## Implementing the Davis-Putnam Method (2000)

Venue: | Journal of Automated Reasoning |

Citations: | 53 - 3 self |

### BibTeX

@ARTICLE{Zhang00implementingthe,

author = {Hantao Zhang and Mark E. Stickel},

title = {Implementing the Davis-Putnam Method},

journal = {Journal of Automated Reasoning},

year = {2000},

volume = {24},

pages = {277--296}

}

### Years of Citing Articles

### OpenURL

### Abstract

The method proposed by Davis, Putnam, Logemann, and Loveland for propositional reasoning, often referred to as the Davis-Putnam method, is one of the major practical methods for the satisfiability (SAT) problem of propositional logic. We show how to implement the Davis-Putnam method efficiently using the trie data structure for propositional clauses. A new technique of indexing only the first and last literals of clauses yields a unit propagation procedure whose complexity is sublinear to the number of occurrences of the variable in the input. We also show that the Davis-Putnam method can work better when unit subsumption is not used. We illustrate the performance of our programs on some quasigroup problems. The efficiency of our programs has enabled us to solve some open quasigroup problems.

### Citations

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Citation Context ...y sought. Empirical research has been very fruitful for the development of efficient methods for SAT problems. The method proposed by Davis, Putnam, Logemann, and Loveland for propositional reasoning =-=[3, 4]-=-, often referred as the Davis--Putnam method, has long been a major practical method for solving SAT problems. It is based on unit propagation (i.e., unit resolution and unit subsumption) and case spl... |

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Citation Context ...so large sets of clauses with hundreds of thousands of literals must be handled. Recently, some incomplete methods based on local search have been proposed that can solve very large size SAT problems =-=[10, 14]-=-. The usefulness of these methods for solving quasigroup problems remains to be seen. However, these methods cannot entirely replace the Davis-- Putnam method because many quasigroup problems have no ... |

550 |
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Citation Context ...y sought. Empirical research has been very fruitful for the development of efficient methods for SAT problems. The method proposed by Davis, Putnam, Logemann, and Loveland for propositional reasoning =-=[3, 4]-=-, often referred as the Davis--Putnam method, has long been a major practical method for solving SAT problems. It is based on unit propagation (i.e., unit resolution and unit subsumption) and case spl... |

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Citation Context ... both theoretically and practically, than the approach used in LDPP and many other systems. That approach appeared earlier in Dowling and Gallier's linear algorithm for satisfiability of Horn clauses =-=[6]-=-. We think our ideas can be used to design a new sublinear algorithm for the satisfiability of Horn clauses. zhang-stickel-implementing-dp.tex; 19/01/2000; 14:39; p.18 Implementing the Davis--Putnam M... |

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Citation Context ...sing tries in the Davis--Putnam method. By using the trie data structure, our programs gain something in efficiency, and much in elegance. Some preliminary results of our experiments are presented in =-=[15, 16, 18]-=-. In this paper, we present in detail the data structures used in our programs. One of the major motivations for developing our programs was to solve open problems in algebra concerning the existence ... |

200 | Experimental results on the crossover point in satisfiability problems
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Citation Context ...gnment can be undone during backtracking before trying an alternative assignment. Many other implementations of the Davis--Putnam method employ a similar approach, including Crawford and Auton's NTAB =-=[2]-=-, Letz's SEMPROP, and McCune's MACE [12]. LDPP 0 is a faster variant of LDPP that explores exactly the same search space as LDPP but does not perform the subsumption operation (see Section 7.2.2). 7. ... |

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Citation Context ....tex; 19/01/2000; 14:39; p.20 Implementing the Davis--Putnam Method 21 Table VII. POSIT, SATZ, NTAB: default settings; search is halted after finding a model in satisfiable cases (marked by *). POSIT =-=[7]-=- SATZ [11] NTAB [2] Problem Branches Search Total Branches Total Branches Total (sec) (sec) (sec) (sec) QG1.7* 6 0.0 3.0 7 33 75 3.4 .8* 5151 34 40 7770 218 2346 106 QG2.7* 21 0.1 3.0 10 53 12 2.5 .8*... |

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Citation Context ...g before trying an alternative assignment. Many other implementations of the Davis--Putnam method employ a similar approach, including Crawford and Auton's NTAB [2], Letz's SEMPROP, and McCune's MACE =-=[12]-=-. LDPP 0 is a faster variant of LDPP that explores exactly the same search space as LDPP but does not perform the subsumption operation (see Section 7.2.2). 7. SATO: A New Algorithm for Unit Propagati... |

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Citation Context ...01/2000; 14:39; p.20 Implementing the Davis--Putnam Method 21 Table VII. POSIT, SATZ, NTAB: default settings; search is halted after finding a model in satisfiable cases (marked by *). POSIT [7] SATZ =-=[11]-=- NTAB [2] Problem Branches Search Total Branches Total Branches Total (sec) (sec) (sec) (sec) QG1.7* 6 0.0 3.0 7 33 75 3.4 .8* 5151 34 40 7770 218 2346 106 QG2.7* 21 0.1 3.0 10 53 12 2.5 .8* 5761 41 4... |

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Citation Context ...e that no solution exists or count the number of solutions. Quasigroup completion problems (completion of partially filled in Latin squares, but without the constraints) are now a subject of research =-=[9]-=-. 2. The Davis--Putnam Method The Davis--Putnam method is based on three simple facts about truth table logic. First, where A and B are any formulae, the conjunction A (AB) is equivalent to AB and the... |

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Citation Context ...sing tries in the Davis--Putnam method. By using the trie data structure, our programs gain something in efficiency, and much in elegance. Some preliminary results of our experiments are presented in =-=[15, 16, 18]-=-. In this paper, we present in detail the data structures used in our programs. One of the major motivations for developing our programs was to solve open problems in algebra concerning the existence ... |

54 |
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Citation Context ...e open problems in algebra concerning the existence of quasigroups satisfying certain constraints [1]. The usefulness of computer programs to attack these quasigroup problems has been demonstrated in =-=[19, 8, 15]-=-. We prefer these quasigroup problems as benchmarks over randomly generated SAT problems for testing constraint solving methods: The problems have fixed solutions; descriptions of the problems are sim... |

39 |
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Citation Context ... using tries in the Davis--Putnam method. By using the trie data structure, our programs gain something in e#ciency, and much in elegance. Some preliminary results of our experiments are presented in =-=[15, 16, 18]-=-. In this paper, we present in detail the data structures used in our programs. One of the major motivations for developing our programs was to solve open problems in algebra concerning the existence ... |

34 | Local search for satisfiability (SAT) problem
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(Show Context)
Citation Context ...so large sets of clauses with hundreds of thousands of literals must be handled. Recently, some incomplete methods based on local search have been proposed that can solve very large size SAT problems =-=[10, 14]-=-. The usefulness of these methods for solving quasigroup problems remains to be seen. However, these methods cannot entirely replace the Davis-- Putnam method because many quasigroup problems have no ... |

31 |
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(Show Context)
Citation Context ...and MARK STICKEL choice of variable for splitting, and so forth. In this paper, we will concentrate on the use of tries (discrimination trees) and related refinements for the Davis--Putnam method. In =-=[5]-=-, de Kleer used tries to represent propositional clauses for efficient subsumption. In the past, both of us have used tries to represent first-order terms and to implement efficient rewriting-based th... |

21 |
Sato: A decision procedure for propositional logic
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(Show Context)
Citation Context ...es not imply that the trie data structure is ineffective for the Davis--Putnam method. Actually, the implementations of the Davis--Putnam method in the SATO program (SAtisfiability Testing Optimized) =-=[16]-=- did not use the trie-merge operation. In this section, we describe some ideas used in SATO to improve the performance of the Davis--Putnam method based on the trie data structure. SATO was used to se... |

14 |
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(Show Context)
Citation Context ... structures used in our programs. One of the major motivations for developing our programs was to solve open problems in algebra concerning the existence of quasigroups satisfying certain constraints =-=[1]-=-. The usefulness of computer programs to attack these quasigroup problems has been demonstrated in [19, 8, 15]. We prefer these quasigroup problems as benchmarks over randomly generated SAT problems f... |

7 |
H.: Specifying Latin squares in propositional logic
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(Show Context)
Citation Context ...shown that adding these "transposes" to the input can reduce the search space; this is also true of QG3, QG4, QG6, and QG7. More information on quasigroup problems can be found in [1], [8], =-=[15], and [17]-=-. 5. DDPP: A Nondestructive Trie-based Implementation DDPP (Discrimination-tree-based Davis--Putnam Prover) is a straightforward implementation of the Davis--Putnam method based on the trie-merge oper... |

6 |
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(Show Context)
Citation Context ...e open problems in algebra concerning the existence of quasigroups satisfying certain constraints [1]. The usefulness of computer programs to attack these quasigroup problems has been demonstrated in =-=[19, 8, 15]-=-. We prefer these quasigroup problems as benchmarks over randomly generated SAT problems for testing constraint solving methods: The problems have fixed solutions; descriptions of the problems are sim... |

3 |
Davis-Putnam engineered reversely. Available by anonymous FTP from arp.anu.edu.au
- Meglicki
- 1993
(Show Context)
Citation Context ...ion nondestructively, and the result shares (nearly) maximal structure with the original trie to minimize the memory allocation. DDPP is written in Common Lisp. A detailed description can be found in =-=[13]-=-. Performance of DDPP (and LDPP) on some quasigroup problems is shown in Table I. Search was continued until the search space was exhausted and all models had been found. The number of branches is one... |