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Simulating Strong Practical Proof Systems with Extended Resolution

Benjamin Kiesl, Adrián Rebola-Pardo, Marijn J. H. Heule, Armin Biere
2020 Journal of automated reasoning  
We do so by showing that (1) extended resolution polynomially simulates DRAT and (2) DRAT polynomially simulates DPR.  ...  We implemented our simulations as proof-transformation tools and evaluated them to observe their behavior in practice.  ...  Together, these two simulations show how extended resolution is related to modern propagation-based proof systems used in practical SAT solving.  ... 
doi:10.1007/s10817-020-09554-z fatcat:2rw4irwe6bamhk4j66t7mdyg4u

Preface: Special Issue of Selected Extended Papers from IJCAR 2018

Didier Galmiche, Stephan Schulz, Roberto Sebastiani
2020 Journal of automated reasoning  
results, from proof systems to analysis of complexity and decidability, from automated reasoning to the production of stateful ML programs together with proofs of correctness, from extensions of model  ...  providing a refutationally complete first-order prover based on ordered resolution with literal selection.  ...  The paper "Simulating Strong Practical Proof Systems with Extended Resolution" focuses on two proof systems: DRAT, used in SAT solving, and DPR that is a generalization of DRAT that allows for short proofs  ... 
doi:10.1007/s10817-020-09556-x fatcat:u32hsri2yjh57nuqcevx75234y

On the proof complexity of MCSAT [article]

Gereon Kremer and Erika Abraham and Vijay Ganesh
2021 arXiv   pre-print
In this paper, we extend this program to the MCSAT approach for SMT solving by showing that the MCSAT architecture is polynomially equivalent to the Res*(T) proof system.  ...  In an attempt to resolve this apparent discrepancy between theory and practice, theorists have proposed the study of these solvers as proof systems that would enable establishing appropriate lower and  ...  MCSAT needs no theory rules to simulate Resolution and a single application of T-Conflict to simulate Strong Theory Derivation.  ... 
arXiv:2109.01585v1 fatcat:rqkb4twdjzfezgfnflekajxg3u

Some trade-off results for polynomial calculus

Chris Beck, Jakob Nordstrom, Bangsheng Tang
2013 Proceedings of the 45th annual ACM symposium on Symposium on theory of computing - STOC '13  
We present size-space trade-offs for the polynomial calculus (PC) and polynomial calculus resolution (PCR) proof systems.  ...  We achieve this by extending essentially all known size-space trade-offs for resolution to PC and PCR.  ...  Acknowledgements This article is the result of a long process, and various subsets of the authors would like to acknowledge useful discussions had during the last few years with various subsets of Paul  ... 
doi:10.1145/2488608.2488711 dblp:conf/stoc/BeckNT13 fatcat:7vd2etdq7fcebbfakn5uj3gt3u

Trade-offs Between Time and Memory in a Tighter Model of CDCL SAT Solvers [chapter]

Jan Elffers, Jan Johannsen, Massimo Lauria, Thomas Magnard, Jakob Nordström, Marc Vinyals
2016 Lecture Notes in Computer Science  
A long line of research has studied the power of conflictdriven clause learning (CDCL) and how it compares to the resolution proof system in which it searches for proofs.  ...  It has been shown that CDCL can polynomially simulate resolution even with an adversarially chosen learning scheme as long as it is asserting.  ...  simulates resolution with respect to size/time.  ... 
doi:10.1007/978-3-319-40970-2_11 fatcat:4jiqks3o7rgsrim2njfx36rt54

The Proof Complexity of SMT Solvers [chapter]

Robert Robere, Antonina Kolokolova, Vijay Ganesh
2018 Lecture Notes in Computer Science  
Further, we show that Res * (EUF) (and thus SMT algorithms with clause learning over EUF, new literal introduction rules and perfect branching) can simulate the Frege proof system, which is well-known  ...  The resolution proof system has been enormously helpful in deepening our understanding of conflict-driven clause-learning (CDCL) SAT solvers.  ...  For example, the Frege proof system p-simulates the Resolution proof system, but the converse is widely conjectured not to hold.  ... 
doi:10.1007/978-3-319-96142-2_18 fatcat:jgsweuz5rbbghf2p2ofiqagpc4

On the power of clause-learning SAT solvers as resolution engines

Knot Pipatsrisawat, Adnan Darwiche
2011 Artificial Intelligence  
systems as powerful as general resolution.  ...  In this work, we improve on existing results on the relationship between proof systems obtained from conflict-driven clause-learning SAT solvers and general resolution.  ...  CLR with any k-bounded-asserting learning scheme p-simulates general resolution. Proof.  ... 
doi:10.1016/j.artint.2010.10.002 fatcat:jzupr4mg7ne2begdew4sp23ii4

On the Power of Clause-Learning SAT Solvers with Restarts [chapter]

Knot Pipatsrisawat, Adnan Darwiche
2009 Lecture Notes in Computer Science  
In this work, we improve on existing work that studied the relationship between the proof system of modern SAT solvers and general resolution.  ...  In this paper, we prove that modern SAT solvers that learn asserting clauses indeed p-simulate general resolution without the need for any additional techniques.  ...  In this work, we are concerned only with proof systems based on propositional resolution [14] .  ... 
doi:10.1007/978-3-642-04244-7_51 fatcat:vlidq64gyfacbawf3fexwkkrq4

Towards NP–P via proof complexity and search

Samuel R. Buss
2012 Annals of Pure and Applied Logic  
We discuss propositional proof complexity, Cook's program, proof automatizability, proof search, algorithms for satisfiability, and the state of the art of our (in)ability to separate P and NP.  ...  This is a survey of work on proof complexity and proof search from a logicoalgorithmic viewpoint, as motivated by the P versus NP problem.  ...  Possibly this can be extended to prove that pool resolution does not simulate general resolution (but see [18] ).  ... 
doi:10.1016/j.apal.2011.09.009 fatcat:oud37acsqfgrdio62ir6ci24xi

Page 4445 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
Two relevant questions are whether the encod- ing preserves strong normalisation of lambda terms, and whether the calculus extended with variables is confluent.  ...  The authors present a resolution-based proof system for a propo- sitional temporal logic of knowledge, called KL,, and show that it is correct.  ... 

Different Approaches to Proof Systems [chapter]

Olaf Beyersdorff, Sebastian Müller
2010 Lecture Notes in Computer Science  
into strong proof systems as Frege systems and their extensions [Kra95] .  ...  In fact, Cook and Krajíček even exhibit a natural proof system with advice that is polynomially bounded if PV proves NP ⊆ P/poly: the system is an extended Frege system with constant advice.  ... 
doi:10.1007/978-3-642-13562-0_6 fatcat:5hpjwtndsffhtb2uzsoazf6xhm

Are moving punctures equivalent to moving black holes?

Jonathan Thornburg, Peter Diener, Denis Pollney, Luciano Rezzolla, Erik Schnetter, Ed Seidel, Ryoji Takahashi
2007 Classical and quantum gravity  
When simulating the inspiral and coalescence of a binary black-hole system, special care needs to be taken in handling the singularities.  ...  To investigate this question we use both techniques to evolve a binary system of equal-mass non-spinning black holes.  ...  For either the CE or MP approach, we have carried out simulations with at least three different resolutions.  ... 
doi:10.1088/0264-9381/24/15/009 fatcat:k7mow47im5g4pjly6foymnhhfa

On Expansion and Resolution in CEGAR Based QBF Solving [article]

Leander Tentrup
2018 arXiv   pre-print
A quantified Boolean formula (QBF) is a propositional formula extended with universal and existential quantification over propositions.  ...  We compare those CEGAR approaches using proof theory developed around QBF solving and present a unified calculus that combines the strength of both approaches.  ...  The proof system without strengthening rule does not p-simulate the proof system with strengthening rule. Proof.  ... 
arXiv:1803.09559v1 fatcat:rja7icixlvdcth7gqik7trlce4

On Expansion and Resolution in CEGAR Based QBF Solving [chapter]

Leander Tentrup
2017 Lecture Notes in Computer Science  
A quantified Boolean formula (QBF) is a propositional formula extended with universal and existential quantification over propositions.  ...  We compare those CEGAR approaches using proof theory developed around QBF solving and present a unified calculus that combines the strength of both approaches.  ...  The proof system without strengthening rule does not p-simulate the proof system with strengthening rule. Proof.  ... 
doi:10.1007/978-3-319-63390-9_25 fatcat:nuabyzxfp5dltpgsltvocztwmu

Understanding cutting planes for QBFs

Olaf Beyersdorff, Leroy Chew, Meena Mahajan, Anil Shukla
2018 Information and Computation  
We define a cutting planes system CP+∀red for quantified Boolean formulas (QBF) and analyse the proof-theoretic strength of this new calculus.  ...  weaker than QBF Frege and stronger than the CDCL-based QBF resolution systems Q-Res and QU-Res, it turns out to be incomparable to even the weakest expansion-based QBF resolution system ∀Exp+Res.  ...  Semantic cutting planes for QBFs The classical Cutting Planes proof system can be extended to the semantic Cutting Planes proof system by allowing the following semantic inference rule: from inequalities  ... 
doi:10.1016/j.ic.2018.08.002 fatcat:v5qjxywoqnexldwvfwrvsrj4l4
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