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A Theory of Satisfiability-Preserving Proofs in SAT Solving

Adrián Rebola-Pardo, Martin Suda
unpublished
as SAT, and can be reduced in a way that is well-behaved for modern SAT solvers.  ...  These are characterized by modifying a CNF formula in ways that preserve satisfiability but not necessarily logical truth.  ...  We then show that any DPR (DRAT) proof can be seen as a truth preserving proof in overwrite logic.  ... 
doi:10.29007/tc7q fatcat:qimbokwfa5bbhe2uptskoxacyi

Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer [chapter]

Marijn J. H. Heule, Oliver Kullmann, Victor W. Marek
2016 Lecture Notes in Computer Science  
Exploiting recent progress in unsatisfiability proofs of SAT solvers, we produced and verified a proof in the DRAT format, which is almost 200 terabytes in size.  ...  The boolean Pythagorean Triples problem has been a longstanding open problem in Ramsey Theory: Can the set N = {1, 2, ...} of natural numbers be divided into two parts, such that no part contains a triple  ...  Acknowledgements The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing grid resources that have contributed to the research results reported  ... 
doi:10.1007/978-3-319-40970-2_15 fatcat:kiqj5ts7ivfkflzgpskdflpyhm

NP-hard sets are not sparse unless P=NP: An exposition of a simple proof of Mahaney's Theorem, with applications [article]

Joshua A. Grochow
2016 arXiv   pre-print
We give an exposition of a very simple unpublished proof of Manindra Agrawal whose ideas appear in Agrawal-Arvind ("Geometric sets of low information content," Theoret. Comp. Sci., 1996).  ...  To this author, the fact that sparsity results on NP-complete sets have an application to classical questions in representation theory says that they are not only a gem of classical theoretical computer  ...  Certainly I am not the only person aside from Agrawal to have been aware of this proof; at the very least Thomas Thierauf was also aware, and was very supportive of writing it up.  ... 
arXiv:1610.05825v1 fatcat:yrcok3rckncszi27l7ache5jea

A Solver for a Theory of Strings and Bit-vectors [article]

Sanu Subramanian, Murphy Berzish, Yunhui Zheng, Omer Tripp, Vijay Ganesh
2016 arXiv   pre-print
The first accelerates convergence on a consistent assignment of string lengths, and the second, dubbed library-aware SMT solving, fixes summaries for built-in string functions (e.g., strlen in C/C++),  ...  Current approaches either reduce strings to bit-vectors and use a bit-vector solver as a backend, or model bit-vectors as natural numbers and use a solver for the combined theory of strings and natural  ...  , and provide a (constructive) proof of decidability for this theory.  ... 
arXiv:1605.09446v1 fatcat:iqedcp2v25e6jlcsmd2q4pmydi

SAT and Interactions (Dagstuhl Seminar 20061)

Olaf Beyersdorff, Uwe Egly, Meena Mahajan, Cláudia Nalon
2020 Dagstuhl Reports  
The seminar brought together theoreticians and practitioners from the areas of proof complexity and proof theory, SAT and QBF solving, MaxSAT, and modal logics, who discussed recent developments in their  ...  fields and embarked on an interdisciplinary exchange of ideas and techniques between these neighbouring subfields of SAT.  ...  preservation of strong normalisation.  ... 
doi:10.4230/dagrep.10.2.1 dblp:journals/dagstuhl-reports/BeyersdorffEMN20 fatcat:q6vjxmce4bd2nkm3vym2qkvqam

Advances in Symmetry Breaking for SAT Modulo Theories [article]

Saket Dingliwal, Ronak Agarwal, Happy Mittal, Parag Singla
2020 arXiv   pre-print
SMT solvers typically use a combination of SAT solving techniques augmented with calls to the theory solver.  ...  Symmetry breaking is a popular technique to reduce the search space for SAT solving by exploiting the underlying symmetry over variables and clauses in a formula.  ...  Any opinions, findings, conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views or official policies, either expressed or implied, of the  ... 
arXiv:1908.00860v2 fatcat:2mihevn7brhdjdfyr7mtyq4urm

Max NP-completeness made easy

Pierluigi Crescenzi, Luca Trevisan
1999 Theoretical Computer Science  
As a first application, we prove the Max NP-completeness of MAX 3SAT without using the PCP theorem (thus solving an open question posed in Khanna et al., 1994) .  ...  We introduce a simple technique to obtain reductions between optimization constraint satisfaction problems with respect to an approximation preserving redu~ibil~~ more powerful than the commonly used L-reduc  ...  The approximation thresholds of MAX SAT and MAX k(n)SAT are equal, provided k(n) is a monotone non-decreasing unbounded function. Proof.  ... 
doi:10.1016/s0304-3975(98)00200-x fatcat:w76vu5nmqvgwrhxoiaqykoz44e

Instantiation and Pretending to be an SMT Solver with Vampire

Giles Reger, Martin Suda, Andrei Voronkov
2017 International Workshop on Satisfiability Modulo Theories  
Secondly, it focuses on the problem of instantiation of quantified formulas and asks whether VAMPIRE needs it (it does) and whether it can directly borrow techniques from SMT solving (maybe).  ...  We discuss how Vampire reasons with problems containing both quantification and theories, the limitations this places on what it can do, and the advantages this provides over the standard SMT approach.  ...  In typical saturation-based proof search there is no concept of a model to be in conflict with.  ... 
dblp:conf/smt/RegerSV17 fatcat:nvbolygdh5gcrahjgmpccuwwaa

Decision Procedures for the Grand Challenge [chapter]

Daniel Kroening
2008 Lecture Notes in Computer Science  
A framework for reducing decision problems to propositional logic is described, which allows the surprising improvements in the performance of propositional SAT solvers to be exploited.  ...  The Verifying Compiler checks the correctness of the program it compiles. The workhorse of such a tool is the reasoning engine, which decides validity of formulae in a suitably chosen logic.  ...  Advanced implementations of lazy encodings also preserve learning done within the decision procedure for the non-propositional theory.  ... 
doi:10.1007/978-3-540-69149-5_46 fatcat:yi7stktfv5ewtpvl2726khnwme

Solving Very Hard Problems: Cube-and-Conquer, a Hybrid SAT Solving Method

Marijn J.H. Heule, Oliver Kullmann, Victor W. Marek
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
A recent success of SAT solving has been the solution of the boolean Pythagorean Triples problem [Heule et al., 2016], delivering the largest proof yet, of 200 terabytes in size.  ...  We present this and the underlying paradigm Cube-and-Conquer, a powerful general method to solve big SAT problems, based on integrating the "old" and "new" methods of SAT solving.  ...  The basic proof step is adding a clause, and while resolution only allows to add clauses which preserve all solutions, DRAT allows to add clauses which might require flipping of satisfying assignments  ... 
doi:10.24963/ijcai.2017/683 dblp:conf/ijcai/HeuleKM17 fatcat:sab7hccyanhcngia42ntarvlh4

Clause Elimination for SAT and QSAT

Marijn Heule, Matti Järvisalo, Florian Lonsing, Martina Seidl, Armin Biere
2015 The Journal of Artificial Intelligence Research  
It turns out that the importance of applying the clause elimination procedures developed in this work is empirically emphasized in the context of state-of-the-art QSAT solving.  ...  The famous archetypical NP-complete problem of Boolean satisfiability (SAT) and its PSPACE-complete generalization of quantified Boolean satisfiability (QSAT) have become central declarative programming  ...  The authors gratefully acknowledge financial support from DARPA contract number N66001-10-2-4087 (MH); Academy of Finland under grants 251170 COIN Centre of Excellence in Computational Inference Research  ... 
doi:10.1613/jair.4694 fatcat:elpzpnuci5e3bffetdy3mhmwna

An Online Proof-Producing Decision Procedure for Mixed-Integer Linear Arithmetic [chapter]

Sergey Berezin, Vijay Ganesh, David L. Dill
2003 Lecture Notes in Computer Science  
In practical examples, however, arithmetic constraints are often mixed with constraints from other theories like the theory of arrays, Boolean satisfiability (SAT), bit-vectors, etc.  ...  This work augments CVC with a decision procedure for the theory of mixed integer linear arithmetic based on the Omega-test [Pug91] extended to be online and proof producing.  ...  The authors would like to thank the principal developers of CVC Aaron Stump and Clark Barrett for many insightful discussions about the theory and implementation of this decision procedure.  ... 
doi:10.1007/3-540-36577-x_38 fatcat:p6ye4ep2pjbtzpu4ffb77hnizi

Analysis of One-to-One Matching Mechanisms via SAT Solving: Impossibilities for Universal Axioms

Ulle Endriss
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We develop a powerful approach that makes modern SAT solving techniques available as a tool to support the axiomatic analysis of economic matching mechanisms.  ...  Our central result is a preservation theorem, establishing sufficient conditions under which the possibility of designing a matching mechanism meeting certain axiomatic requirements for a given number  ...  SAT solving and then present human-readable proofs for two such theorems.  ... 
doi:10.1609/aaai.v34i02.5561 fatcat:4pqtjhnannhmdgdduzxedzwgrq

An Instantiation-Based Approach for Solving Quantified Linear Arithmetic [article]

Andrew Reynolds, Tim King, Viktor Kuncak
2016 arXiv   pre-print
This paper presents a framework to derive instantiation-based decision procedures for satisfiability of quantified formulas in first-order theories, including its correctness, implementation, and evaluation  ...  Experimental results on standardized benchmarks from model checking, static analysis, and synthesis show that our implementation of the procedure in the SMT solver CVC4 outperforms existing tools for quantified  ...  Acknowledgements We would like to thank Peter Baumgartner for his help with converting the benchmarks used in the evaluation to the TPTP format.  ... 
arXiv:1510.02642v4 fatcat:kbudlxebt5dqrf2iisnwjdsuxe

A Verified Decision Procedure for Pseudo-Boolean Formulas

Tobias Philipp, Anna Tigunova
2016 Workshop of the UK Planning and Scheduling Special Interest Group  
State-of-the-art SAT solvers that emit unsatisfiability proofs are used to solve the resulting instances.  ...  The verification of the encoding is carried out in the Coq proof assistant.  ...  Acknowledgements The authors thank the ZIH of TU Dresden for providing the computational resources to produce the experimental data for the empirical evaluation.  ... 
dblp:conf/plansig/PhilippT16 fatcat:hzedmdlh3fedzlpai4flzkz6xe
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