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DRAT and Propagation Redundancy Proofs Without New Variables [article]

Sam Buss, Neil Thapen
2021 arXiv   pre-print
These inference rules include BC, RAT, SPR and PR (respectively short for blocked clauses, resolution asymmetric tautologies, subset propagation redundancy and propagation redundancy), which arose from  ...  The systems without deletion are BC^-, RAT^-, SPR^-, PR^- and SR^-. With deletion, we show that DRAT^-, DSPR^- and DPR^- are equivalent.  ...  We thank the reviewers of the conference and journal versions of this paper for suggestions and comments that improved the paper.  ... 
arXiv:1909.00520v6 fatcat:4qubgnlak5eyfbmtdt2agnmqi4

What a Difference a Variable Makes [chapter]

Marijn J. H. Heule, Armin Biere
2018 Lecture Notes in Computer Science  
The PR proof system allows short proofs without new variables for some hard problems, while the DRAT proof system is supported by top-tier SAT solvers.  ...  Our simulation algorithm uses only one new Boolean variable and the size increase is at most quadratic in the size of the propositional formula and the PR proof.  ...  However, we succeeded to manually produce short PR proofs without new variables for these formulas and convert them into DRAT proofs.  ... 
doi:10.1007/978-3-319-89963-3_5 fatcat:jxqfz6wcyncvlixc4yry23v65q

Simulating Strong Practical Proof Systems with Extended Resolution

Benjamin Kiesl, Adrián Rebola-Pardo, Marijn J. H. Heule, Armin Biere
2020 Journal of automated reasoning  
Moreover, just recently, the proof system DPR has been proposed as a generalization of DRAT that allows for short proofs without the need of new variables.  ...  Since every extendedresolution proof can be regarded as a DRAT proof and since every DRAT proof is also a DPR proof, it was clear that both DRAT and DPR generalize extended resolution.  ...  without introducing new variables.  ... 
doi:10.1007/s10817-020-09554-z fatcat:2rw4irwe6bamhk4j66t7mdyg4u

Strong Extension-Free Proof Systems

Marijn J. H. Heule, Benjamin Kiesl, Armin Biere
2019 Journal of automated reasoning  
We demonstrate the strength of our proof systems on the famous pigeon hole formulas by providing short clausal proofs without new variables.  ...  The resulting proof systems are surprisingly strong, even without the introduction of new variables-a key feature of short proofs presented in the proof-complexity literature.  ...  reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s10817-019-09516-0 pmid:32226181 pmcid:PMC7089731 fatcat:i6es4zm4hjfx5fwyeltxtigpdi

Towards the shortest DRAT proof of the Pigeonhole Principle [article]

Isaac Grosof, Naifeng Zhang, Marijn J.H. Heule
2022 arXiv   pre-print
Using auxiliary variables and by recursively decomposing the original program into smaller sizes, we manually obtain proofs having length O(n^3) and leading coefficient 5/2.  ...  We construct the shortest known proofs of PHP in the standard proof format of modern SAT solving, DRAT.  ...  Heule, Kiesl, and Biere [15] describe a novel extension-free proof system called "Propagation Redundancy" (PR), in which they find O(n 3 ) length proofs for Pigeonhole Principle formulas.  ... 
arXiv:2207.11284v1 fatcat:b3dcraeln5alnpx4xp3lsmst7y

Frying the egg, roasting the chicken: unit deletions in DRAT proofs

Johannes Altmanninger, Adrián Rebola Pardo
2020 Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs  
The clausal proof format DRAT is the standard de facto to certify SAT solvers' unsatisfiability results. DRAT proofs act as logs of clause inferences and clause deletions in the solver.  ...  We find that our proof incorrectness certificates can be of help when debugging SAT solvers and DRAT checkers.  ...  Acknowledgments This work was funded through the LogiCS doctoral program W1255-N23 of the Austrian Science Fund (FWF), the Vienna Science and Technology Fund (WWTF) through grant VRG11-005, and Microsoft  ... 
doi:10.1145/3372885.3373821 dblp:conf/cpp/AltmanningerP20 fatcat:dyeuxz5qqbajvaloyayrzdrohy

Compositional Propositional Proofs [chapter]

Marijn J. H. Heule, Armin Biere
2015 Lecture Notes in Computer Science  
We present a new framework to produce clausal proofs for cube-and-conquer, arguably the most effective parallel SAT solving paradigm for hard-combinatorial problems.  ...  We evaluate the presented approach on some hard-combinatorial problems and validate constructed clausal proofs in parallel.  ...  Acknowledgements The authors thank Nathan Wetzler for his helpful comments to improve the paper and acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing  ... 
doi:10.1007/978-3-662-48899-7_31 fatcat:efu6b4i545g5jbct6o2yef7xfy

Expressing Symmetry Breaking in DRAT Proofs [chapter]

Marijn J. H. Heule, Warren A. Hunt, Nathan Wetzler
2015 Lecture Notes in Computer Science  
We applied this method to generate proofs of problems that have not been solved without symmetry-breaking predicates.  ...  We present a method to express symmetry-breaking predicates in DRAT, a proof format that is supported by the top-tier solvers.  ...  The tool drat-trim can reduce the new proof to 850 Mb by removing redundant lemmas and discarding the deletion information. Two Pigeons per Hole.  ... 
doi:10.1007/978-3-319-21401-6_40 fatcat:gp34uw53tbb2vdsalfm2cegley

Efficient Verified (UN)SAT Certificate Checking

Peter Lammich
2019 Journal of automated reasoning  
Our tool supports the full DRAT standard, and is even faster than the unverified state-of-the-art tool drat-trim, on a realistic set of benchmarks drawn from the 2016 and 2017 SAT competitions.  ...  They are commonly used for software and hardware verification. Modern SAT solvers are highly complex and optimized programs.  ...  Moreover, we thank Mathias Fleury and Simon Wimmer for very useful comments on the draft version of this paper, and Lars Hupel for instant help on any problems related to the benchmark server.  ... 
doi:10.1007/s10817-019-09525-z fatcat:hkuphe2mofeq5kvz3lxmo6lnve

Fast Verifying Proofs of Propositional Unsatisfiability via Window Shifting [article]

Jingchao Chen
2018 arXiv   pre-print
The robustness and correctness of SAT solvers are receiving more and more attention. In recent SAT competitions, a proof of unsatisfiability emitted by SAT solvers must be checked.  ...  This new checker uses a window shifting technique to improve the level of efficiency at which it verifies proofs of unsatisfiability.  ...  Acknowledgements The author is grateful to students at writing center of Stanford University who helped to improve the language of the paper, and to Nigel Horspool who gave helpful discussions and tested  ... 
arXiv:1611.04838v4 fatcat:fwlatkmp3fbnrlxwvc3pppgmz4

Efficient Verified (UN)SAT Certificate Checking [chapter]

Peter Lammich
2017 Lecture Notes in Computer Science  
We present an efficient formally verified checker for satisfiability and unsatisfiability certificates for Boolean formulas in conjunctive normal form.  ...  On a realistic benchmark suite drawn from the 2016 SAT competition, our approach is more than two times faster than the unverified standard tool drat-trim.  ...  Acknowledgements We thank Jasmin Blanchette and Mathias Fleury for very useful comments on the draft version of this paper, and Lars Hupel for instant help on any problems related to the benchmark server  ... 
doi:10.1007/978-3-319-63046-5_15 fatcat:dgzevmsvvbathmt37dpku3qqsi

Efficient Certified Resolution Proof Checking [chapter]

Luís Cruz-Filipe, Joao Marques-Silva, Peter Schneider-Kamp
2017 Lecture Notes in Computer Science  
We then formalize the theory underlying propositional proof checking in Coq, and extract a correct-by-construction proof checker for our format from the formalization.  ...  An empirical evaluation using 280 unsatisfiable instances from the 2015 and 2016 SAT competitions shows that this certified checker usually performs comparably to a state-of-the-art non-certified proof  ...  are used in reverse unit propagation to verify redundancy of these clauses.  ... 
doi:10.1007/978-3-662-54577-5_7 fatcat:ip2hfwhsobcmtcj5fsza3bhwfm

Encoding Redundancy for Satisfaction-Driven Clause Learning [chapter]

Marijn J. H. Heule, Benjamin Kiesl, Armin Biere
2019 Lecture Notes in Computer Science  
For the first time, we are able to generate and automatically check clausal proofs for large instances of these problems.  ...  Using one of these variants allows SDCL to solve harder problems, in particular the well-known Tseitin formulas and mutilated chessboard problems.  ...  SDCL solver, called SaDiCaL, that uses one of our new pruning predicates. (4) We show by an experimental evaluation that this new pruning predicate enables SaDiCaL to produce short proofs (without new  ... 
doi:10.1007/978-3-030-17462-0_3 fatcat:jm3wxiwjubhnpiq5wvdqto77j4

A Flexible Proof Format for SAT Solver-Elaborator Communication [article]

Seulkee Baek, Mario Carneiro, Marijn J.H. Heule
2022 arXiv   pre-print
We introduce FRAT, a new proof format for unsatisfiable SAT problems, and its associated toolchain.  ...  The format is easy to parse forward and backward, and it is extensible to future proof methods.  ...  Although the elaboration speed advantage is gone without proof hints, FRAT0 still trails DRAT closely thanks to the new optimizations.  ... 
arXiv:2109.09665v3 fatcat:o32afl4wfvdjrgcqr7kfns56iq

Scalable Proof Producing Multi-Threaded SAT Solving with Gimsatul through Sharing instead of Copying Clauses [article]

Mathias Fleury, Armin Biere
2022 arXiv   pre-print
This design gives quite remarkable parallel scalability, allows aggressive clause sharing while keeping memory usage low and produces more compact proofs.  ...  We give a first account of our new parallel SAT solver Gimsatul.  ...  Some of the design choices for the clause sharing architecture of Gimsatul are inspired by discussions with Christoph Kirsch and his former students Martin Aigner and Andreas Haas and other colleagues  ... 
arXiv:2207.13577v2 fatcat:6nzqklxbszg65kw43asu6cyaou
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