A Gröbner Basis Approach to CNF-Formulae Preprocessing

Condrat, Christopher; Kalla, Priyank

doi:10.1007/978-3-540-71209-1_48

Cited by 13 publications

(6 citation statements)

References 29 publications

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“…This CNF-to-ANF conversion is trivial, unlike that in [24]; sophisticated techniques are then applied to simplify the problem on the ANF level. In this use-case, converting problem from CNF to ANF and back to CNF give a suboptimal description of the original problem.…”

Section: Cnf To Anf Conversionmentioning

confidence: 99%

Bosphorus: Bridging ANF and CNF Solvers

Choo

Soos

Meel

2019

2019 Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE)

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Algebraic Normal Form (ANF) and Conjunctive Normal Form (CNF) are commonly used to encode problems in Boolean algebra. ANFs are typically solved via Gröbner basis algorithms, often using more memory than is feasible; while CNFs are solved using SAT solvers, which cannot exploit the algebra of polynomials naturally. We propose a paradigm that bridges between ANF and CNF solving techniques: the techniques are applied in an iterative manner to learn facts to augment the original problems. Experiments on over 1,100 benchmarks arising from four different applications domains demonstrate that learnt facts can significantly improve runtime and enable more benchmarks to be solved.

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Section: Cnf To Anf Conversionmentioning

confidence: 99%

Bosphorus: Bridging ANF and CNF Solvers

Choo

Soos

Meel

2019

2019 Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE)

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“…However, the root of 1 − x remains the same. In other approaches, for example in [19], such equivalences are used to translate propositional logic into computer algebra.…”

Section: Combining Subproblems In a Single Ringmentioning

confidence: 99%

Proof logging for computer algebra based SMT solving

Marx

Wedler

Stoffel

et al. 2013

2013 IEEE/ACM International Conference on Computer-Aided Design (ICCAD)

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In formal verification, proof logging is a technique for automatically reviewing the reasoning steps of a proof engine by a separate tool. This is useful for enhancing the confidence in the prover's result, especially in the case of a positive answer when no counterexample exists. Mature proof logging techniques exist for single-theory provers. SMT solvers, however, combine several theories so that developing an unified proof logging technique is more challenging. This paper proposes an approach for logging the proofs of the SMT solver STABLE which is a prover combining SAT and computer algebra engines. We show how to translate the SAT proofs into algebraic forms (polynomials) and how to check the combined Boolean and word-level proofs using a separate computer algebra engine

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“…This is the area, where still much research needs to be done, in a much wider scope: touching both the field of computational algebra as well as the very optimized toolset of SAT-solvers. An initial (quite theoretical) publication on these aspects is [23,25]. We do not have a special selection strategy for the bits at the moment.…”

Section: Guessing Of Key Bitsmentioning

confidence: 99%

Obtaining and Solving Systems of Equations in Key Variables Only for the Small Variants of AES

Bulygin

Brickenstein

2010

Math.Comput.Sci.

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This work is devoted to attacking the small scale variants of the Advanced Encryption Standard (AES) via systems that contain only the initial key variables. To this end, we investigate a system of equations that naturally arises in the AES, and then introduce an elimination of all the intermediate variables via normal form reductions. The resulting system in key variables only is solved then. We also consider a possibility to apply our method in the meet-in-the-middle scenario especially with several plaintext/ciphertext pairs. We elaborate on the method further by looking for subsystems which contain fewer variables and are overdetermined, thus facilitating solving the large system.

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A Gröbner Basis Approach to CNF-Formulae Preprocessing

Cited by 13 publications

References 29 publications

Bosphorus: Bridging ANF and CNF Solvers

Bosphorus: Bridging ANF and CNF Solvers

Proof logging for computer algebra based SMT solving

Obtaining and Solving Systems of Equations in Key Variables Only for the Small Variants of AES

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