Intertwined Forward-Backward Reachability Analysis Using Interpolants

Vizel, Yakir; Grumberg, Orna; Shoham, Sharon

doi:10.1007/978-3-642-36742-7_22

Cited by 17 publications

(8 citation statements)

References 14 publications

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“…The use of interpolation and generalization from bounded unreachability has been used in many works since [e.g. Henzinger et al 2004;Jhala and McMillan 2007;McMillan 2006;Vizel and Grumberg 2009;Vizel et al 2013]. Combining ideas from interpolation and PDR has also been studied [e.g.…”

Section: Invariant Inference Algorithmsmentioning

confidence: 99%

Complexity and information in invariant inference

Feldman

Immerman

Sagiv

et al. 2019

Proc. ACM Program. Lang.

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This paper addresses the complexity of SAT-based invariant inference, a prominent approach to safety verification. We consider the problem of inferring an inductive invariant of polynomial length given a transition system and a safety property. We analyze the complexity of this problem in a black-box model, called the Hoare-query model, which is general enough to capture algorithms such as IC3/PDR and its variants. An algorithm in this model learns about the system's reachable states by querying the validity of Hoare triples.We show that in general an algorithm in the Hoare-query model requires an exponential number of queries. Our lower bound is information-theoretic and applies even to computationally unrestricted algorithms, showing that no choice of generalization from the partial information obtained in a polynomial number of Hoare queries can lead to an efficient invariant inference procedure in this class.We then show, for the first time, that by utilizing rich Hoare queries, as done in PDR, inference can be exponentially more efficient than approaches such as ICE learning, which only utilize inductiveness checks of candidates. We do so by constructing a class of transition systems for which a simple version of PDR with a single frame infers invariants in a polynomial number of queries, whereas every algorithm using only inductiveness checks and counterexamples requires an exponential number of queries.Our results also shed light on connections and differences with the classical theory of exact concept learning with queries, and imply that learning from counterexamples to induction is harder than classical exact learning from labeled examples. This demonstrates that the convergence rate of Counterexample-Guided Inductive Synthesis depends on the form of counterexamples.

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Section: Invariant Inference Algorithmsmentioning

confidence: 99%

Complexity and information in invariant inference

Feldman

Immerman

Sagiv

et al. 2019

Proc. ACM Program. Lang.

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“…Other papers also introduced multiple state sequences. The approach of "Dual Approximated Reachability" maintains two over-approximate state sequences to check safety in both forward and backward directions [13]. In contrast, we maintain two complementary (over-and under-) approximate state sequences to check safety and unsafety at the same time.…”

Section: Related Workmentioning

confidence: 99%

Safety model checking with complementary approximations

Zhu

Zhang

et al. 2017

2017 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)

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Abstract-Formal-verification techniques, such as model checking, are becoming popular in hardware design. SAT-based model checking techniques, such as IC3/PDR, have gained a significant success in the hardware industry. In this paper, we present a new framework for SAT-based safety model checking, named Complementary Approximate Reachability (CAR). CAR is based on standard reachability analysis, but instead of maintaining a single sequence of reachable-state sets, CAR maintains two sequences of over-and under-approximate reachable-state sets, checking safety and unsafety at the same time. To construct the two sequences, CAR uses standard Boolean-reasoning algorithms, based on satisfiability solving, one to find a satisfying cube of a satisfiable Boolean formula, and one to provide a minimal unsatisfiable core of an unsatisfiable Boolean formula. We applied CAR to 548 hardware model-checking instances, and compared its performance with IC3/PDR. Our results show that CAR is able to solve 42 instances that cannot be solved by IC3/PDR. When evaluated against a portfolio that includes IC3/PDR and other approaches, CAR is able to solve 21 instances that the other approaches cannot solve. We conclude that CAR should be considered as a valuable member of any algorithmic portfolio for safety model checking.

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“…As stated above, Avy is a synergy between an interpolation-based approach and Pdr. Ideas for combining the two have also appeared in [16,17]. In [16], the authors suggest to use both forward and backward reachable sets of states.…”

Section: Introductionmentioning

confidence: 99%

“…Ideas for combining the two have also appeared in [16,17]. In [16], the authors suggest to use both forward and backward reachable sets of states. This allows them to try and block a set of all bad states in a local manner that resembles the blocking of a bad state applied by Pdr.…”

Section: Introductionmentioning

confidence: 99%

Interpolating Property Directed Reachability

Vizel

Gurfinkel

2014

Computer Aided Verification

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Current SAT-based Model Checking is based on two major approaches: Interpolation-based (Imc) (global, with unrollings) and Property Directed Reachability/IC3 (Pdr) (local, without unrollings). Imc generates candidate invariants using interpolation over an unrolling of a system, without putting any restrictions on the SAT-solver's search. Pdr generates candidate invariants by a local search over a single instantiation of the transition relation, effectively guiding the SAT solver's search. The two techniques are considered to be orthogonal and have different strength and limitations. In this paper, we present a new technique, called Avy, that effectively combines the key insights of the two approaches. Like Imc, it uses unrollings and interpolants to construct an initial candidate invariant, and, like Pdr, it uses local inductive generalization to keep the invariants in compact clausal form. On the one hand, Avy is an incremental Imc extended with a local search for CNF interpolants. On the other, it is Pdr extended with a global search for bounded counterexamples. We implemented the technique using ABC and have evaluated it on the HWMCC benchmark-suite from 2012 and 2013. Our results show that the prototype significantly outperforms Pdr and McMillan's interpolation algorithm (as implemented in ABC) on the industrial sub-category of the benchmark.

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Intertwined Forward-Backward Reachability Analysis Using Interpolants

Cited by 17 publications

References 14 publications

Complexity and information in invariant inference

Complexity and information in invariant inference

Safety model checking with complementary approximations

Interpolating Property Directed Reachability

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