A More Pragmatic CDCL for IsaSAT and Targetting LLVM

IsaSAT is the most advanced verified SAT solver, but it did not yet feature inprocessing (to simplify and strengthen clauses). In order to improve performance, we enriched the base calculus to not only do CDCL but also inprocess clauses. We also replaced the target of our code synthesis by Isabelle/LLVM. With these improvements, we can solve 4 times more SAT Competition 2022 problems than the original IsaSAT version, and 4.5 times more problems than any other verified SAT solver we are aware of. Additionally, our changes significantly reduce the trusted code base of our verification

Faster LRAT Checking Than Solving with CaDiCaL

DRAT is the standard proof format used in the SAT Competition. It is easy to generate but checking proofs often takes even more time than solving the problem. An alternative is to use the LRAT proof system. While LRAT is easier and way more efficient to check, it is more complex to generate directly. Due to this complexity LRAT is not supported natively by any state-of-the-art SAT solver. Therefore Carneiro and Heule proposed the mixed proof format FRAT which still suffers from costly intermediate translation. We present an extension to the state-of-the-art solver CaDiCaL which is able to generate LRAT natively for all procedures implemented in CaDiCaL. We further present Lrat-Trim, a tool which not only trims and checks LRAT proofs in both ASCII and binary format but also produces clausal cores and has been tested thoroughly. Our experiments on recent competition benchmarks show that our approach reduces time of proof generation and certification substantially compared to competing approaches using intermediate DRAT or FRAT proofs

Alethe: Towards a Generic SMT Proof Format (extended abstract)

The first iteration of the proof format used by the SMT solver veriT was presented ten years ago at the first PxTP workshop. Since then the format has matured. veriT proofs are used within multiple applications, and other solvers generate proofs in the same format. We would now like to gather feedback from the community to guide future developments. Towards this, we review the history of the format, present our pragmatic approach to develop the format, and also discuss problems that might arise when other solvers use the format.Comment: In Proceedings PxTP 2021, arXiv:2107.0154

Passive microrheology as a useful tool for milk gel analyses

Passive microrheology based on Diffusing Wave Spectroscopy (DWS) [1,2] is presented as a straightforward tool for the analysis of milk gel preparation. Diffusing Wave Spectroscopy consists of analysing the interferential images of light, which is backscattered by the sample. This so called speckles images, which are detected by a CCD camera, change in time due to the Brownian motion of the particles that scatter the light. The variation of the images as a function of time can be directly correlated to the viscoelastic properties of the sample. As it is an optical method, it is perfectly adapted to study the weak gels of milk products. Nowadays, milk gels such as yogurts or chees have attracted lots of interest due to its growing market. The milk properties, such as pH, calcium content and protein content are very important and change significantly the cheese properties. This work shows how passive microrheology can be used to follow up the milk gel formation with exact gel time determination. Gel time was determined by a new rescaling method, namely Time-Cure Superposition (TCS) [3,4]. This data processing determines the gel point according to the Winter-Chambon criterion [5]. Moreover, the viscoelastic properties of the preparation can be compared according to parameters, such as the protein enrichment, calcium ion addition or others. Results were compared to other instruments (texturometers, rheometer, Optigraph®, etc.). References: [1] D. A. Weitz et al., in Dynamic Light Scattering, W. Brown (Ed.) (Oxford Univ. Press, New York (1993), Chap. 16. [2] D. J. Pine et al., Phys. Rev. Lett. 1988, 60, 1434. [3] T. H. Larsen, E. M. Furst, Phys. Rev. Letters, 2008, 100, 14600 [4] K. M. Schultz, E. M. Furst, Soft Matter, 2012, 8, 6198 [5] H. H. Winter, F. Chambon, J. Rheology 1986, 30, 364-38

Better SMT Proofs for Easier Reconstruction

International audienceProof assistants are used in verification, formal mathematics, and other areas to provide trustworthy , machine-checkable formal proofs of theorems. Proof automation reduces the burden of proof on users, thereby allowing them to focus on the core of their arguments. A successful approach to automation is to invoke an external automatic theorem prover, such as a satisfiability-modulo-theories (SMT) solver, reconstructing any generated proofs using the proof assistant's inference kernel. The success rate of reconstruction, and hence the usefulness of this approach, depends on the quality of the generated proofs. We report on the experience gained by working on reconstruction of proofs generated by an SMT solver while also improving the solver's output

A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality (Extended Abstract)

International audienceWe developed a formal framework for CDCL (conflict-driven clause learning) in Isabelle/HOL. Through a chain of refinements, an abstract CDCL calculus is connected to a SAT solver expressed in a functional programming language, with total correctness guarantees. The framework offers a convenient way to prove metatheorems and experiment with variants. Compared with earlier SAT solver verifications, the main novelties are the inclusion of rules for forget, restart, and incremental solving and the application of refinement

Reliable Reconstruction of Fine-Grained Proofs in a Proof Assistant

International audienceWe present a fast and reliable reconstruction of proofs generated by the SMT solver veriT in Isabelle. The fine-grained proof format makes the reconstruction simple and efficient. For typical proof steps, such as arithmetic reasoning and skolemization, our reconstruction can avoid expensive search. By skipping proof steps that are irrelevant for Isabelle, the performance of proof checking is improved. Our method increases the success rate of Sledgehammer by halving the failure rate and reduces the checking time by 13%. We provide a detailed evaluation of the reconstruction time for each rule. It reveals that the runtime is influenced by both simple rules that appear very often and common complex rules

Reliable Reconstruction of Fine-Grained Proofs in a Proof Assistant

International audienceWe present a fast and reliable reconstruction of proofs generated by the SMT solver veriT in Isabelle. The fine-grained proof format makes the reconstruction simple and efficient. For typical proof steps, such as arithmetic reasoning and skolemization, our reconstruction can avoid expensive search. By skipping proof steps that are irrelevant for Isabelle, the performance of proof checking is improved. Our method increases the success rate of Sledgehammer by halving the failure rate and reduces the checking time by 13%. We provide a detailed evaluation of the reconstruction time for each rule. It reveals that the runtime is influenced by both simple rules that appear very often and common complex rules

A Verified SAT Solver Framework with Learn, Forget, Restart, and Incrementality

International audienceWe developed a formal framework for CDCL (conflict-driven clause learning) in Isabelle/HOL. Through a chain of refinements, an abstract CDCL calculus is connected to a SAT solver expressed in a functional programming language, with total correctness guarantees. The framework offers a convenient way to prove metatheorems and experiment with variants. Compared with earlier SAT solver verifications, the main novelties are the inclusion of rules for forget, restart, and incremental solving and the application of refinement

Topological Acoustic Polaritons: Robust Sound Manipulation at the Subwavelength Scale

Topological insulators, a hallmark of condensed matter physics, have recently reached the classical realm of acoustic waves. A remarkable property of time-reversal invariant topological insulators is the presence of unidirectional spin-polarized propagation along their edges, a property that could lead to a wealth of new opportunities in the ability to guide and manipulate sound. Here, we demonstrate and study the possibility to induce topologically non-trivial acoustic states at the deep subwavelength scale, in a structured two-dimensional metamaterial composed of Helmholtz resonators. Radically different from previous designs based on non- resonant sonic crystals, our proposal enables robust sound manipulation on a surface along predefined, subwavelength pathways of arbitrary shapes