inductive reasoning. This approach has been extremely successful in recent years in supporting implicit inductive reasoning, but is not as well-developed in the context of coinductive reasoning. This paper reviews the general method of non-well-founded proofs, and puts forward a concrete natural framework for (co)inductive reasoning, based on (co)closure operators, that offers a concise framework in which inductive and coinductive reasoning are captured as we intuitively understand and use them. Through this framework we demonstrate the enormous potential of non-well-founded deduction, both in the foundational theoretical exploration of (co)inductive reasoning and in the provision of proof support for (co)inductive reasoning within (semi-)automated proof tools.

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K-induction without unrolling

Cited by 13 publications

References 8 publications

Interpolating Strong Induction

Interpolating Strong Induction

A Cooperative Parallelization Approach for Property-Directed k-Induction

Non-well-founded Deduction for Induction and Coinduction

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