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Simulating Strong Practical Proof Systems with Extended Resolution
2020
Journal of automated reasoning
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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
2020
Journal of automated reasoning
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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]
2021
arXiv
pre-print
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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
2013
Proceedings of the 45th annual ACM symposium on Symposium on theory of computing - STOC '13
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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]
2016
Lecture Notes in Computer Science
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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]
2018
Lecture Notes in Computer Science
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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
2011
Artificial Intelligence
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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]
2009
Lecture Notes in Computer Science
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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
2012
Annals of Pure and Applied Logic
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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
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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]
2010
Lecture Notes in Computer Science
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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?
2007
Classical and quantum gravity
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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]
2018
arXiv
pre-print
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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]
2017
Lecture Notes in Computer Science
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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
2018
Information and Computation
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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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