A Hybrid of Counterexample-Based and Proof-Based Abstraction

Amla, Nina; McMillan, Kenneth L.

doi:10.1007/978-3-540-30494-4_19

Cited by 26 publications

(28 citation statements)

References 10 publications

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“…A number of methods for construction of localization abstractions have been proposed. Following [13], SATbased abstraction methods can be classified into proof-based [1], [2] (those that use unsatisfiable cores to remove logic unnecessary to the proof), counterexample-based [14] (that build abstractions by adding logic to refute counterexamples), and hybrid counterexample-and proof-based [15], [9] (that alternate proof-based and counterexample-based stages). Note that in counterexample-based abstraction (CBA) the abstraction is built ground-up, starting from an empty set of gates, while PBA works in the opposite way -it starts from the full design, and removes logic, resulting in successively smaller abstractions.…”

Section: A Abstractionmentioning

confidence: 99%

Core Minimization in SAT-based Abstraction

Belov¹,

Chen²,

Mishchenko³

et al. 2013

Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE), 2013

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Abstract-Automatic abstraction is an important component of modern formal verification flows. A number of effective SATbased automatic abstraction methods use unsatisfiable cores to guide the construction of abstractions. In this paper we analyze the impact of unsatisfiable core minimization, using state-ofthe-art algorithms for the computation of minimally unsatisfiable subformulas (MUSes), on the effectiveness of a hybrid (counterexample-based and proof-based) abstraction engine. We demonstrate empirically that core minimization can lead to a significant reduction in the total verification time, particularly on difficult testcases. However, the resulting abstractions are not necessarily smaller. We notice that by varying the minimization effort the abstraction size can be controlled in a non-trivial manner. Based on this observation, we achieve a further reduction in the total verification time.

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Section: A Abstractionmentioning

confidence: 99%

Core Minimization in SAT-based Abstraction

Belov¹,

Chen²,

Mishchenko³

et al. 2013

Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE), 2013

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show abstract

“…The chosen abstraction can be based on different computation methods; SAT-based techniques have largely replaced BDD-based and other methods. In SAT-based methods, abstraction refinement can rely on computing a sequence of UNSAT cores [16] or counterexamples [17] or by applying a hybrid approach, which utilizes both proofs and counterexamples [1] [10]. Finally, in terms of the granularity, abstraction can be flop-level [17] [10] or gatelevel [3], depending on whether it is constructed using entire next-state logic cones or single gates as primitives.…”

Section: Introductionmentioning

confidence: 99%

GLA: Gate-Level Abstraction Revisited

Mishchenko¹,

Eén²,

Brayton³

et al. 2013

Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE), 2013

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Verification benefits from removing logic that is not relevant for a proof. Techniques for doing this are known as localization abstraction. Abstraction is often performed by selecting a subset of gates to be included in the abstracted model; the signals feeding into this subset become unconstrained cut-points. In this paper, we propose several improvements to substantially increase the scalability of automated abstraction. In particular, we show how a better integration between the BMC engine and the SAT solver is achieved, resulting in a new hybrid abstraction engine, that is faster and uses less memory. This engine speeds up computation by constant propagation and circuit-based structural hashing while collecting UNSAT cores for the intermediate proofs in terms of a subset of the original variables. Experimental results show improvements in the abstraction depth and size.

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“…As a by-product of this research, we are also translating AIGER benchmarks into first-order TPTP benchmarks which can be used to evaluate first-order theorem provers on hardware verification problems. As a future work we are planning to compare and combine our approach with other property directed methods such as PDR/IC3 [19] and interpolation [18,22,29].…”

Section: Resultsmentioning

confidence: 99%

“…For induction, in addition to the speedup, this can decrease the unrolling depths required to achieve full proofs. In the context of SAT-based BMC, interpolation [18] and PDR [19], at the bit-level, some of the ideas in this paper are similar to the counter-example and proof-based abstraction refinement procedures in [20,17,21,22,23,24], although our algorithm differs significantly from these approaches in technical detail. In abstraction-refinement for SAT-BMC, the abstract model is usually fully unrolled to a current bound k. In our approach each part of the transition relation can be added/removed separately at non-consecutive bounds, guided by the abstraction-refinement process.…”

Section: Introductionmentioning

confidence: 99%

EPR-based k-induction with Counterexample Guided Abstraction Refinement

Khasidashvili¹,

Korovin²,

Tsarkov³

EPiC Series in Computing

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In recent years it was proposed to encode bounded model checking (BMC) into the effectively propositional fragment of first-order logic (EPR). The EPR fragment can provide for a succinct representation of the problem and facilitate reasoning at a higher level. In this paper we present an extension of the EPR-based bounded model checking with k-induction which can be used to prove safety properties of systems over unbounded runs. We present a novel abstraction-refinement approach based on unsatisfiable cores and models (UCM) for BMC and k-induction in the EPR setting. We have implemented UCM refinements for EPR-based BMC and k-induction in a first-order automated theorem prover iProver. We also extended iProver with the AIGER format and evaluated it over the HWMCC'14 competition benchmarks. The experimental results are encouraging. We show that a number of AIG problems can be verified until deeper bounds with the EPR-based model checking.

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A Hybrid of Counterexample-Based and Proof-Based Abstraction

Cited by 26 publications

References 10 publications

Core Minimization in SAT-based Abstraction

Core Minimization in SAT-based Abstraction

GLA: Gate-Level Abstraction Revisited

EPR-based k-induction with Counterexample Guided Abstraction Refinement

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