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Using DPLL for Efficient OBDD Construction [chapter]

Jinbo Huang, Adnan Darwiche
2005 Lecture Notes in Computer Science  
Specifically, we propose two DPLL-based algorithms that construct OBDDs for CNF formulas.  ...  We discuss the advantage of this new construction method over the traditional approach, where OBDDs for subsets of the CNF formula are built and conjoined.  ...  Acknowledgment We wish to thank the anonymous reviewers for the SAT 2004 conference for commenting on an earlier version of this paper.  ... 
doi:10.1007/11527695_13 fatcat:nzc5t4znrjfgldctqnuitnyyqe

On the Relative Efficiency of DPLL and OBDDs with Axiom and Join [chapter]

Matti Järvisalo
2011 Lecture Notes in Computer Science  
Hence DPLL and OBDDs constructed using only the axiom and join rules are polynomially incomparable.  ...  Especially, we show that OBDDs, even when constructed using only the rather weak axiom and join rules, can be exponentially more efficient than DPLL or, equivalently, tree-like resolution.  ...  Another interesting question is the relative efficiency of tree-like and DAG-like OBDD aj proofs. Especially, the OBDD aj proofs constructed in Lemma 2 are not tree-like.  ... 
doi:10.1007/978-3-642-23786-7_33 fatcat:trqwrkyj2jek5gv6dtikrh27pu

The Language of Search

J. Huang, A. Darwiche
2007 The Journal of Artificial Intelligence Research  
In particular, we show that several versions of exhaustive DPLL search correspond to such well-known languages as FBDD, OBDD, and a precisely-defined subset of d-DNNF.  ...  By thus mapping search algorithms to propositional languages, we provide a uniform and practical framework in which successful search techniques can be harnessed for compilation of knowledge into various  ...  We thank Rina Dechter and the anonymous reviewers for their feedback on earlier drafts of this paper.  ... 
doi:10.1613/jair.2097 fatcat:zirfwvbbfnfpjavois56s4h434

Search vs. Symbolic Techniques in Satisfiability Solving [chapter]

Guoqiang Pan, Moshe Y. Vardi
2005 Lecture Notes in Computer Science  
Recent work has shown how to use OBDDs for satisfiability solving.  ...  To that end, we conduct a direct comparison with the DPLL-based ZChaff, as well as evaluate a variety of optimization techniques for the symbolic approach.  ...  In the last ten years, much progress have been made in developing highly optimized DPLL solvers, leading to efficient solvers such as ZChaff [46] and BerkMin [28] , all of which use advanced heuristics  ... 
doi:10.1007/11527695_19 fatcat:uhikpb5u4rfa7ee4adtea47gfe

COSMOS: a compiled simulator for MOS circuits

R. E. Bryant, D. Beatty, K. Brace, K. Cho, T. Sheffler
1987 24th ACM/IEEE conference proceedings on Design automation conference - DAC '87  
OBDDs provide a uniform representation for operations to define simple functions and then construct representations of more complex functions via the operations of Boolean algebra, as well as function  ...  OBDD to the unique form for that function, and (3) there is an associated set of algorithms to implement a wide variety of operations on Boolean functions represented as OB-DDs.  ...  they can be constructed and analyzed using efficient graph algorithms.  ... 
doi:10.1145/37888.37890 dblp:conf/dac/BryantBBCS87 fatcat:w7pcly66oreg5bxkmwrt4m43jy

Exploiting Functional Dependencies of Variables in All Solutions SAT Solvers

Takahisa Toda, Takeru Inoue
2017 Journal of Information Processing  
Our solver is designed based on the OBDD compilation technique, which allows us to efficiently handle intractable CNFs with a number of solutions in dynamic programming manner.  ...  CNF encoding, which translates original problems for AllSAT solvers, spawns many auxiliary variables and, what is worse, obscures functional dependencies over variables.  ...  (c) Constructed OBDD with our method. Nodes of label 3 are eliminated because 3-rd variable, i.e., x 6 , is dominated. Cutsets are used for equivalence test.  ... 
doi:10.2197/ipsjjip.25.459 fatcat:dtqfo2d6drd2basnita5pvdtdi

Non-FPT lower bounds for structural restrictions of decision DNNF [article]

Andrea Calì, Florent Capelli, Igor Razgon
2017 arXiv   pre-print
Both models are known to be of FPT size for CNFs of bounded primal treewidth.  ...  We give a non-FPT lower bound on the size of structured decision DNNF and OBDD with decomposable AND-nodes representing CNF-formulas of bounded incidence treewidth.  ...  Thus, for reasonable values of k, if the right elimination order and the right caching policy is chosen, exhaustive DPLL can solve these instances efficiently.  ... 
arXiv:1708.07767v1 fatcat:7cfgd3nnpvgcpnvtrnf77vovfq

An Exhaustive DPLL Algorithm for Model Counting

Umut Oztok, Adnan Darwiche
2018 The Journal of Artificial Intelligence Research  
State-of-the-art model counters are based on exhaustive DPLL algorithms, and have been successfully used in probabilistic reasoning, one of the key problems in AI.  ...  Furthermore, we obtain the first top-down SDD compiler, and show orders-of-magnitude improvements in SDD construction time against the existing bottom-up SDD compiler.  ...  In fact, exhaustive DPLL (and its variants) can be seen as constructing a tree.  ... 
doi:10.1613/jair.1.11201 fatcat:wgj7krkkargrxniumyrtobqnzy

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.  ...  Razborov for comments on an earlier draft of this paper. We also thank two anonymous referees for their careful reading and useful comments.  ...  They have also been used for conditional constructions of nonstandard models [68] .  ... 
doi:10.1016/j.apal.2011.09.009 fatcat:oud37acsqfgrdio62ir6ci24xi

A Symbolic Search Based Approach for Quantified Boolean Formulas [chapter]

Gilles Audemard, Lakhdar Saïs
2005 Lecture Notes in Computer Science  
Using DPLL-likes (resp. local search) techniques, our approach gives rise to a complete QBDD(DPLL) (resp. incomplete QBDD(LS)) solver.  ...  Many QBF solvers has been proposed, most of them perform decision tree search using the DPLL-like techniques.  ...  For completeness and efficiency reasons, our approach is enhanced with two key features.  ... 
doi:10.1007/11499107_2 fatcat:nzvuplefsjgyfbbicjkadapsie

On the Relative Efficiency of Resolution-Like Proofs and Ordered Binary Decision Diagram Proofs

Nathan Segerlind
2008 2008 23rd Annual IEEE Conference on Computational Complexity  
In particular, this system abstracts satisfiability algorithms based upon explicit construction of OBDDs and satisfiability algorithms based upon symbolic quantifier elimination.  ...  We show that tree-like OBDD proofs of unsatisfiability require an exponential increase (s → 2 s Ω(1) ) in proof size to simulate unrestricted resolution, and that unrestricted OBDD proofs of unsatisfiability  ...  DPLL with clause learning algorithms generate "DAGlike" derivations whereas existing OBDD-based solvers using explicit construction and symbolic quantifier elimination methods [19, 1, 38, 22, 44] construct  ... 
doi:10.1109/ccc.2008.34 dblp:conf/coco/Segerlind08 fatcat:22donfgbbzdwjhpns2goc5m2cy

Ordered Binary Decision Diagrams, Pigeonhole Formulas and Beyond1

Olga Tveretina, Carsten Sinz, Hans Zantema
2010 Journal on Satisfiability, Boolean Modeling and Computation  
We also present a family of CNFs that show an exponential blow-up for all OBDD refutations compared to unrestricted resolution refutations.  ...  Here we show that an arbitrary OBDD refutation of the pigeonhole formula has exponential size: we prove that for any order of computation at least one intermediate OBDD in the proof has size Ω(1.14 n )  ...  They are often used as a standart benchmark for checking efficiency of (UN)SAT algorithms.  ... 
doi:10.3233/sat190074 fatcat:qh7bfzz4fncefnys4apiradtgu

Resolution Simulates Ordered Binary Decision Diagrams for Formulas in Conjunctive Normal Form [article]

Olga Tveretina
2017 arXiv   pre-print
A related fundamental problem is to determine the relative efficiency of standard proof systems, where the relative complexity is measured using the notion of polynomial simulation.  ...  An Ordered Binary Decision Diagram (OBDD) is a data structure that is used to represent Boolean functions.  ...  Acknowledgments The author thanks Erika Ábrahám for helpful discussions at the early stage of this study.  ... 
arXiv:1701.02275v3 fatcat:qtkqc5bd7ndkhelzyphgfme3ea

Reduced ordered binary decision diagram with implied literals: a new knowledge compilation approach

Yong Lai, Dayou Liu, Shengsheng Wang
2012 Knowledge and Information Systems  
Finally, we propose an ROBDD-i compilation algorithm for any i and a ROBDD-\infty compilation algorithm.  ...  According to this approach, knowledge bases are converted off-line into a target compilation language which is tractable for on-line querying.  ...  Acknowledgements We thank Professor Bart Selman for the suggestions about this paper. We also thank Dr. Knot Pipatsrisawat for the useful information about c2d provided by him.  ... 
doi:10.1007/s10115-012-0525-6 fatcat:xa47xe2bsfh7blktxfryqjfaxi

New Limits for Knowledge Compilation and Applications to Exact Model Counting [article]

Paul Beame, Vincent Liew
2015 arXiv   pre-print
We show new limits on the efficiency of using current techniques to make exact probabilistic inference for large classes of natural problems.  ...  A consequence is that for representing unions of conjunctive queries, SDDs are not qualitatively more concise than OBDDs.  ...  Acknowledgements We thank Dan Suciu and Guy Van den Broeck for helpful comments and suggestions.  ... 
arXiv:1506.02639v2 fatcat:keokbhma5zhutm7u3jnqksghmu
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