Fast Machine Words in Isabelle/HOL

Lochbihler, Andreas

doi:10.1007/978-3-319-94821-8_23

Cited by 6 publications

(5 citation statements)

References 40 publications

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“…The big difference is due to the use of machine-integers supporting atomic bitwise-or for finding set unions (and that operation is heavily trough out the whole formalization). Therefore, the proof checking time could be significantly reduced if machine-integers were also used in Isabelle/ML (a support for this has been added to Isabelle recently [12]).…”

Section: Resultsmentioning

confidence: 99%

Fully Automatic, Verified Classification of all Frankl-Complete (FC(6)) Set Families

Marić,

Vučković,

Živković

2019

Preprint

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The Frankl's conjecture, formulated in 1979. and still open, states that in every family of sets closed for unions there is an element contained in at least half of the sets. A family F c is called Frankl-complete (or FC-family) if in every union-closed family F ⊇ F c , one of the elements of F c occurs in at least half of the elements of F (so F satisfies the Frankl's condition). FC-families play an important role in attacking the Frankl's conjecture, since they enable significant search space pruning. We extend previous work by giving a total characterization of all FC-families over a 6-element universe, by defining and enumerating all minimal FC and maximal nonFC-families. We use a fully automated, computer assisted approach, formally verified within the proof-assistant Isabelle/HOL.

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Section: Resultsmentioning

confidence: 99%

Fully Automatic, Verified Classification of all Frankl-Complete (FC(6)) Set Families

Marić,

Vučković,

Živković

2019

Preprint

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“…The implementations using uint32 and uint64 have the advantage that generated code will be more efficient as they can be mapped to machine integers [24]. It should be taken into account that they work only for sufficiently small primes, so that no overflows occur in multiplications: e.g., 65535 • 65535 < 2 32 .…”

Section: Lemma 8 Assumes P = Card(α)mentioning

confidence: 99%

“…It should be taken into account that they work only for sufficiently small primes, so that no overflows occur in multiplications: e.g., 65535 • 65535 < 2 32 . The corresponding soundness statements look as follows, and are proven in a straightforward manner using the native words library [24]. To obtain an implementation of GCD for polynomials over GF( p), we need further work: instantiating τ by α GFp poly.…”

Section: Lemma 8 Assumes P = Card(α)mentioning

confidence: 99%

“…At some points in our development, however, the type-based setting becomes too restrictive. Hence we also introduce the second integer representation, which explicitly applies the remainder operation modulo m. For efficient implementation we also introduce the third representation, which allows us to employ machine integers [24] for reasonably small m.…”

Section: Introductionmentioning

confidence: 99%

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A Verified Implementation of the Berlekamp–Zassenhaus Factorization Algorithm

et al. 2019

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We formally verify the Berlekamp-Zassenhaus algorithm for factoring square-free integer polynomials in Isabelle/HOL. We further adapt an existing formalization of Yun's squarefree factorization algorithm to integer polynomials, and thus provide an efficient and certified factorization algorithm for arbitrary univariate polynomials. The algorithm first performs factorization in the prime field GF(p) and then performs computations in the ring of integers modulo p k , where both p and k are determined at runtime. Since a natural modeling of these structures via dependent types is not possible in Isabelle/HOL, we formalize the whole algorithm using locales and local type definitions. Through experiments we verify that our algorithm factors polynomials of degree up to 500 within seconds.

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“…In Isabelle and HOL4, one can use the bit-vector libraries to conform SMT-LIB operations, see [17] for example. Under the frame of Coq, coq-bits is a formalization of logical and arithmetic operations on bit-vectors [15].…”

Section: Introductionmentioning

confidence: 99%

CoqQFBV: A Scalable Certified SMT Quantifier-Free Bit-Vector Solver

Shi

Liu

et al. 2021

Computer Aided Verification

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We present a certified SMT QF_BV solver CoqQFBV built from a verified bit blasting algorithm, Kissat, and the verified SAT certificate checker GratChk in this paper. Our verified bit blasting algorithm supports the full QF_BV logic of SMT-LIB; it is specified and formally verified in the proof assistant Coq . We compare CoqQFBV with CVC4, Bitwuzla, and Boolector on benchmarks from the QF_BV division of the single query track in the 2020 SMT Competition, and real-world cryptographic program verification problems. CoqQFBV surprisingly solves more program verification problems with certification than the 2020 SMT QF_BV division winner Bitwuzla without certification.

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Fast Machine Words in Isabelle/HOL

Cited by 6 publications

References 40 publications

Fully Automatic, Verified Classification of all Frankl-Complete (FC(6)) Set Families

Fully Automatic, Verified Classification of all Frankl-Complete (FC(6)) Set Families

A Verified Implementation of the Berlekamp–Zassenhaus Factorization Algorithm

CoqQFBV: A Scalable Certified SMT Quantifier-Free Bit-Vector Solver

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