Satisfiability Modulo Transcendental Functions via Incremental Linearization

Cimatti, Alessandro; Griggio, Alberto; Irfan, Ahmed; Roveri, Marco; Sebastiani, Roberto

doi:10.1007/978-3-319-63046-5_7

Cited by 13 publications

(9 citation statements)

References 22 publications

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“…This article brings together and extends the ideas presented in the conference papers [19] (where the case of VMT(NRA) is discussed), and Reference [20] (where the SMT(NTA) case is discussed). The article differs from and extends References [19] and [20] in various directions. First, the article has been completely rewritten to cover in a systematic manner all the combinations of both SMT and VMT with both NRA and NTA, and present it in the light of incremental linearization.…”

Section: Introductionmentioning

confidence: 62%

“…First, the article has been completely rewritten to cover in a systematic manner all the combinations of both SMT and VMT with both NRA and NTA, and present it in the light of incremental linearization. Second, the case VMT(NTA) was not covered in References [19,20]. Third, the SMT approach is now based on a much tighter integration into SMT(UFLRA).…”

Section: Introductionmentioning

confidence: 99%

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Incremental Linearization for Satisfiability and Verification Modulo Nonlinear Arithmetic and Transcendental Functions

Cimatti

Griggio

Irfan

et al. 2018

ACM Trans. Comput. Logic

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Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a first-order formula with respect to some theory or combination of theories; Verification Modulo Theories (VMT) is the problem of analyzing the reachability for transition systems represented in terms of SMT formulae. In this article, we tackle the problems of SMT and VMT over the theories of nonlinear arithmetic over the reals (NRA) and of NRA augmented with transcendental (exponential and trigonometric) functions (NTA). We propose a new abstraction-refinement approach for SMT and VMT on NRA or NTA, called Incremental Linearization. The idea is to abstract nonlinear multiplication and transcendental functions as uninterpreted functions in an abstract space limited to linear arithmetic on the rationals with uninterpreted functions. The uninterpreted functions are incrementally axiomatized by means of upper-and lower-bounding piecewiselinear constraints. In the case of transcendental functions, particular care is required to ensure the soundness of the abstraction. The method has been implemented in the MathSAT SMT solver and in the nuXmv model checker. An extensive experimental evaluation on a wide set of benchmarks from verification and mathematics demonstrates the generality and the effectiveness of our approach. CCS Concepts: • Theory of computation → Automated reasoning; Constraint and logic programming; Verification by model checking; Logic and verification; • Mathematics of computing → Solvers;

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Section: Introductionmentioning

confidence: 62%

Section: Introductionmentioning

confidence: 99%

Incremental Linearization for Satisfiability and Verification Modulo Nonlinear Arithmetic and Transcendental Functions

Cimatti

Griggio

Irfan

et al. 2018

ACM Trans. Comput. Logic

Self Cite

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“…While some SMT solvers support quantifiers and trigonometric functions [8,9], our preliminary attempts showed they cannot directly prove eq. ( 2) for the circuit transformations generated by Quartz.…”

Section: Circuit Equivalence Verifiermentioning

confidence: 99%

Quartz: Superoptimization of Quantum Circuits (Extended Version)

Xu¹,

Li²,

Padon³

et al. 2022

Preprint

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Existing quantum compilers optimize quantum circuits by applying circuit transformations designed by experts. This approach requires significant manual effort to design and implement circuit transformations for different quantum devices, which use different gate sets, and can miss optimizations that are hard to find manually. We propose Quartz, a quantum circuit superoptimizer that automatically generates and verifies circuit transformations for arbitrary quantum gate sets. For a given gate set, Quartz generates candidate circuit transformations by systematically exploring small circuits and verifies the discovered transformations using an automated theorem prover. To optimize a quantum circuit, Quartz uses a cost-based backtracking search that applies the verified transformations to the circuit. Our evaluation on three popular gate sets shows that Quartz can effectively generate and verify transformations for different gate sets. The generated transformations cover manually designed transformations used by existing optimizers and also include new transformations. Quartz is therefore able to optimize a broad range of circuits for diverse gate sets, outperforming or matching the performance of hand-tuned circuit optimizers.

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“…Implementation-Our implementation of IC3PO is publicly available at https://github.com/aman-goel/ic3po. The implementation accepts protocol descriptions in the Ivy language [63] and uses the Ivy compiler to extract a quantified, logical formulation P in a customized VMT [21] format. We use a modified version [4] of the pySMT [33] library to implement our prototype, and use the Z3 [23] solver for all SMT queries.…”

Section: Ic3po: Ic3 For Proving Protocol Propertiesmentioning

confidence: 99%

On Symmetry and Quantification: A New Approach to Verify Distributed Protocols

Goel

Sakallah

2021

Lecture Notes in Computer Science

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Proving that an unbounded distributed protocol satisfies a given safety property amounts to finding a quantified inductive invariant that implies the property for all possible instance sizes of the protocol. Existing methods for solving this problem can be described as search procedures for an invariant whose quantification prefix fits a particular template. We propose an alternative constructive approach that does not prescribe, a priori, a specific quantifier prefix. Instead, the required prefix is automatically inferred without any search by carefully analyzing the structural symmetries of the protocol. The key insight underlying this approach is that symmetry and quantification are closely related concepts that express protocol invariance under different re-arrangements of its components. We propose symmetric incremental induction, an extension of the finite-domain IC3/PDR algorithm, that automatically derives the required quantified inductive invariant by exploiting the connection between symmetry and quantification. While various attempts have been made to exploit symmetry in verification applications, to our knowledge, this is the first demonstration of a direct link between symmetry and quantification in the context of clause learning during incremental induction. We also describe a procedure to automatically find a minimal finite size, the cutoff, that yields a quantified invariant proving safety for any size.Our approach is implemented in IC3PO, a new verifier for distributed protocols that significantly outperforms the state-of-the-art, scales orders of magnitude faster, and robustly derives compact inductive invariants fully automatically.

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Satisfiability Modulo Transcendental Functions via Incremental Linearization

Cited by 13 publications

References 22 publications

Incremental Linearization for Satisfiability and Verification Modulo Nonlinear Arithmetic and Transcendental Functions

Incremental Linearization for Satisfiability and Verification Modulo Nonlinear Arithmetic and Transcendental Functions

Quartz: Superoptimization of Quantum Circuits (Extended Version)

On Symmetry and Quantification: A New Approach to Verify Distributed Protocols

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