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A Complete Resolution Calculus for Signed Max-SAT

Carlos Ansotegui, Maria L. Bonet, Jordi Levy, Felip Manya
2007 Proceedings - International Symposium on Multiple-Value Logic  
We define a resolution-style rule for solving the Max-SAT problem of Signed CNF formulas (Signed Max-SAT) and prove that our rule provides a complete calculus for that problem.  ...  From the completeness proof we derive an original exact algorithm for solving Signed Max-SAT. Finally, we present some connections between our approach and the work done in the Weighted CSP community.  ...  In this paper, we define a resolution-style rule for solving the Max-SAT problem of Signed CNF formulas (Signed Max-SAT) and prove that our rule provides a complete calculus for that problem.  ... 
doi:10.1109/ismvl.2007.2 dblp:conf/ismvl/AnsoteguiBLM07 fatcat:zq23nc7v7zg67agyr6mpg7wfb4

A First Polynomial Non-Clausal Class in Many-Valued Logic [article]

Gonzalo E. Imaz
2021 arXiv   pre-print
Thirdly, we define Regular Non-Clausal Unit-Resolution, or RUR-NC , and prove both that it is complete for RH and that checks its satisfiability in polynomial time.  ...  As a consequence, a first polynomial propositional class in non-clausal (NC) form has recently been proposed.  ...  Signed-SAT is NP-complete: its NP-membership is verified as for classical SAT and its NP-completeness is obvious because it includes classical SAT.  ... 
arXiv:2110.12901v1 fatcat:xgh5xriufvampbfxh5hsoyls3i

Model Evolution-Based Theorem Proving

2014 IEEE Intelligent Systems  
The one is the integration of reasoning methods for propositional and for first-order logic, with a best-of-both-worlds motivation.  ...  I will survey the major paradigms in this space from the perspective of our own developments, mainly the model evolution calculus.  ...  [2] is an important method for building (complete) SAT solvers.  ... 
doi:10.1109/mis.2013.124 fatcat:bvktw7sgsrg6djtg75dr6wvpua

A Collaborative Framework for Non-Linear Integer Arithmetic Reasoning in Alt-Ergo

Sylvain Conchon, Mohamed Iguernelala, Alain Mebsout
2013 2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing  
In this paper, we describe a collaborative framework for reasoning modulo simple properties of non-linear integer arithmetic.  ...  The interval calculus component is used -in addition to standard linear operations over inequalities -to refine bounds of non-linear terms and to inform the SAT solver about judicious case-splits on bounded  ...  Following standard CDCL solvers, our SAT engine has two distinct behaviors: a search mode (Mode = search) and a resolution mode (Mode = resolution).  ... 
doi:10.1109/synasc.2013.29 dblp:conf/synasc/ConchonIM13 fatcat:57jfxmg7ubfddgjhgsmp7kwx3a

Enhancing Search-Based QBF Solving by Dynamic Blocked Clause Elimination [chapter]

Florian Lonsing, Fahiem Bacchus, Armin Biere, Uwe Egly, Martina Seidl
2015 Lecture Notes in Computer Science  
Among preprocessing techniques for quantified Boolean formula (QBF) solving, quantified blocked clause elimination (QBCE) has been found to be extremely effective.  ...  This dynamic application of QBCE is in sharp contrast to its typical use as a mere preprocessing technique.  ...  Let φ = Π.ψ be a PCNF. The rules of the Q-resolution calculus (QRES) are as follows.  ... 
doi:10.1007/978-3-662-48899-7_29 fatcat:caqxrjkbe5c6znryjj5uviyafe

The Effects of Bounding Syntactic Resources on Presburger LTL

Stephane Demri, Regis Gascon
2007 14th International Symposium on Temporal Representation and Reasoning (TIME'07)  
In order to establish the PSPACE upper bound, we show that the nonemptiness problem for Büchi one-counter automata taking values in Z and allowing zero tests and sign tests, is only NLOGSPACE-complete.  ...  We provide a complete picture refining known results from the literature, in some cases pushing forward the known decidability limits.  ...  Model-checking one-counter automata against modal µcalculus is in PSPACE [28] and more generally modelchecking pushdown systems against modal µ-calculus is EXPTIME-complete [33] as well as linear µ-calculus  ... 
doi:10.1109/time.2007.63 dblp:conf/time/DemriG07 fatcat:t5ezrbvzxvdvjmdkt2waoxeyx4

The Effects of Bounding Syntactic Resources on Presburger LTL

S. Demri, R. Gascon
2009 Journal of Logic and Computation  
In order to establish the PSPACE upper bound, we show that the nonemptiness problem for Büchi one-counter automata taking values in Z and allowing zero tests and sign tests, is only NLOGSPACE-complete.  ...  We provide a complete picture refining known results from the literature, in some cases pushing forward the known decidability limits.  ...  Model-checking one-counter automata against modal µcalculus is in PSPACE [28] and more generally modelchecking pushdown systems against modal µ-calculus is EXPTIME-complete [33] as well as linear µ-calculus  ... 
doi:10.1093/logcom/exp037 fatcat:cvjzyvtqurfitjyst3egbl6tma

Minimum propositional proof length is NP-hard to linearly approximate [chapter]

Michael Alekhnovich, Sam Buss, Shlomo Moran, Toniann Pitassi
1998 Lecture Notes in Computer Science  
Resolution is a propositional proof system which is popular as a foundation for automated theorem provers.  ...  These results are very robust in that they hold for almost all natural proof systems, including: Frege systems, extended Frege systems, resolution, Horn resolution, the polynomial calculus, the sequent  ...  Razborov for extremely helpful discussions. We also would like to thank S. Arora for pointing out that Minimum Label Cover can be reduced to Monotone Minimum Satisfying Assignment.  ... 
doi:10.1007/bfb0055766 fatcat:s2afoecam5fzbfqg5jkoz2pofu

Resolution and model building in the infinite-valued calculus of L̵ukasiewicz

Daniele Mundici, Nicola Olivetti
1998 Theoretical Computer Science  
We discuss resolution and its complexity in the infinite-valued sentential calculus of Lukasiewicz, with special emphasis on model building algorithms for satisfiable sets of clauses.  ...  Generalizing the pre-existing literature on resolution in infinite-valued logic, by a positive literal we mean a negationless formula in one variable, built only from the connectives @, 0, V, A.  ...  Hahnle for pointing out the importance of the study of complexity-theoretic issues concerning fragments of the infinite-valued calculus. We thank S. Aguzzoli and A.  ... 
doi:10.1016/s0304-3975(98)00012-7 fatcat:ne6ptkdjsrga3o7hhaxdxy53zm

On the virtue of succinct proofs

Trinh Huynh, Jakob Nordstrom
2012 Proceedings of the 44th symposium on Theory of Computing - STOC '12  
However, for other relevant proof systems in the context of SAT solving, such as polynomial calculus (PC) and cutting planes (CP), very little has been known.  ...  A crucial technical ingredient in these results is a new twoplayer communication complexity lower bound for composed search problems in terms of block sensitivity, a contribution that we believe to be  ...  We are also grateful to the anonymous referees for several comments that helped to improve the presentation of this paper.  ... 
doi:10.1145/2213977.2214000 dblp:conf/stoc/HuynhN12 fatcat:il3fpwscg5crjle2mnnbm3jihq

Report on BCTCS 2013

Guy McCusker
2014 Bulletin of the European Association for Theoretical Computer Science  
for a modified DPLL proof system combined with unit resolution and extract a conflict driven clause learning SAT algorithm.  ...  In 1995 the class S LUR (Single Lookahead Unit Resolution) was introduced as an umbrella class for efficient satisfiability (SAT) solving.  ... 
dblp:journals/eatcs/McCusker14 fatcat:6mbueqohg5fxjk2advza4yktr4

Present and Future of Practical SAT Solving [chapter]

Oliver Kullmann
2008 Lecture Notes in Computer Science  
A general "modern" scheme for DPLL algorithms is presented, which allows natural representations for "modern" solvers of these two types.  ...  We review current SAT solving, concentrating on the two paradigms of conflict-driven and look-ahead solvers, and with a view towards the unification of these two paradigms.  ...  A classic references for the resolution calculus is [45] , while a recent overview on proof systems is [41] .  ... 
doi:10.1007/978-3-540-92800-3_11 fatcat:lihr6k7mfbd5bbcn6456urdcwa

Influences of Frege's Predicate Logic on Some Computational Models

Mohamad Awwad
2018 Future Human Image  
In addition, the resolution principle turned out to be a very effective tool of Automated Theorem Proving, a sort of effective logic programs used to verify and prove important, usually hard, constraints  ...  Robinson's improved resolution principle is a cornerstone in logic programming languages; it has initiated a decisive consequence in the development of PROLOG (Programming in Logic) by Colmerauer and Roussel  ...  As for the worth-mentioning Waldmeister prover is a unit-equational first-order logic developed at Max Planck Institute for Computer Science in 1998.  ... 
doi:10.29202/fhi/9/1 fatcat:zfn5mgjsinfljdc2sucqf6rori

Partition-based logical reasoning for first-order and propositional theories

Eyal Amir, Sheila McIlraith
2005 Artificial Intelligence  
Craig's interpolation theorem serves as a key to proving soundness and completeness of all of these algorithms.  ...  We characterize a class of reasoning procedures that ensures completeness and soundness of our message-passing algorithms.  ...  Acknowledgements We particularly wish to thank Rina Dechter for many helpful and clarifying comments on a draft of this paper.  ... 
doi:10.1016/j.artint.2004.11.004 fatcat:s6nv5iqqdrfmpieoixjgz7te4y

A Decision Procedure for Equality Logic with Uninterpreted Functions [chapter]

Olga Tveretina
2004 Lecture Notes in Computer Science  
They are more properly characterized as max-sat methods. They cannot even report a formula to be unsatisfiable.  ...  In [Rish and Dechter, 2000 ] Rish and Dechter use directional resolution (a form of ordered resolution) to search for SAT problems.  ...  It is time to make the attempt" Chapter 9 A BDD-representation for the EUF-logic "If the only tool you have is a hammer, then every problem you see looks like a nail" [Confucian saying] "Can you do addition  ... 
doi:10.1007/978-3-540-30210-0_7 fatcat:g4healncqfdirk7wwp62pnf4pe
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